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# 次世代技術の芽と新しい物理をつくる

## 見えないものを数学的に表現する

### 数理物理学・非線型偏微分方程式研究

[English]

 小澤　徹 [教授] e-mail homepage http://www.ozawa.phys.waseda.ac.jp/index2.html 専門分野 数理物理学・非線型偏微分方程式研究 研究テーマ・研究活動 1984 年 早稲田大学理工学部物理学科卒業 1988 年 名古屋大学理学部・助手 1990 年 京都大学理学博士　数理解析研究所・助手 1992 年 北海道大学理学部・講師 1993 年 北海道大学理学部・助教授 1995 年 北海道大学大学院理学研究科・教授 1998 年 日本数学会賞春季賞　受賞 2008 年 早稲田大学理工学術院・教授

ほとんど全ての物理現象は微分方程式としてモデル化・抽象化されます。しかし「シュレディンガー方程式、ディラック方程式、ナビエ・ストークス方程式などの物理学的に由緒正しい方程式には解が在って当たり前か？」となると、話はそう単純ではありません。物理現象を記述しているのは方程式の「解」であって「方程式そのもの」ではありません。「方程式そのもの」は書き下した瞬間「存在する」と言えるのでしょうが、方程式の「解の存在」は全く次元の異なる話題となります。また、「解の公式・具体的表示」と「解の存在」とは異なる概念です。後者は前者よりも広い意味を持っています。例えば、複素函数論で「複素係数のn（ 1）次多項式は重複を許して丁度n 個の根を持つ」というガウスの代数学の基本定理を学びますが、これは「5 次以上の方程式は代数的には解けない」というアーベル・ガロアの理論とは何ら矛盾するものではありません。
さて、それでは「解の存在」とは何を意味するものなのでしょうか？そのためには、まず「解の概念」を明確に定義し、その上で「解の存在証明」を与える事が必要です。では何をもって「存在する」事を証明すれば良いのでしょうか？我々はその手段を解析学、特に函数解析学、調和解析学に求めます。そうなると、元来物理学から現れた偏微分方程式といえども、数学的対象として考える限り、徹頭徹尾数学的に扱わねばなりません。物理学的直感は役に立つ事もありますが、それを的確な数学的表現に置き換える作業が求められます。その様な思考過程の修業を経て初めて、物理現象の「数学的実在」が実感できるようになります。「数学的実在」とは目に見えないものですが、確かに実感できるものであり、数式などの記号を用いて自由に表現する事のできるものです。それは同時に、自分の個性の表現でもあり、自己の実現・実在を強烈に感じる機会を与えてくれるものです。小澤研究室は、物理と数学が交錯する場であると共に、志の高い人間の思考が相互作用し、世界の最先端の成果を発信する数理物理学道場を目指しています。

 Tohru Ozawa [Professor] e-mail homepage http://www.ozawa.phys.waseda.ac.jp/index2.html research field The mathematical reality of classical field theory research keywords Mathematical physics Classical field theory Scattering theory link Research Profiles (at Faculty of Science and Engineering) Research Profiles (Elsevier SciVal Experts)

###### The mathematical reality of classical field theory

We cannot be assured of the validity of quantum field theory in any formulation without the deep mathematical theories drawn from the corresponding classical field theory.
In an address at the 1962 Conference on Analysis at Yale University on the occasion of Professor Hill’s retirement, Irving E. Segal remarked as follows: “To a considerable extent, relativistic physics is based in a theoretical way on non-linear partial differential equations. Until recently, however, there has been little applicable mathematical theory even in the classical (i.e., unquantized) case, although the subject is one of much intrinsic mathematical appeal. Probably the simplest non-trivial non-linear relativistic equations are those of the form \box \phi = F(\phi), …” (from his paper entitled “Non-linear Semigroups,” Annals of Mathematics, 78(1963), 339-364.)
Given this common motivation, studies of nonlinear partial differential equations in classical field theory got their start as a subject in mathematical physics.
Up to the 1980s, the world’s leading centers of research in this area were located in New York and Paris.
The names of some of the prominent scientists working in this area immediately come to mind: Morawetz, Strauss, Nirenberg, Klainerman, Shatah in the U.S. and Jorgens, Lions, Ginibre, Velo, Choquet, and Christodoulou in Europe. In Japan, the first research group in this area took shape here in the Department of Applied Physics at Waseda University. Based on original and pioneering work by Professor Riichi Iino and Professor Masayoshi Tsutsumi, research results gradually percolated out into the world community during the 1980s.

Since then, the Mathematical Physics Laboratory, Department of Applied Physics, Waseda University has produced a number of mathematical physicists active in this area, including Nakao Hayashi, Yoshio Tsutsumi, Hayato Nawa, Takayoshi Ogawa, and myself, to name a few. Individuals active in these laboratories are now recognized as a world-leading group in the mathematical study of classical field theory.

I returned to Waseda in 2008 to succeed Professor Masayoshi Tsutsumi. With Professor Mitsuharu Otani, I oversee the Laboratory of Mathematical Physics. My chief research interests involve classical field theory as a topic in mathematical physics. In terms of nonlinear partial differential equations, I have done work in the areas of nonlinear hyperbolic equations, nonlinear dispersive equations, and nonlinear elliptic and parabolic equations arising in pure and applied physics, particularly nonlinear Dirac, Klein-Gordon, Schrodinger equations, several associated systems of these equations, and fundamental equations in fluid mechanics. By exploring basic issues associated with these equations, such as the well-posedness of the Cauchy problem, long-time behavior of global solutions, regularity and singularity in local solutions, scattering theory, and asymptotic analysis, I seek to obtain a clearer picture of the mathematical reality of classical field theory. For more information, I encourage you to visit our Laboratory website.

