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a very active investigation of excitons in coupled quantum wells for more than two decades was first motivated by the possibility to reach bose condensation and superfluidity in this system . further experiments discovered a very large number of related phenomena and quite rich physics of the system ( see refs.@xcite and references therein ) . theory predicts the existence of many phases with different and unusual properties.@xcite the most expected and searched for is the settling in of coherence in such 2d exciton systems . a coherence of the exciton bose condensate has to reveal itself in some coherent properties of the exciton luminescence . investigation of the luminescence led to discovery of not only its coherence @xcite but also a number of patterns not completely understood so far @xcite .    a substantial role in these phenomena is played by the interaction between excitons . typically , interaction between bosons ( @xmath0he atoms and alkali - atoms ) is of a short range and the theory of non - ideal bose gas has been developed for contact interaction . @xcite in coupled quantum wells where the electrons and holes are separated in the two adjacent layers , all the indirect , dipolar excitons that are formed by the coulomb binding of pairs of these spatially separated electrons and holes are polarized in the same way and their interaction is mainly dipole dipole repulsion , fig.[fig : x_in_cqw ] . contrary to the contact interaction the dipole dipole interaction has a significant tail and due to this tail the exciton gas in some respects is dramatically different from bose gas with contact - like interactions . excitons in coupled quantum wells . @xmath1 is the separation between the centers of the wells ( given @xmath1 the dependence of the exciton - exciton interaction on the well widths is very weak @xcite ) . @xmath1 and the average separation between excitons are assumed to be larger than the exciton radius @xmath2 . ] the dipole dipole repulsion increases the exciton energy and leads to a blue shift of its luminescence line . the blue shift is usually evaluated as an average value of the exciton interaction energy with other excitons and can be easily obtained with the help of the mean field approximation that produces `` plate capacitor formula''@xcite @xmath3 where @xmath4 is the exciton 2d concentration , @xmath1 is the separation between the centers of the wells , and @xmath5 is the dielectric constant . this formula can be understood in the following way . equal concentration @xmath4 of electrons and holes in two wells creates potential difference @xmath6 between them . creation of one more indirect exciton in these wells requires transfer of an electron or a hole from one well to the other . in the presence of other excitons this increases the necessary energy by @xmath7 that gives eq.([eq:1 ] ) . this expression is typically used in experiments for an estimate of the exciton concentration from the measured blue shift of the luminescence . recently zimmermann and schindler @xcite noticed , however , that dipole dipole repulsion leads to a significant exciton pair correlation . the repulsion prevents excitons to come very close to each other and creates a depleted region around each exciton . the pair correlation leads to a reduction of the coefficient in eq.([eq:1 ] ) by about 10 times ( depending on the excitons temperature).@xcite this means that previous experimental estimates of the exciton concentration based on the capacitor formula underestimated the concentration by up to 10 times ! it makes sense to note that the reduction of the pair correlation function to zero at small distance in a bose gas with repulsion has been noticed long ago and used in the construction of a many particle variational wave function.@xcite it is well known in exact solutions for one dimensional bose gas.@xcite in the exciton gas with dipole dipole repulsion this behavior of the pair correlation function was noticed by astrakharchik et al.@xcite . this behavior was also used by kash et al to explain a narrowing of the exciton luminescence line at low temperature.@xcite    the significant pair correlation between excitons substantially affects our understanding of the behavior of this system . this motivated us to develop a general picture of the interaction and correlation between excitons in the whole temperature  concentration plane . this is the subject of this paper . we show that eq.