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in the last decade transport properties of mesoscopic superconductor / normal metal ( s / n ) structures were intensively studied ( see for example the review articles @xcite and references therein ) . it was established that in these nano - structures , i.e. in structures whose dimensions are less than the phase coherence length @xmath1 and the inelastic scattering length @xmath2 , the conductance changes when decreasing the temperature below the critical temperature @xmath3 of the superconducting transition and this variation may be both positive ( @xmath4 ) and negative ( @xmath5 ) @xcite . the increase or decrease of the conductance @xmath6 depends , in particular , on the interface resistances and is determined by a competition between two contributions caused by the proximity effect . one of them is due to the suppression of the density - of - state ( dos ) and leads to a decrease of the conductance . the second one results in increasing @xmath6 and is similar to the maki - thompson term @xcite . these studies apparently were stimulated by the theoretical work @xcite in which a weak - localization correction to the conductance of a s / n / s mesoscopic structure was calculated and an oscillatory dependence of this correction on the phase difference @xmath7 between the superconductors s was predicted . these oscillations have been indeed observed @xcite but their amplitude turned out to be two orders of magnitude larger than the predicted one . in order to overcome this discrepancy between theory and experiment one should take into account the proximity effect . it was shown that the latter leads to much larger amplitudes of the conductance oscillations than the weak - localization corrections @xcite . the proximity effect manifests itself also in other interesting peculiarities of the transport properties of s / n structures . one of them is an interesting dependence of the josephson current @xmath8 on an additional dissipative current @xmath9 through a n wire in a 4-terminal s / n / s structure similar to the one shown in the inset of fig.[fig_geometry_triplet ] . according to theoretical predictions the current @xmath8 changes sign if the current @xmath9 is large enough @xcite . this behavior of the josephson current ( @xmath10-contact ) was later experimentally confirmed@xcite . another interesting effect is a non - monotonic temperature @xmath11 ( or voltage @xmath12 ) dependence of the correction to the conductance @xmath13 @xcite . when decreasing the temperature , @xmath13 increases , reaches a maximum and with further decrease of the temperature drops to zero . this behavior has been explained theoretically for the case of a short s / n contact ( @xmath14 ) @xciteand a  long  s / n structure ( @xmath15 ) @xcite , here @xmath16 is the thouless energy , @xmath17 is the diffusion constant , @xmath18 is the length of the n wire ( film ) . the reason for this behavior is the competition between two contributions to the conductance mentioned above . it is interesting to note that low - energy states play an important role in transport properties of s / n structures . the reason is that the condensate penetrates into the n wire over a length @xmath19 which may be much larger than the thermodynamic correlation length @xmath20 provided the characteristic energy @xmath21 therefore , in the limit of low ( compared to @xmath11 ) thouless energy @xmath22 the phase coherence is maintained over distances @xmath23 of the order of the length @xmath18 of the n wire . these long - range phase - coherent effects have been predicted in @xcite and observed on a 4-terminal s / n / s structure @xcite . in ref.@xcite the conductance oscillations related to the phase coherence were observed in a s / n / s mesoscopic structure . it was established for the first time that these oscillations survive in a temperature range where the josephson coupling between the superconductors becomes negligible . the authors of ref.@xcite observed an increase in the josephson critical current when an additional dissipative current was injected into the n region in a 4-terminal s / n / s structure . this current leads to long - range effects affecting the critical current .    