## 宇宙を通して探る物理学の最先端

### 宇宙物理

[English]

 前田　恵一 [教授] e-mail homepage http://www.gravity.phys.waseda.ac.jp/ 専門分野 宇宙物理 研究テーマ・研究活動 ○素粒子統一理論を基礎にした宇宙論・ブラックホール ○非線形物理学としての宇宙の構造形成 ○一般相対性理論の基礎的問題と重力波 ●日本物理学会 日本天文学会 国際天文連合（ＩＡＵ） アメリカ物理学会 日本「一般相対性および重力」学会組織委員 「一般相対性および重力」国際学会編集委員

（１）素粒子的宇宙物理学：ビッグバンは非常に成功した理論であるが、それらは同時に宇宙のはじまりを予言する。その宇宙のはじまりがどのようであったのか、どのようにビッグバン宇宙へと進化していくのかなどを素粒子論や超ひも理論をもとに考察している。また、素粒子の統一理論に基づいた新しいタイプのブラックホール解を見つけ、研究することにより、重力現象のより深い理解をめざしている。
（２）宇宙の構造形成と非線型物理学：宇宙の温度が４０００度ぐらいの時、宇宙は中性化され光が自由に行き来できるようになる。そのときに存在した密度のでこぼこが成長し、現在の銀河や銀河団といった宇宙の構造が形成されるのであるが、そのメカニズムはまだ解明されていない。本研究室ではこの構造形成問題をカオスやフラクタルなどの非線型物理学の立場から研究している。
（３）ブラックホール・中性子星と重力波：アインシュタインの一般相対論によって新しく予言されたものに、ブラックホールと重力波がある。ブラックホールは星の進化の最後に形成されたり、銀河の中心に存在することが観測から示唆されている。一方、重力波も連星パルサーPSR1913+16の観測から間接的にはその存在が証明されている。現在では、その重力波を直接観測し、ブラックホールや中性子星の性質や形成過程を解明しようという大規模観測プロジェクトが世界各地で進められており、理論的にもその現象の詳細な解析が求められている。そこで数値相対論などを駆使し、中性子星やブラックホール形成過程やそれに伴う重力波放出過程の理論的解析にも力を入れている。

 Kei-ichi Maeda [Professor] e-mail homepage http://www.gravity.phys.waseda.ac.jp/index_e.html research field Research on cosmology and black holes as fundamental physics research keywords General relativity and gravitational physics The Early Universe in unified theory of fundamental interactions Black holes and relativistic astrophysics link Research Profiles (at Faculty of Science and Engineering) Research Profiles (Elsevier SciVal Experts)

###### Research on cosmology and black holes as fundamental physics

I mainly work on gravitational physics and cosmology based on unified theories of fundamental interactions. In 1986, when I was a postdoc at the Meudon Observatory, I worked with Professor Gary Gibbons (Cambridge), who at the time was a visiting professor there,and found black hole solutions in string theory. The paper written with Gary is now one of the most popular papers in this field. The citation number in the SPIRES database at SLAC is now 712. When I visit Cambridge now, I always go to Gary’s office for useful discussions. This helps my research significantly.
In 1999, a workshop was held at the Isaac Newton Institute on “Structure Formation in the Universe.” During my sabbatical, I attended this workshop for three months. I had interesting discussions with numerous prominent scientists, including people at Cambridge. I began work on “a brane cosmology” there.
In particle physics, all interactions could be unified in higher dimensions.
However, our universe should be three dimensional. To explain our universe in the context of higher-dimensional unified theories, we introduce the idea of a brane, a three dimensional object moving in higher-dimensional spacetime.

Taking this model, many researchers have studied the early stage of the Universe or strong gravitational phenomena such as a black hole.
During the workshop, I finished four papers, which became the most widely cited ones in this field (The citation numbers are 831, 215, 176, and 124). One of these written with Professors Tetsuya Shiromizu (TITech) and Misao Sasaki (Kyoto) derives an effective gravitational theory for our universe based on the Randall-Sundrum brane world scenario.
I have published 181 papers to date. The total number of citations is over 5000, and the h index is 36.
I also manage international research collaborations. For example, I am the PI of the Japan-U.K. Research Cooperative Program (2005-09). I am also a member of the International Committee on General Relativity and Gravitation (GRG) and editor of the Journal of GRG.
Current topics include research on “cosmology and black holes” as fundamental physics. Inflation, which is believed to occur in the early stage of the Universe, is also entering a new stage and can now be discussed based on unified theories such as superstring theory. I recently presented a new type of inflation in a string model with correction terms.
I am also working on black hole solutions in string theory. More recently, my interests have turned to so-called dark energy, one of the most important subjects in modern cosmology. My goal is to continue this research and to find interesting new aspects in cosmology or gravitational physics.

Based on the unified theory of fundamental interactions, our universe may be a membrane (three-dimensional space) moving in higher-dimensional spacetime. Standard model particles such as quarks and leptons as well as gauge particles such as photons and gluons are confined to the three-dimensional brane (our world), but gravitons can propagate in the higher-dimensional bulk space. This world view may change the scenario of the evolution of the early universe. It is called a brane world.

## 多数の電子が作る新しい性質を探る

### 複雑量子物性

[English]

 勝藤　拓郎 [教授] e-mail homepage http://www.f.waseda.jp/katsuf/lab/index.htm 専門分野 物性物理学 研究テーマ・研究活動 ○遷移金属酸化物の物質開発 ○光学測定による強相関電子系の研究 ○巨大外場応答を示す物質の開発、研究 ●日本物理学会 ●応用物理学会 ●アメリカ物理学会

みなさんの身の回りにある物質のほとんどは「固体」と呼ばれるもので、ミクロに見ると、原子が順序よく整列しており、その間を電子が飛び回っています。一見簡単に見える舞台ですが、実はこれだけで驚くほど多様な性質が生み出されるのです。よく知られている例として、電気が流れたり（金属）、流れなかったり（絶縁体）、磁石についたり（強磁性）、もう少し高級な例としては、近年のノーベル賞の対象となった超伝導、量子ホール効果などは、すべて固体中の電子が生み出す性質です。固体中においては、一つの現象に対して数多くの電子が一度に寄与するために、このような多彩な性質が現れるのです。１つ１つの電子は波動方程式（シュレディンガー方程式）に従いますが、電子が多数集まったとき、そこは単純な方程式を超えた新しい物理の宝庫です。