([eq:1 ] ) has a very limited region of applicability and limited accuracy . with a decrease of the temperature and an increase of the concentration the role of the pair correlation becomes crucial for interpretation of such phenomena as the blue shift . it appears also that the degeneracy of the exciton system at any small concentration is accompanied by setting in of not pair but multi - particle correlation characteristic for liquids . in other words , a consistent theory of a quantum coherent state has to include multi - exciton correlation at any dilute gas . more than this , at higher concentrations the dipole  dipole repulsion reduces the overlap of the wave functions of different excitons . as a result the exciton system can be considered as classical liquid down to temperature well below than the temperature of quantum degeneracy of a system with contact interaction . our main purpose is to develop a qualitative understanding of the structure of the system of interacting bosons . therefore we do nt pursue a high accuracy of the results but instead use simplified models and qualitative arguments . although the results of such an approach are really accurate only in extreme cases with respect to some large or small parameters , they allow us to make analytical calculations and produce a very clear physical picture of relevant phenomena . availability of such a picture facilitates precise calculations when they are necessary .    in the next section we consider in detail the applicability of the mean field approximation that neglects any correlation between excitons an exciton gas at lower temperatures where strong pair correlation is important but quantum correlations are still negligible is considered in sec.[sec : cxg ] . further reduction of temperature at low exciton concentrations , when the exciton wavelength becomes larger than the characteristic scale of exciton - exciton interaction , leads to an important role of quantization in the exciton - exciton scattering while the exciton gas itself is still statistically non - degenerate . this situation is considered in sec.[sec : xgqs ] . in sec.[sec : lsxs ] we consider the situation where multi - exciton correlation is important . this happens at low enough temperature in a dilute system and in a more wide range of temperatures in a dense system . it appears that with a temperature decrease in a dilute system degeneracy is accompanied by a set in of a multi - exciton correlation . contrary , in a dense system the classical multi - exciton correlations appear to be more important for the blue shift than the quantization of exciton dynamics . in the last section we discuss the obtained results . the discussion of exciton correlation in different parts of the concentration - temperature plane involves quite a large number of physical parameters . to facilitate reading of the paper we present here the list of main parameters with their physical definitions . exact mathematical definitions , if necessary , will be given as soon as the corresponding parameter comes into the discussion . .[tab : parameters]the main parameters characterizing an exciton gas in coupled quantum wells [ cols="^,<,^ , < " , ]     two of the lines in fig.[fig : nt ] , between regions iii and iv and between regions ii and v , actually comprise one line at which the gas parameter condition is violated . the gas parameter is the product of the concentration and the scattering crosssection squared . between regions ii and v this crosssection is classical , @xmath8 , while between regions iii and iv it is quantum , @xmath9 . the other two lines , between regions ii and iii and between regions iv and v , separate classical and quantum interactions between excitons . also , it is necessary to note that at the bottom of region v some quantum coherent phenomena are possible . it is important to note that the lines separating different regions in fig.[fig : nt ] do not correspond to sharp transitions . crossing of one of the lines by changing the temperature or the concentration leads to a gradual change of the correlation between excitons . fig.[fig : nt ] demonstrates only the role of correlation but not phases of the system . we studied an exciton system in coupled quantum wells where electrons and holes are confined in different wells and the main interaction between excitons is a dipole  dipole repulsion . we found that in the most part of the temperature  concentration plane the system is characterized by a strong exciton  exciton correlation . at some parts of this plane the system behaves as a gas with a strong pair correlation . in other parts where the gas parameter condition is violated , i.e. , where the probability to find more than two excitons close to each other becomes of the order of unity , the correlation is multi - excitonic and the system