recently , similar investigations have been carried out on mesoscopic f / s structures in which ferromagnets ( f ) are used instead of normal ( nonmagnetic ) metals . it is well known that in the dirty limit , when the relaxation momentum time @xmath24 is very small ( @xmath25 , where @xmath26 is the exchange energy ) , the condensate penetrates into a ferromagnet over a length @xmath27 . the latter is extremely short ( 5 - 50  ) for  strong ferromagnets like fe or ni . therefore one might expect that the influence of the proximity effect on transport properties of such structures should be negligibly small . experiments carried out recently on f / s structures showed however that the conductance variation @xmath13 is quite visible ( varying from about 1 to 10% ) when the temperature decreases below @xmath3 @xcite . it is worth mentioning that the conduction variation was both positive and negative . in some experiments the variation @xmath13 was related to a variation of the interface conductance ( resistance ) @xcite , whereas in others @xcite to the conduction variation of the ferromagnetic wire @xmath28 . the theory also predicts both an increase @xcite and decrease@xcite of the conductance .    in refs . @xcite a ballistic contact was analyzed . it was shown that at @xmath29 the contact conductance @xmath30 is twice as large as its conductance @xmath31 in the normal state ( above @xmath3 ) , which agrees with a theoretical prediction for a n / s ballistic contact , and drops to zero at @xmath32 where @xmath33 is the fermi energy . the conductance of a diffusive point contact @xmath30 has been calculated by golubov @xcite who showed that @xmath30 is always smaller than the conductance @xmath31 in the normal state . in the case of a mixed conductivity mechanism ( partly diffusive and partly ballistic ) @xmath34 has been calculated in ref . @xcite and it may be both larger or smaller than the conductance in the normal state @xmath31 .    in order to obtain the resistance of the system shown in fig.[fig_geometry_triplet ] one should add the interface resistances @xmath35 and the resistance of the f wire @xmath36 . the conductance of the f wire @xmath37 under the assumption that @xmath35 is sufficiently small has been calculated in refs . @xcite . as in ref.@xcite , the proximity effect was neglected . it turned out that the conductance of the f wire in the normal state was @xmath38 and was equal to @xmath39 in the superconducting state ( these formulas are valid for a f wire shorter than the spin relaxation length , see @xcite ) . thus , the conductance of the f wire decreases below @xmath3 . the mechanism responsible for this behavior is in this case purely kinetic , since the form of the distribution function depends only on the boundary conditions at the interfaces : if the interface transparencies are perfect the distribution function is continuous in the normal state , while in the superconducting state the boundary condition is changed providing the spinless current through the f / s interface . these two different boundary conditions for the distribution function lead to the different values of the conductance above and below @xmath3 . in the present paper we analyze the conductivity of a f / s structure in the dirty limit when the condition @xmath25 is satisfied .    in the next section we study the kinetic mechanism of the conductance variation in a f / s mesoscopic structure neglecting the proximity effect . the diffusion coefficients and the interface transparencies are assumed to be different for each spin direction . it will be shown that in this case the conductance variation is always negative , _ i.e. _ the conductance decreases with decreasing temperature below @xmath3 .    in the third section we take into account the proximity effect ( the condensate penetration into the ferromagnetic wire ) and present the results for the conductance on the basis of exact calculations assuming equal diffusion constants and interface transparencies for spin up and down . we will see that for a strong exchange field @xmath40 , the resistance variation @xmath41 is positive at any temperature and interface resistance . finally , in section 4 we calculate the conductance variation assuming that the magnetization near the f / s interface has a local inhomogeneity . it will be shown that not only a singlet component arises in the f wire in this case but also a triplet one which penetrates into the f wire over a long distance of the order of @xmath42 , where @xmath43 . the penetration of the triplet component leads to a positive @xmath13 which may be comparable with the conductance variation observed in n / s structures . the singlet component exists only in a very short region near the f / s interface and leads to a negligible contribution to the conductance . in this section , we calculate the conductance of the system shown in fig.