こうした多様で複雑な性質を研究するにはどうしたらいいでしょうか？まず、舞台となる物質をつくってやらなければなりません。新しい物理は新しい物質から生み出されるというのは、これまでの歴史の教えるところです。我々のグループは、新しい物理を生み出すべく、新物質の開発を行っています。特に、動きまわる電子同士の間に強い相互作用が働く「強相関電子系」の物質開発に力を入れています。さらに、新しい現象を見つけるためには、それを「見る」ための手段を手に入れなければなりません。我々のグループは、光を用いた測定手法を中心に、新しい物理を見るための手段を開発しています。このように、物質開発と測定の両輪をフル回転させて、新しい物理の探索にいそしんでいます。

 Takuro Katsufuji [Professor] e-mail homepage http://www.f.waseda.jp/katsuf/lab/index.htm research field New physics through new materials research keywords Strongly-correlated electron systems Synthesis of new materials Optical spectroscopy of materials link Research Profiles (at Faculty of Science and Engineering) Research Profiles (Elsevier SciVal Experts)

###### New physics through new materials

While the behavior of a single electron obeys the Schrodinger equation and is physically counterintuitive, the principle in question is quite simple. However, real-world objects consist of countless electrons, and the collective motion of such large numbers of electrons differs radically from the motion of a single electron. Each material acts as a “stage” for electrons which, in this analogy, may be regarded as “actors.” The actors (the electrons) behave in different ways in different materials (on different stages). The potentially novel behavior of electrons on novel stages presents an avenue for exploring the physics of new materials.

Our group is currently seeking to synthesize new materials, grow new crystals, and explore new physics in these materials. In particular, we focus on transition-metal oxides, in which electrons are strongly correlated and tend to act collectively (called “strongly-correlated electron systems”). Due to the collective behavior of correlated electrons, transition-metal oxides often exhibit a large response to external fields, sometimes generating surprising behavior. For example, applying a magnetic field to some common materials will result in magnetization. Applying a magnetic field to transition-metal oxides may lead to changes in electrical resistance, dielectric constants, crystal structures, and even color. In addition to their interest in terms of basic physics, such phenomena present the potential for future applications.

To date, we have observed the following phenomena: (1) Magnetic-field-induced structural phase transitions in spinel MnV2O4, a phenomenon arising from the coupling of the orbital and spin degrees of freedom of the V ion; (2) large changes in dielectric constant in a perovskite (EuTiO3) when a magnetic field is applied, a phenomenon arising from the coupling between Eu spins and the electric dipole on Ti; (3) significant changes in color in a perovskite (Pr0.6Sr0.4MnO3) and pyrochlore (Yb2V2O7) when a magnetic field is applied; (4) significant changes in electrical resistance when a magnetic field is applied to La- and Cr-doped perovskite (SrTiO3). We wish to emphasize that such physical phenomena represent only a small portion of those related to new materials; we expect many more to appear in the near future.

In conventional electromagnetics, magnetic fields induce magnetization only. In some transition-metal oxides, however, the effects of magnetic fields can be quite varied. (Left) Crystal structure of spinel MnV2O4 changes when a magnetic field is applied. (Right) Dielectric constants of perovskite (EuTiO3) change when a magnetic field is applied.

## 無限に大きい核物質の研究と 天体物理学への応用

### 理論核物理学

[English]

 鷹野　正利　［教授・理工研］ e-mail 専門分野 原子核物理学 Homepage www.np.phys.waseda.ac.jp 研究テーマ・研究活動 ◯核物質状態方程式の研究と天体物理学への応用 ◯強い粒子間相関をもつFermi粒子系に対する変分法 ●日本物理学会 ●アメリカ物理学会

そこで我々は、無限個の核子から成る無限に大きい仮想的な原子核（以下では核物質と呼びます）を考えます。そして、主に変分法を用いて、核物質の多体問題的研究を行う事により、核物質の観点から原子核の大局的性質を理解する事を目指します。　核物質エネルギーの理論計算により、いわゆる核物質の状態方程式(EOS)が得られます。計算された核物質EOSの信頼性を調べるために、我々は宇宙に目を向けます。

「仮想的」な無限に大きい核物質は、中性子星という天体の姿で存在します。中性子星は超高密度の天体で、非常に強い自己重力に対して、内部核物質の硬さが星を支えています。よって、中性子星の構造研究には、核物質EOSの情報が必要です。また逆に、中性子星観測結果との比較で、計算された核物質EOSの信頼性が確認できます。（図は中性子星の半径と質量の関係を表します。）さらに、恒星の進化の最終段階で起こる超新星爆発のきっかけも、核物質の硬さにあると考えられ、そのような天体現象の理解には、核物質EOSの情報が不可欠です。　このように核物質EOSは、原子核物理学、天体物理学で重要な役割を果たしますが、これを実験的に決定する事は困難で、信頼性の高い理論多体計算が必要です。我々のグループでは、こうした中性子星、超新星爆発等の天体現象の理論的研究に適用可能な核物質EOSの研究を行っています。

 Masatoshi Takano [Professor] e-mail homepage www.np.phys.waseda.ac.jp research field Theoretical study of Nuclear Equation of State research keywords Equation of state for nuclear matter Variational method Neutron stars Supernovae link Research Profiles (at Faculty of Science and Engineering) Research Profiles (Elsevier SciVal Experts)

###### Theoretical study of Nuclear Equation of State

The atomic nucleus is a quantum-mechanical system composed of nucleons (protons and neutrons) interacting through nuclear and Coulomb forces. One of the fundamental properties of the atomic nucleus is the so-called “saturation property of nuclear forces,” i.e., that the nucleon number densities inside the nuclei and the binding energies per nucleon are nearly constant for all nuclei. In order to explain this basic property of the atomic nucleus quantitatively, the Schrodinger equation for the atomic nucleus must be solved. So far, however, this has not been achieved because the nuclear Hamiltonian, especially the potential of the nuclear force, has some uncertainty. More seriously, the quantum many-body problem is especially difficult to solve.