has to be considered as a liquid . in particular , at low concentrations degeneracy of the system is accompanied by a setting in of multi - exciton correlations . at high concentration the strong confinement of each exciton wave function due to repulsion between excitons suppresses quantum correlations . the blue shift of the exciton luminescence has a different value and a different dependence on the exciton temperature and concentration depending on how close excitons can come to each other . therefore it is a sensitive tool for measuring of the exciton  exciton correlations . b.l . appreciates discussions with m. stern and a. l. efros . here the problem of the exciton - exciton scattering is considered under the condition of small energy of relative motion ,            under the condition eq.([eq : xxs.1a ] ) the minimal distance between excitons is much larger than @xmath1 ( i.e. , at @xmath15 the wave function is negligibly small ) and the interaction potential can be approximated with eq.([eq : cxg.7 ] ) . the condition of a very long exciton wavelength , eq.([eq : xxs.1b ] ) , makes it possible to simplify eq.([eq : xxs.4 ] ) in two regions . in the region where the distance between excitons is much smaller than the wavelength of their relative motion , @xmath16 , the coordinate dependence of the wave function comes only from the potential energy and the characteristic scale @xmath17 . at this scale the kinetic energy can be neglected and eq.([eq : xxs.4 ] ) is reduced to @xmath18 when the distance between the excitons is much larger than @xmath19 the interaction energy is small compared to the kinetic energy and @xmath20 due to @xmath21 the two regions overlap at @xmath22 . solutions to both eqs.([eq : xxs.5 ] ) and ( [ eq : xxs.6 ] ) are expressed in bessel functions . when @xmath23 only s scattering is important and it is enough to find angular independent solution of eq.([eq : xxs.5 ] ) . the solution that goes to zero at @xmath24 is @xmath25 the solution to eq.([eq : xxs.6 ] ) describing scattering is @xmath26 making use of asymptotes @xcite        where @xmath28 is the euler constant it is easy to match the solutions in the intermediate region @xmath29 : @xmath30 . \label{eq : xxs.10}\ ] ] this gives @xmath31 according to eq.([eq : xxs.1b ] ) the argument of the logarithm is small and with the logarithmic accuracy @xmath32          m. stern , v. garmider , v. umansky , and i. bar - joseph , phys . * 100 * , 256402 ( 2008 ) ; m. stern , v. garmider , e. segre , m. rappaport , v. umansky , y. levinson , and i. bar - joseph , phys . lett . * 101 * , 257402 ( 2008 ) . j. fernndez - rossier , c. tejedor , l. muoz and l. via , phys . b * 54 * , 11582 ( 1996 ) ; j. fernndez - rossier and c. tejedor , phys . rev * 78 * , 4809 ( 1997 ) ; phys . solidi ( a ) * 164 * , 343 ( 1997 ) . g. e. astrakharchik , j. boronat , i. l. kurbakov , and yu . e. lozovik , phys . lett . * 98 * , 060405 ( 2007 ) ; yu . e. lozovik , i. l. kurbakov , g. e. astrakharchik , j. boronat , and m. willander , arxiv:0801.0150v1 [ cond-mat.str-el ] 30 dec 2007 . l. v. butov , a. c. gossard and d. s. chemla , nature * 418 * , 751 ( 2002 ) ; l. v. butov , c. w. lai , a. l. ivanov , a. c. gossard , and d. s. chemla , nature * 417 * , 47 ( 2002 ) ; l.v . butov , l. s. levitov , a.v . mintsev , b. d. simons , a.c . gossard , and d. s. chemla , phys . lett . * 92 * , 117404 ( 2004 ) . d. snoke , s. denev , y. liu , l. pfeiffer , and k. west , nature * 418 * , 754 ( 2002 ) ; d. snoke , y. liu , s. denev , l. pfeiffer , and k. west , solid state commun . * 127 * , 187 ( 2003 ) ; d. snoke , phys . stat . solidi b * 238 * , 389 ( 2003 ) .
in this paper we present a study of an exciton system where electrons and holes are confined in double quantum well structures . the dominating interaction between excitons in such systems 
 is a dipole - dipole repulsion . 
 we show that the tail of this interaction leads to a strong correlation between excitons and substantially affects the behavior of the system . making use of qualitative arguments and estimates 
 we develop a picture of the exciton - exciton correlations in the whole region of temperature and concentration where excitons exist . 
 it appears that at low concentration degeneracy of the excitons is accompanied with strong multi - particle correlation so that the system can not be considered as a gas . at high concentration 
 the repulsion suppresses the quantum degeneracy down to temperatures that could be much lower than in a bose gas with contact interaction . 
 we calculate the blue shift of the exciton luminescence line which is a sensitive tool to observe the exciton - exciton correlations .