[fig_geometry1 ] . we neglect influence of the proximity effect on the conductance assuming that the penetration length of the condensate is very small in comparison with the length of the f wire . the penetration length of the condensate is equal to @xmath27 in the dirty limit and to the mean free path @xmath44 in the clean  limit ( to be more exact , in the limit of a strong ferromagnet , when the condition @xmath45 is satisfied ) . the conduction variation is related in this case to different forms of the distribution function in the normal and superconducting states . the form of the distribution function is determined by boundary conditions at the interfaces f / n ( @xmath46 ) or f / s ( @xmath47 ) . in the normal state the spin current is finite , whereas in the superconducting one it is equal to zero . in the superconducting state at low temperatures , charge is transferred via andreev reflections , i.e. an incident electron is reflected from the f / s boundary and moving back as a hole with the opposite spin direction ( in the s region the charge is carried by singlet cooper pairs with zero total spin ) . in order to find the charge or spin current we need to calculate the distribution function @xmath48 obeying the diffusion equation    @xmath49    here @xmath50 is the distribution function of electrons for a given spin direction @xmath51 , @xmath52 is the distribution function of holes , @xmath53 is the diffusion coefficient which depends on the spin index @xmath54 @xmath55 is the inelastic collision integral . the inelastic collision integral is of the order of @xmath56 , where @xmath57 is the inelastic scattering time . we ignore spin relaxation processes in the f wire assuming that the spin relaxation length exceeds the length @xmath18 . it will be seen that the conductance in the superconducting state is always larger than in the normal one . the simplest formulas are obtained in the case of a perfect f / s interface . therefore , we assume that there is no barrier at the f / s interface and the f/f interface transparency is arbitrary ( f is the ferromagnetic or normal reservoir ) . in the next section we will show that the non - zero reflection coefficient at the f / s interface leads also to an increase of the resistance when temperature is lowered below @xmath58    the boundary conditions at the f/f interface have the same form in the normal and superconducting states ( see appendix )    @xmath59    here @xmath60 @xmath61 is the barrier resistance per unit area for a given spin direction @xmath51 , @xmath62 @xmath63 is the density - of - states ( dos ) . the function @xmath64/2 $ ] is the distribution function in the f reservoir . at the f / s interface the boundary conditions are different in the normal and superconducting case . above @xmath65 they are    @xmath66    below @xmath3 they have the form ( see appendix )    @xmath67    @xmath68    physically , eqs.([k2 ] ) and ( [ k3 ] ) mean that the electric potential at the perfect f / n(s ) interface is chosen to be zero . the potential @xmath69 is expressed in terms of @xmath70 as @xcite @xmath71 $ ] . the condition ( [ k3 ] ) implies that the spin current is zero . this fact is a result of the andreev reflections . it is worth mentioning that , in the model under consideration , the conductance related to the andreev reflections differs from zero only if the amplitude of the condensate function at the f / s interface is not equal to zero . therefore , strictly speaking , we neglect the proximity effect everywhere in the f wire except the nearest neighborhood of the f / s interface . the electrical current is given by the formula    @xmath72 \label{k5}\ ] ]    the spin current @xmath73 is given by the same formula with sign `` - '' instead of `` + '' in the brackets and a factor of @xmath74 in front of the integral ( @xmath75 is the bohr magneton ) . the problem is reduced to finding a solution for eq.([k1 ] ) with the boundary conditions ( [ k2]-[k4 ] ) . the inelastic collision integral has a complicated form and finding a solution is in general an unrealistic task . therefore , we consider limiting cases only .      