In order to overcome the latter difficulty, we have been studying the quantum variational many-body theory for infinitely-large fermion systems. The variational method is a powerful technique to treat the quantum systems in which the particles interact through strong short-range forces, such as infinite hypothetical nuclear matter and liquid helium. In the case of liquid 3He, the spin-1/2 3He atoms interact through intermolecular forces, and the Hamiltonian bears some resemblance to that of nuclear matter. Furthermore, the experimental data to be compared with the theoretical calculations for liquid 3He are more abundant than in the case of nuclear matter. Therefore, we are studying not only nuclear matter but also liquid 3He.

Infinitely-large nuclear matter can be found as neutron stars. A neutron star is a compact object whose mass is about twice the solar mass (or somewhat less), with the radius being about 10 kilometers. Inside the star is high-density nuclear matter. Against strong self-gravity, the stiffness of the interior nuclear matter supports the neutron star. Therefore, the neutron star structure is determined by the stiffness of the interior nuclear matter, or more generally, by the equation of state (EOS) of nuclear matter. Furthermore, owing to the recent development of neutron star observations, various constraints are imposed on the nuclear EOS. We are studying the neutron star structure in connection with the nuclear EOS obtained with our variational method.

The nuclear EOS is also important for studies of core-collapse supernovae and other high-energy astrophysical phenomena such as hypernovae, black-hole formations, and neutron star mergers. In order to study these astrophysical phenomena with numerical hydrodynamic simulations, the EOS of nuclear matter covering an extremely wide range of densities, temperatures, and proton fractions is necessary. We are constructing a new nuclear EOS appropriate for these astrophysical phenomena based on the variational many-body theory.

Energies per nucleon of asymmetric nuclear matter at zero temperature E/N for various proton fractions x, as functions of the nucleon number density ρ. The AV18 and UIX potentials are employed for the two-body and three-body nuclear forces, respectively. The dotted curves with crosses are with the Fermi Hypernetted Chain calculation for x = 0 (upper one) and x = 0.5 (lower one) by Akmal et al. (PRC58[1998]1804).

## 宇宙で探る高エネルギー物理学

### 宇宙物理

[English]

 山田　章一 [教授] e-mail homepage http://www.heap.phys.waseda.ac.jp/index.html 専門分野 宇宙物理 研究テーマ・研究活動 ○高エネルギー天体の物理 ●日本天文学会 ●日本物理学会

 Shoichi Yamada [Professor] e-mail homepage http://www.heap.phys.waseda.ac.jp/index.html research field Neutrino and gravitational wave astronomy of massive-star collapse research keywords High energy astrophysics Mechanism of collapse-driven supernovae and physics of hadronic matter at high densities Neutrinos and gravitational waves from the formation of black holes and neutron stars link Research Profiles (at Faculty of Science and Engineering) Research Profiles (Elsevier SciVal Experts)

###### Neutrino and gravitational wave astronomy of massive-star collapse

Gravitational collapse is the common fate of massive stars, followed by the formation of compact objects such as neutron stars and black holes. This gravitational collapse is initiated by the central core of a massive star, which is surrounded by massive envelopes and cannot be probed by electromagnetic waves. The actual conditions in these regions have been inferred over the years based on indirect evidence for example, nucleosynthetic yields. This may have already changed dramatically, however, with multiple terrestrial detectors of neutrinos and gravitational waves now deployed, operating, and poised to detect the next event.

Since neutrinos and gravitational waves interact very weakly with matter, they escape the central core unhindered, carrying information on the environment where the emissions originate. Although the very weakness of the interactions once constituted a major challenge for experimentalists, this is no longer the case. The ball is once again in the theoreticians’ court. Needed now are quantitative predictions to compare against observations. As the detection of neutrinos from SN1987A clearly demonstrates, neutrinos from core-collapse supernovae and the proto-neutron stars that form subsequently should be among the primary targets in neutrino astronomy.

Also emerging now is gravitational-wave astronomy. Over the last decade, we have witnessed significant progress in the international network of detectors, including LIGO, VIGRO, GEO600, TAMA300, and AIGO, and the direct detection of gravitational waves from astrophysical events should soon be possible.
Promising sources would include a massive star collapse, particularly within our own galaxy.

Over the years, in large-scale numerical simulations, we have demonstrated that the detection of neutrinos and/or gravitational waves emitted by the gravitational collapse of massive stars will convey much information not just about what goes on under the thick veil of the massive envelopes, but about the properties of dense and hot baryonic matter. In so doing we have pointed out the importance of black-hole-forming events, which are still putative but, if observed, will provide invaluable and otherwise inaccessible information. In fact, the neutrino bursts from the optically silent collapses of massive stars have unique characteristics that distinguish them from ordinary supernova neutrinos; hence, they can be used not just as indicators of black hole formation, but as probes of dense baryonic matter. It is fascinating that such an event may be confirmed by the detection of “the disappearance of one of the numerous massive stars” monitored optically as another proposed initiative. If the progenitor star is rotating, we will also have the chance to detect the event via gravitational waves.

Four snapshots of our 3D supernova simulation. The length of each side of the plot corresponds to 1000 km. The entropy distributions are shown. The second and fourth quadrants of each panel show the surface of the shock wave. The high entropy bubbles (colored red) in the section cut by the $ZX$ plane are displayed in the first and third quadrants. The insets show gravitational waveforms from anisotropic neutrino emissions.

## 極微の世界の物理法則を探る

### 量子力学基礎論

[English]

 中里　弘道 [教授] e-mail homepage http://www.hep.phys.waseda.ac.jp/index-j.html 専門分野 量子力学基礎論、素粒子理論 研究テーマ・研究活動 ○量子論の基礎に関わる諸問題 ○量子化法の研究 ○場の量子論 ●日本物理学会 ●アメリカ物理学会

このように電子のような極微の世界の粒子は空間的に広がった波としての性質と空間的に局在した粒子としての性質を兼ね備えていると考えざるを得ないのです。状況によって波になったり粒子になったり．．．なんとも不可思議な状況です。このような状況を適切に記述しているのが量子論と呼ばれる理論体系で、現代物理学の柱の一つとなっています。実際、これまでのところ量子論に矛盾した実験事実は一つとして報告されていません。

 Hiromichi Nakazato [Professor] e-mail homepage http://www.hep.phys.waseda.ac.jp/ research field Theoretical study of quantum dynamics and its applications research keywords Quantum dynamics Quantum-classical border Quantum field theories link Research Profiles (at Faculty of Science and Engineering) Research Profiles (Elsevier SciVal Experts)

###### Theoretical study of quantum dynamics and its applications

Since its advent more than 80 years ago, quantum theory, which describes behavior in the microscopic world from molecules and atoms down to elementary particles, has solidified its status as one of the most successful theories in modern physics. Although its validity has been confirmed in many fields in physics to an unprecedented degree of precision, quantum theory has been plagued since its birth with certain fundamental issues, which remain unresolved due to the difficulty of achieving experimental counterproof. Recent technological advances have dramatically altered this landscape, allowing the examination of such issues in laboratory experiments. To date, no results that contradict quantum theory have been reported. Moreover, new ideas based on the very fundamental rules of quantum theory (e.g., the superposition principle) have emerged and are being applied in the laboratory in real-world physical systems.
At the same time, these technological innovations have forced major reappraisals of physical processes. For example, an ideal system consisting of an isolated atom cannot in fact exist in the real world. At all times, we must account for the environment, or external agency, including the act of measurement, with which quantum systems are unavoidably implicated. The environment affects dynamics and causes phenomena like dephasing and/or dissipation resulting in loss of quantum coherence (decoherence), a key issue in quantum information and technologies for which the preservation of quantum coherence is crucial. A correct understanding of quantum processes is essential to realizing real-world applications of the ideas proposed in association with such fascinating keywords as quantum computers and quantum cryptography; these applications must be realized as real physical processes in the laboratory, not as mathematical formulas on paper.
Our research explores the dynamics of quantum systems under the influence of the environment, first by treating the whole system composed of the quantum system and its environment as a closed quantum system, then by tracing the environmental degrees of freedom. The resulting dynamics is no longer unitary and would lead to decoherence in the quantum system. Understanding the associated mechanisms and finding possible ways to avoid decoherence are key issues related to the primary subjects of our current research. These issues have deep connections to profound and interesting questions, including where or how the border between quantum and classical worlds can be defined and when classical rules predominate over quantum rules. These questions also fall within the scope of our research efforts, and we study the transitions between different theoretical frameworks (e.g., classical or quantum, particle or field), seeking a deeper understanding of the meaning of quantization or devising novel methods of quantization.

## 究極の物理法則を求めて

### 素粒子理論

[English]

 安倍 博之 ［教授］ e-mail homepage http://www.hep.phys.waseda.ac.jp/index-j.html 専門分野 素粒子理論 研究テーマ・研究活動 ○素粒子標準理論を超える物理 ○超対称理論・高次元時空理論 ○超重力理論・超弦理論の現象論的側面 ○素粒子の究極的統一理論 ●日本物理学会

私たちの研究室では、（現在知られている唯一矛盾のない量子重力理論である）超弦理論の有効理論として標準理論が実現されている可能性を念頭に置いて、素粒子理論の研究、特に標準理論を超える物理の理論的研究を行っています。超弦理論が素粒子の究極的統一理論だとすると、標準理論を超える物理として、ボーズ粒子とフェルミ粒子を入れ換える超対称性や、高次元時空に起因する余剰空間次元の存在などが予言され、これらの力学や幾何学が、観測されている素粒子の複雑な質量階層構造などを決定していると考えられます。また、超対称性や余剰次元から帰結される数々の新粒子の存在は、高エネルギー物理現象や宇宙の歴史にも重要な影響を与えると考えられ、これらの理論を研究し高エネルギー実験や宇宙論的観測による検証を行うことは現代の基礎物理学の重要な課題の１つです。

 Hiroyuki Abe [Professor] e-mail homepage http://www.hep.phys.waseda.ac.jp research field Theoretical high-energy physics research keywords Particle phenomenology Quantum field theory Supersymmetry Supergravity and superstring Higher-dimensional spacetime link Research Profiles (at Faculty of Science and Engineering) Research Profiles (Elsevier SciVal Experts)

###### Theoretical high-energy physics

The most fundamental elements of nature observed by people are elementary particles called quarks, leptons (matter particles), and gauge bosons (force mediators). The electron and the neutrino are classified as leptons, while the proton and the neutron are composite particles each formed by three quarks. A quantum field theory with special local symmetries, called the “standard model” of elementary particles, describes whole observed phenomena at the present time without inconsistencies. From the theoretical point of view, however, there exist many unsatisfactory points in the standard model, beginning with the unpredictability of the masses of elementary particles, the lack of gravitational interactions, and so on.

In a quest for an ultimate fundamental theory of nature beyond the standard mode, one of the most severe obstacles is the extension of quantum field theory as it includes gravitational interactions, i.e. the harmonization of quantum theory with general relativity. A single known theory that overcomes such obstacles without any theoretical inconsistencies is the “superstring theory.” It possesses a special symmetry called supersymmetry under the exchange of bosons and fermions, and is defined in ten-dimensional spacetime. If our real world is a product of superstring theory, there should exist supersymmetry and six extra space dimensions that are possibly hidden in such a way that we never detect them due to the energy shortage of present particle colliders.

Considering the possibility that the standard model appears as a low-energy effective theory for superstring, we perform various theoretical and phenomenological studies for physics beyond the standard model. We have to search candidates for realistic structures among huge numbers of superstring vacua, for which the key ingredients are “supersymmetry” and “extra-dimensions.” These imply the existence of new particles at low energy called superparticles and moduli. We aim to find an ultimate unifying theory of elementary particles and gravity, by analyzing the dynamics and the geometry of these ingredients and accomplishing the harmonization of the standard model with the superstring theory. In these studies, we derive theoretical predictions for precise values of known and possibly new observables, which are compared with real observed values in the past and future high-energy experiments as well as cosmological observations, and then verify the validity of each candidate for an ultimate unified theory of elementary particles.