in this case of a long inelastic relaxation length @xmath77 , we can neglect the inelastic collision integral and seek a solution in the form    @xmath78    where @xmath79 is a constant that determines the current and , hence , the conductance . the constants @xmath80 and @xmath81 can be determined from the boundary conditions ( [ k2]-[k4 ] ) and are equal to    @xmath82    in the normal case , and    @xmath83    in the superconducting case , where @xmath84 is the resistance of the f wire in the normal state . knowing the distribution function we can compute the conductances and the spin current @xmath73 . in the normal state , we obtain    @xmath85 \;. \label{k9}\ ] ]    whereas the result for the superconducting state reads    @xmath86    as follows from eqs.([k9]-[k10 ] ) , the spin current in the normal state is absent only if the conductances in each spin band @xmath87 and @xmath88  are the same . in the superconducting state this current is always zero . the conductances @xmath87 and @xmath88 enter the formulas for @xmath89 and @xmath90 ( [ k9]-[k10 ] ) symmetrically . in the case of a small f/f interface resistance , we obtain for @xmath89 and @xmath90 the formulas presented in @xciteand in the introduction . the conductance in the normal state @xmath89 is always larger than or equal to ( if conductances in each spin channel are the same ) the conductance in superconducting state @xmath90 . indeed , the difference between @xmath89 and @xmath90 can be written in the form    @xmath91 ^{2}/{\cal d}_{f / n}{\cal d}_{f / s},\;.   \label{k12}\ ] ]    where @xmath92 and @xmath93 are the denominators in the expressions ( [ k9]-[k10 ] ) . therefore , in the model under consideration ( dirty limit , no condensate penetration , zero f / s interface resistance ) the conductance decreases with decreasing temperature below @xmath3 . note that the formula for the conductance eq.([k10 ] ) is valid at low temperatures ( @xmath94 ) when the contribution of the states with @xmath95@xmath96 to the conductance can be neglected . at arbitrary temperatures the conductance can be easily found with the help of eq.([k5 ] ) and has the form    @xmath97    where @xmath98 is the conductance of the f / s structure at zero temperature determined by eq.([k10 ] ) . we took into account that at   @xmath99 the boundary conditions for the distribution function are given by eq.(3 ) . let us consider another limiting case when the length @xmath18 of the f - wire exceeds the energy relaxation length @xmath101 in this case the inelastic scattering term in eq.([eq_1 ] ) dominates . it turns to zero provided the distribution function has the equilibrium form    @xmath102/2\;.   \label{k13}\ ] ]    where the potential @xmath103 depends on the spin index @xmath51 and is linear as a function of the coordinate @xmath104 : @xmath105 . integrating eq . ( [ k1 ] ) over the energies we obtain a relation between the current in the @xmath51 spin band and @xmath106    @xmath107    let us consider first the normal case . in the f wire we have    @xmath108    from the last two equations we find @xmath106    @xmath109    the electric field and the total current are equal to the sum of @xmath110 and @xmath111 over spin indices respectively . we easily obtain an expression for the conductance @xmath89 , which is identical to eq . ( [ k9 ] ) . in the superconducting case the current @xmath111 is given by    @xmath112    the potentials @xmath113 and @xmath114 are related to each other by eq . ( [ k3 ] ) : @xmath115 . although the form of the distribution function differs from eqs.([k6]-[k7 ] ) , the conductance @xmath90 below @xmath3 remains unchanged with respect to the previous case ( see eq . ( [ k10 ] ) ) . thus , regardless of the relationship between the lengths @xmath18 and @xmath116 , the conductance of the structure under consideration is given by eqs . ( [ k9]-[k10 ] ) , _ i.e _ it decreases with decreasing temperature below @xmath3 . in the preceding section we neglected the proximity effect and assumed that the f / s interface resistance was equal to zero . we have shown that the conductance decreases with decreasing temperature provided the conductivities of the ferromagnetic wire or the f/f interface for spin up and down differ from each other . in the present section we calculate the conductance for an arbitrary f / s interface resistance taking into account the proximity effect ( the penetration of the superconducting condensate into the f wire ) . in this case the problem becomes more complicated and , for simplicity , we assume that conductivities for the both spin directions are the same . an equation for the distribution function can be solved exactly and this allows one to present the normalized zero - bias conductance @xmath117 in the form    @xmath118    where @xmath119 are the normalized resistances of the f / s and f/f interfaces respectively ( in the normal state ) , @xmath120 @xmath121 is the retarded green s function in the superconductor , @xmath122 is the quasiparticle normalized conductance at a given energy , @xmath123 is the normalized subgap conductance ( the conductance related to andreev reflections ) , @xmath124 . the angle brackets mean the averaging over the length : @xmath125 the physical meaning of the denominator is simple : the first term in the angle brackets is the normalized resistance of the f wire in the presence of the condensate , the second and third terms are the resistances of the f/f and f / s interfaces below @xmath3 respectively . one can see that the  andreev conductance @xmath126 is not zero only if the condensate function at the interface ( from the ferromagnetic side ) @xmath127 differs from zero . the factor @xmath128 in the numerator arises from the normalization of the conductance . in order to calculate the normalized conductance @xmath129 , we have to find the green functions @xmath130 and @xmath131 in the ferromagnetic wire . these functions obey the usadel equation which upon the substitution @xmath132 and @xmath133 acquires the well known form    @xmath134    this equation is complemented by the boundary conditions    @xmath135    @xmath136    the solution for eq.([k19 ] ) can be found analytically in some limiting cases @xcite . it has an especially simple form in the case of a weak proximity effect when @xmath137 and eq.(19 ) may be linearized ( numerical calculations show that the linearized solution differs from the exact solution by less than 10% for @xmath138 ) . here we present the results of a numerical solution of the usadel equation eq.([k19 ] ) and of the calculation of the conductance @xmath139 in fig.[fig_plot1 ] the temperature dependence of the conductance variation @xmath140 is presented for a structure with good interface transparencies at various exchange energies @xmath141 ( normalized to the thouless energy @xmath142 ) . it is seen from this figure that @xmath143 is positive only if @xmath26 is not too large compared to @xmath96 or @xmath3 . a small positive value @xmath143 is observed near @xmath3 for @xmath144 and @xmath145 for @xmath146 the conductance variation is negative and decreases with decreasing @xmath147 for example , in the case of f / al structure the threshold exchange energy @xmath148 above which the conductance deviation is negative for all temperatures , is equal to @xmath149 @xmath150 , that is , this value is much less than the characteristic magnitudes of @xmath26 for ferromagnets as fe , ni , co etc . a slight increase of @xmath90 above @xmath89 is related to the condensate penetration into the f wire . this increase occurs only near @xmath3 because in this temperature range the conductance @xmath90 is close to the conductance @xmath31 in the normal state due to a large contribution of the quasiparticle current . when the temperature decreases , the quasiparticle contribution also decreases and the weak ( at large @xmath141 ) proximity effect can not overcome this decrease of the conductance . the contribution to the conductance due to proximity effect is suppressed even stronger if the f / s interface resistance is not small compared to @xmath151 . in fig . [ fig_plot2 ] we plot the temperature dependence of @xmath143 for the case when the f / s interface resistance ( in the normal state ) is two times larger than the conductance of the f wire . one can see that the normalized conductance decreases with decreasing temperature and becomes very small at low @xmath147 the reason for this behavior of the conductance is quite clear . at high enough temperatures the main contribution to the conductivity is due to quasiparticles with energies @xmath152 with lowering the temperature , this contribution decreases . the contribution caused by andreev reflections ( the term @xmath126 in eq.(19 ) ) at large @xmath141 and not small @xmath153 is very small as the condensate amplitude is small . indeed , in this case one can linearize the usadel equation ( 20 ) and obtain for @xmath154    @xmath155    it follows from this equation that at @xmath156 the amplitude of @xmath157 is small ( we consider low energies @xmath158 therefore the  andreev conductance @xmath126 is also small . the suppression of the andreev reflections in the model considered follows directly from the usadel equation and the widely used boundary conditions of ref . it is worth mentioning that the andreev reflections are responsible for a subgap conductance in n / i / s junctions , which was observed in ref.