The energy dependence of three gauge coupling constants determined by the observed values at low energy in the standard model (dotted-lines) and in a supersymmetric extension of the standard model (solid-lines) at the first order of perturbative expansion. In the latter supersymmetric model, a gauge coupling unification occurs at a high energy, which would imply some underlying unification theory.

## たんぱく質が働く様子を計算機シミュレーションで調べる

### 生物物理

[English]

 髙野　光則 [教授] e-mail homepage http://www.tb.phys.waseda.ac.jp/ 専門分野 生物物理学 研究テーマ・研究活動 ○蛋白質の物性理論。特に分子モーターの動作原理、 エネルギー変換機構、ゆらぎと応答 ●日本生物物理学会 ●日本物理学会 ●アメリカ生物物理学会

 Mitsunori Takano [Professor] e-mail homepage http://www.phys.waseda.ac.jp/wps/aizawa/index-j.html research field research keywords link Research Profiles (at Faculty of Science and Engineering) Research Profiles (Elsevier SciVal Experts)

in preparation

## 「自然の造形」に対する 物理からのアプローチ

### 非平衡系の物理

[English]

 山崎　義弘 [教授] e-mail homepage http://www.f.waseda.jp/yoshy/lab/ 専門分野 物性理論 研究テーマ・研究活動 ○パターン形成の物理 ○粘着の物理 ○相転移・相分離におけるドメイン構造の成長 ○水－粉体混合系の乾燥で生じる迷路状パターン形成 ●日本物理学会 ●日本レオロジー学会

「パターン形成の物理」は自然を理解するための強力な枠組みであり、今後さらに発展していくであろうと確信しています。また、研究対象が物理系にとどまらず、化学系・生物系など広範に渡っている点や、現象の捉え方は必ずしも物理学の既存分野には収まらないかも知れません。私たちは、絶えず変化していく自然の造形に、物理学からアプローチして、地道な研究を重ねることによって学問分野として確立させていきたいと考えています。

 Yoshihiro Yamazaki [Professor] e-mail homepage http://www.phys.waseda.ac.jp/wps/aizawa/index-j.html research field TBA research keywords TBA link Research Profiles (at Faculty of Science and Engineering) Research Profiles (Elsevier SciVal Experts)

TBA

## 量子力学の不思議に迫り それを活用するアイデアを創出する

### 量子相関物理

[English]

 湯浅　一哉 ［教授］ e-mail homepage http://www.f.waseda.jp/yuasa/ 専門分野 量子物理学・量子情報 研究テーマ・研究活動 ○量子物理学 ○量子情報 ●日本物理学会

さらに，「量子コンピューター」，「量子暗号」，「量子通信」をはじめ，量子論の世界の不思議を積極的に活用することで従来の情報処理の限界を超えようとする「量子情報」など，「量子技術」の様々なアイデアが出現し，精力的に研究が進められています．キーワードは「エンタングルメント」です．それは，アインシュタインが受け入れることができなかった「量子論の非局所性」という，古典的な考え方では決して説明することができない量子の最たる世界を見せてくれる特異的な量子相関のことです．それをうまく利用すると，古典的な技術を超えられる可能性があるのです．

ません．皆さんも独自のアイデアで奥深い量子力学の世界を

 Kazuya Yuasa [Professor] e-mail homepage http://www.f.waseda.jp/yuasa/ research field research keywords link Research Profiles (at Faculty of Science and Engineering) Research Profiles (Elsevier SciVal Experts)

in preparation


text:
# Differential equation and initial condition

• October 25th 2009, 07:48 AM
ben.mahoney@tesco.net
Differential equation and initial condition
Q) The question is for me to sketch the graph of x(t) for different initial conditions.

dx/dt = sqrt(3) - 2sin(x)

A) i cant see how this is separable variables or integrating factor method.

So do I do: x(t) = sqrt(3)t - 2tsin(x) + C

Saying x = x0 at t=0 just gives me c = x0

Does this look correct?

Thanks

• October 25th 2009, 09:19 AM
CaptainBlack
Quote:

Originally Posted by ben.mahoney@tesco.net
Q) The question is for me to sketch the graph of x(t) for different initial conditions.

dx/dt = sqrt(3) - 2sin(x)

A) i cant see how this is separable variables or integrating factor method.

So do I do: x(t) = sqrt(3)t - 2tsin(x) + C

Saying x = x0 at t=0 just gives me c = x0

Does this look correct?

Thanks

1. Have you checked that that is a solution by differentiating it and seeing if it satisfies the equation?

2. Are you sure that you have typed the equation correctly?

CB
• October 25th 2009, 09:34 AM
ben.mahoney@tesco.net
if you differentiate it you just take away the t's on each part so in that respect it does satisfy equation.

Yes that is definitly the question
• October 25th 2009, 10:28 AM
TheEmptySet
Quote:

Originally Posted by ben.mahoney@tesco.net
if you differentiate it you just take away the t's on each part so in that respect it does satisfy equation.

Yes that is definitly the question

That is false....

x is a function of t. You need to use implict differentation.

$x(t)=\sqrt{3}t-2t\sin(x)+c$

$\frac{dx}{dt}=\sqrt{3}\underbrace{-2\sin(x)-2t\cos(x)\frac{dx}{dt}}_{\text{Product rule}}$

Your equation does seperate but is not easy to integrate

$\frac{dx}{\sqrt{3}-2\sin(x)}=dt$
• October 25th 2009, 11:14 AM
ben.mahoney@tesco.net
thankyou.

you are correct, it isn't easy to integrate!!!
• October 25th 2009, 02:18 PM
Prove It
Quote:

Originally Posted by ben.mahoney@tesco.net
Q) The question is for me to sketch the graph of x(t) for different initial conditions.

dx/dt = sqrt(3) - 2sin(x)

A) i cant see how this is separable variables or integrating factor method.

So do I do: x(t) = sqrt(3)t - 2tsin(x) + C

Saying x = x0 at t=0 just gives me c = x0

Does this look correct?

Thanks

According to Wolfram Integrator, the solution is

$t = 2i\arctan{\left\{\sec{\left(\frac{x}{2}\right)}\le ft[i\sqrt{3}\sin{\left(\frac{x}{2}\right)} - 2i\cos{\left(\frac{x}{2}\right)}\right]\right\} } + C$

Now you can use your initial condition to find $C$.

Edit: Upon further inspection, it appears that this can be simplified to

$t = 2i\arctan{ \left[ i\sqrt{3}\tan{\left(\frac{x}{2}\right)} - 2i \right] } +C$
• October 26th 2009, 01:44 PM
ben.mahoney@tesco.net
The question that this equation involves is:
Use a geometric approach and qualitatively analyse the following equations (in each case find fixed points, sketch the vector field and classify stability of each fixed point, sketch the graph of x(t) for different initial conditions).

Does this mean that I actually do have to integrate dx/dt.

On asking my lecturer he said that the hint is in the brackets.

Im so confused :(

format: plain


text:
Is there always a limiting reagent in every equation?

Is there always a limiting reagent in every equation? For instance, is there a limiting reagent in $\ce{CaCl2 + Na2CO3 -> 2NaCl + CaCO3}$ where the same number of moles are reacting with each other?

• Considering that there are $6.022\times10^{23}$ molecules per mole, it seems unlikely that an exactly 1:1 ratio could ever really be achieved. – MaxW May 3 '18 at 16:36
• @MaxW It is possible using e.g. AFM tips to nudge individual atoms and molecules and cause them to react, which I suppose counts as exact in a very technical manner. – Nicolau Saker Neto May 4 '18 at 13:26

An interesting philosophical question. We are given a chemical equation: $$\ce{CaCl2 + Na2CO3 -> 2NaCl + CaCO3}$$ and that the same number of moles of the reactants are used. Now the OP poses the question "Is there a limiting reagent?"

As chemists we can say that 1.00 moles of $\ce{CaCl2}$ were reacted with 1.00 moles of $\ce{Na2CO3}$. We'd pragmatically say that the moles were equal and that there was no limiting regent.

However this is a significant figure argument, not reality. Avogadro's number is about $6.022\times10^{23}$. There is no lab in the world that can weight out precisely one mole of $\ce{CaCl2}$ accurate to 23 decimal places. We don't even know Avogadro's number accurate to 23 decimal places! The best value is $6.022140857(74)\times10^{23}$.

So in reality, despite our best efforts as chemists, one reagent or the other will be in some small excess which we'd consider to be insignificant given the overall precision of the experiment.

• Note that, since 20 May 2019, the Avogadro number is (by definition) exactly $6.022\,140\,76\times10^{23}$. – Loong Sep 7 at 20:48
1. There can't be any limiting reagents in the equations. Equations are purely theoretical expressions and are always balanced in terms of moles.

2. "Limiting reagents" arise in real world chemical reactions.

The questions on limiting reagents are usually formulated in a form of "we have a reaction according to this equation, and we have X grams of this reagent and Y grams of that reagent, which one is limiting?"

A question "which reagent in this equation is limiting?" without additional info makes no sense.

• The OP has clearly stated "same number of moles are reacting with each other", so the amount of the reagents are given. Using the molar masses you can get to the actual weight. What additional info is required? – Gaurang Tandon May 4 '18 at 12:15

I'd like to explain this problem with an example. The chemical equation in question is:$$\ce{CaCl2 + Na2CO3 -> 2NaCl + CaCO3}$$ Since $K_\mathrm{sp}$ of $\ce{CaCO3}$ is $\pu{3.36\times10^{-9} mol^2\cdot L^{-2}}$, it is safe to assume that this reaction would have proceeded to completion, if $\pu{1 mol}$ of $\ce{CaCl2}$ is reacted with $\pu{1 mol}$ of $\ce{Na2CO3}$ to give $\pu{1 mol}$ of $\ce{CaCO3}$ solid and $\pu{2 mol}$ of aqueous $\ce{NaCl}$. Therefore, no limiting reagent in that calculation because we used exact stoichiometric amounts of starting materials.

What if you have mixed $\pu{100 mL}$ of $\pu{2 M}$ $\ce{CaCl2}$ with $\pu{100 mL}$ of of $\pu{1 M}$ $\ce{Na2CO3}$? You can calculate how many mols in each solution:

\begin{align} \text{Number of moles of}~ \ce{CaCl2}~ \text{in solution} &= M_1V_1=2~\pu{mol L-1}\cdot \pu{0.100L}=\pu{0.2mol}\\ \text{Number of moles of}~ \ce{Na2CO3}~ \text{in solution} &= M_2V_2=1~\pu{mol L-1}\cdot \pu{0.100L}=\pu{0.1mol} \end{align}

Now, according to the chemical equation, only $\pu{0.1 mol}$ of $\ce{CaCl2}$ would react with available $\pu{0.1 mol}$ of $\ce{Na2CO3}$ to give $\pu{0.1 mol}$ of $\ce{CaCO3}$ solid and $\pu{0.2 mol}$ of aqueous $\ce{NaCl}$. The rest of $\pu{0.1 mol}$ of $\ce{CaCl2}$ would remain unreacted in the solution. In this situation, we called $\ce{Na2CO3}$ is the limiting reagent because all of them would be consumed by the reaction. In other word, $\ce{CaCl2}$ would be in excess.

• Okay, your entire solution revolves around a given example, but is missing a conclusion. So, are you implying that whether there would be a limiting reagent or not depends on the amount of the reagents used, correct? – Gaurang Tandon May 4 '18 at 12:29
• @ Gaurang Tandon: correct. There is always a limiting reagent, if at least one of the starting materials is in excess in the reaction mixture. – Mathew Mahindaratne May 4 '18 at 22:19


text:
# A survey of intelligent assistants for data analysis

Serban, Floarea; Vanschoren, Joaquin; Kietz, Jörg-Uwe; Bernstein, Abraham (2013). A survey of intelligent assistants for data analysis. ACM Computing Surveys, 45(3):1-35.