@xcite . the suppression of the andreev conductance by the exchange field is analogous to the suppression of the subgap conductance by an external magnetic field@xcite . in this section , we consider again a ferromagnetic wire with a metallic contact with a superconductor . in the previous sections we have shown that the proximity effect in the presence of a strong exchange field @xmath26 could be neglected , since the superconducting condensate penetrates into the f wire only over a short distance ( @xmath159 in the dirty limit ) . at the same time , the interface resistance  @xmath160 increases when the normal reservoir becomes superconducting . in short , the total conductance decreases with decreasing temperature below the superconducting critical temperature @xmath3 . however , in recent experiments on s / f structures a considerable increase of the conductance below @xmath161 was observed @xcite . the measurements also demonstrate that the entire change of the conductance is due to an increase of the conductivity of the ferromagnetic wire as if the superconducting condensate penetrated into the ferromagnet . a question arises : how can the condensate function penetrate into the f wire over large distances ? we understand that the cooper pairs must be destroyed by the strong exchange field because the electrons of the pairs can no longer have opposite spins    to answer this question we notice that such a simple argument about the destruction of the condensate is based on the assumption that only the singlet pairing exists in the sample . this argument can not be correct if a triplet component of the superconducting condensate penetrates the ferromagnet . an arbitrary exchange field can not destroy the triplet superconducting component since both the electrons of the cooper pair are in the same spin band . in this section , we suggest a mechanism of formation of the triplet pairing , which is due to a local inhomogeneity of the magnetization in the vicinity of the s / f interface . we will show that the penetration length of the triplet component into the ferromagnet is of the order @xmath162 , where the energy @xmath95 is of the order of the temperature @xmath11 or the thouless energy @xmath163 , and therefore the increase of the conductance due to the proximity effect may be comparable with that in a s / n structure . we consider the system shown in fig.[fig_geometry_triplet ] and assume that there is a domain wall in the region @xmath164 described by the angle @xmath165 between the magnetization @xmath166 and the @xmath167-axis . in this region the magnetization is given by @xmath168    for simplicity we assume that @xmath165 varies linearly according to @xmath169 . we consider again the diffusive limit corresponding to a short mean free path and to the condition @xmath170 , which allows us to describe the system using the usadel equation@xcite . we assume that the resistance of the f / s interface is not too small and therefore the condensate amplitude @xmath171 is small . we use the linearized usadel equation for the retarded matrix ( in spin space ) green function @xmath172 , which has the form ( the index @xmath173 is dropped )    @xmath174    here the matrix @xmath175 is defined as @xmath176 . we also assume that the diffusion coefficient is the same for the both spin bands . this equation is supplemented by the boundary condition at the s / f interface , which after linearization takes the form @xcite @xmath177 where @xmath178 is the resistivity of the ferromagnet , @xmath35 is the s / f interface resistance per unit area in the normal state , and @xmath179 . we have assumed that there are no spin - flip processes at the s / f interface . the solution of eq . ( [ a2 ] ) in the region @xmath164 can be sought in the form @xmath180 where @xmath181 is an unitary transformation given by @xmath182 . substituting eq . ( [ rotation2 ] ) into eq . ( [ a2 ] ) we obtain the following equation for @xmath183 @xmath184 where @xmath185 is the anticommutator .    