## Abstract

Research and industry increasingly make use of large amounts of data to guide decision-making. To do this, however, data needs to be analyzed in typically non-trivial refinement processes, which require technical expertise about methods and algorithms, experience with how a precise analysis should proceed, and knowledge about an exploding number of analytic approaches. To alleviate these problems, a plethora of different systems have been proposed that intelligently'' help users to analyze their data.This article provides a first survey to almost 30 years of research on Intelligent Discovery Assistants (IDAs). It explicates the types of help IDAs can provide to users and the kinds of (background) knowledge they leverage to provide this help. Furthermore, it provides an overview of the systems developed over the past years, identifies their most important features, and sketches an ideal'' future IDA as well as the challenges on the road ahead.

## Abstract

Research and industry increasingly make use of large amounts of data to guide decision-making. To do this, however, data needs to be analyzed in typically non-trivial refinement processes, which require technical expertise about methods and algorithms, experience with how a precise analysis should proceed, and knowledge about an exploding number of analytic approaches. To alleviate these problems, a plethora of different systems have been proposed that intelligently'' help users to analyze their data.This article provides a first survey to almost 30 years of research on Intelligent Discovery Assistants (IDAs). It explicates the types of help IDAs can provide to users and the kinds of (background) knowledge they leverage to provide this help. Furthermore, it provides an overview of the systems developed over the past years, identifies their most important features, and sketches an ideal'' future IDA as well as the challenges on the road ahead.

## Statistics

### Citations

Dimensions.ai Metrics
48 citations in Web of Science®
74 citations in Scopus®


text:
# [Dev-luatex] A mechanism to know which registers are already allocated?

Paul Isambert zappathustra at free.fr
Sun Jun 10 11:17:57 CEST 2012

Hello all,

When you write something that isn't tied to any format, the successful
allocation of registers depends on the same macros being defined in all
formats (e.g. \newcount). (Admittedly, you can do very well without
registers by using Lua variable, but only for counts and dimens.)

Unfortunately, for attributes, you either have \newattribute in ConTeXt
(as far as I can tell from the sources), while in plain and LaTeX you
have \newluatexattribute iff you're willing to load luatexbase-attr
(which I'm not, although I appreciate the effort). In other words, there
is no tradition'' here on which one could rely.

Now, could it be possible to implement e.g. a "tex.counts" table, whose
entries would be \countdef'ed names and the values would be the number
of the associated registers? Then one could easily reserve a new register
on the fly without having to rely on the same macros, e.g.:

\def\FindFreeRegister#1{%
\directlua{%
local t = {}
for _, c in pairs(tex["#1"]) do
t[c] = true
end
for i=22, 2^16-1 do
if not t[i] then
tex.print(i)
break
end
end}%
}

\countdef\mycount=\FindFreeRegister{counts}

Actually, any other way to make sure a register isn't associated with a
command would do; the important thing is that it is implemented in the
engine, not in the formats.

Best,
Paul


text:
# Math Help - Help with changing subjects!

1. ## Help with changing subjects!

im having trouble in changing subjects for equations, such as
4n-3nsquared= -1.. is there like a simple formula for changing the numbers around so it makes sense as in axsquared+bx+c=0?
I usually just do simple math to figure where each number goes like for 4n-3nsquared= -1, i usually think about 4-5=1 and rearrange it to make the equation make sense in the form of axsquared+bx+c=0...
This is for quadratics, so if the question is in the form of axsquared+bx+c=0, then its very easy to solve.

2. Originally Posted by xanith_47
im having trouble in changing subjects for equations, such as
4n-3nsquared= -1.. is there like a simple formula for changing the numbers around so it makes sense as in axsquared+bx+c=0?
I usually just do simple math to figure where each number goes like for 4n-3nsquared= -1, i usually think about 4-5=1 and rearrange it to make the equation make sense in the form of axsquared+bx+c=0...
This is for quadratics, so if the question is in the form of axsquared+bx+c=0, then its very easy to solve.

If you mean,
$4n-3n^2=-1$
Multiptly by -1 but sides to get,
$3n^2-4n=1$
Subtract 1 thus,
$3n^2-4n-1=$
Thus,
$\left\{ \begin{array}{c}{a=3\\b=-4\\c=-1\end{array}\right$


text:
Synaptic vesicles containing radioactive acetylcholine have been isolated from slices of Torpedo electric organ incubated with radioactive choline. The recently synthesized radioactive acetylcholine is preferentially removed from the vesicles by iso-osmotic gel filtration. There is therefore a small compartment of loosely bound recently synthesized acetylcholine within the monodisperse vesicle fraction. The specific radioactivity of this compartment correlates most closely with the ‘free’ acetylcholine of electric organ that is lost when the tissue is homogenized. Membrane-associated vesicles did not contain any particular enrichment of this compartment. On standing at 6°C the loosely bound compartment stabilizes so that it survives iso-osmotic filtration. A study of this phenomenon revealed that it was proportional to the extent of the loss of tightly bound acetylcholine from the vesicles. Incubation with Ca2+, at pH5.5, or partial hypo-osmotic shock, caused losses of tightly bound acetylcholine and proportional increases in the stabilization of loosely bound acetylcholine of vesicles. Incubation at 20°C caused less loss of tightly bound, and less stabilization of loosely bound, acetylcholine. A theoretical treatment of these exchanges also shows that the random factors promoting loss of tightly bound acetylcholine are statistically correlated with those which cause stabilization of loosely bound acetylcholine. The reciprocal relationship between the exchanges is inconsistent with there being two distinct populations of vesicles, one containing recently synthesized, loosely bound acetylcholine and the other containing tightly bound acetylcholine. It is proposed that all the vesicles contain a core of tightly bound acetylcholine and a surface layer of loosely bound acetylcholine. The origin of the extravesicular acetylcholine and also of the acetylcholine released on stimulation is discussed in the light of these results.

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