in the region @xmath186 the magnetization is homogeneous and @xmath183 satisfies eq . ( [ a5 ] ) with @xmath187 . we see from eq . ( [ a5 ] ) that the singlet and triplet component of the condensate function are mixed by the rotating exchange field @xmath26 . in the region @xmath186 these components decouple and they should be found by matching the solutions at @xmath188 ( the function @xmath189 is continuous in the entire f wire ) . the solution of eq . ( [ a5 ] ) can be written in the form @xmath190 here the function @xmath191 is the amplitude of the triplet component , whereas @xmath192 and @xmath193 describe the singlet pairing . the structure of eq . ( [ a5 ] ) allows to seek these amplitudes in the form @xmath194 the functions @xmath193 and @xmath191 can be written in a similar way . the coefficients @xmath195 , @xmath196 and @xmath197 obey the algebraic equations    @xmath198    where @xmath199 and @xmath200 ( indices @xmath201 were dropped ) . the eigenvalues @xmath202 are the values at which the determinant of eqs . ( [ 4 ] ) turns to zero . in the case of a strong exchange field @xmath26 , @xmath203 is large ( @xmath204 ) and the eigenvalues @xmath202 are given by @xmath205 the eigenvalues @xmath206 correspond to a sharp decay of the condensate in the ferromagnet , while @xmath207 is associated with the slowly varying part . with the boundary condition , eq . ( [ bound - cond ] ) , we see that in a homogeneous case ( @xmath208 the amplitude of the triplet component @xmath191 is zero . if @xmath209 the function @xmath191 is coupled to the singlet components @xmath192 and @xmath210 and we consider this case . if the width @xmath211 is small , the triplet component changes only a little in the region @xmath212 and spreads over a large distance of the order @xmath213 in the region @xmath214 . in the case of a strong exchange field @xmath26 , @xmath215 is very short ( @xmath216 ) , the singlet component decays very fast over the length @xmath215 , and its slowly varying part @xmath217 is @xmath218 . in order to obtain the expression for the triplet component @xmath219 we use eq . ( [ bound - cond ] ) at @xmath220 and assume that the solution vanishes at @xmath221 then , we find @xmath222 ^{-1}\!\right\ } ^{r(a)}\ ; ,   \label{5}\ ] ] where @xmath223 , @xmath224 is the amplitude of the singlet component at the s / f interface , @xmath225 , @xmath226 , and @xmath227 . it is clear from eq.([5 ] ) that , at the interface , the triplet component is of the same order of magnitude as the singlet one . indeed , for the case @xmath228 we obtain from eq . ( [ 5 ] ) @xmath229 , where @xmath230 is the angle characterizing the rotation of the magnetization . therefore , provided the angle @xmath231 and the s / f interface transparency is not too small , the singlet and triplet components are not small . they are of the same order in the vicinity of the s / f interface but , while the singlet component decays fast over a short distance ( @xmath232 ) , the triplet one varies smoothly along the ferromagnet turning to zero at the f reservoir ( see fig.[fig_penetration ] ) . one can see also that the singlet component oscillates , which is well known @xcite . the penetration of the triplet component into the ferromagnet is similar to the penetration of the superconducting condensate into a normal metal . the presence of the condensate function ( triplet component ) in the ferromagnet can lead to long - range effects and therefore to a significant change of the conductance of a ferromagnetic wire in a s / f structure ( see inset in fig.[fig_geometry_triplet ] ) when the temperature decreases below @xmath3 . the normalized conductance variation @xmath233 is given by the expression @xcite : @xmath234 ^{2}\right\rangle \;. \label{6}\ ] ] here @xmath89 is the conductance in the normal state , @xmath235 denotes the average over the length of the ferromagnetic wire between the f reservoirs , and @xmath236 is given by the expression @xmath237 \;.\ ] ] substituting eqs . ( [ 2 ] , [ 5 ] ) into eq . ( [ 6 ] ) one can determine the temperature dependence @xmath238 shown in fig.[fig_conductance_q ] . we see that @xmath143 increases with decreasing temperature and saturates at @xmath239 . in order to explain the reentrant behavior of @xmath240 observed in refs . @xcite , one should take into account other mechanisms as those analyzed in refs . @xcite and in section 2 . however , this question is beyond the scope of the present analysis . it is also interesting to note that a triplet component of the condensate function with the same symmetry ( odd in frequency @xmath241 and even in momentum @xmath242 ) has been suggested long ago by berezinskii @xcite as a possible phase in superfluid @xmath243 ( this , so called `` odd superconductivity '' , was discussed in a subsequent paper @xcite ) . being symmetric in space , this component is not affected by potential impurities , in contrast to the case analyzed in ref . @xcite , where the triplet component of the condensate was odd in space . while this hypothetical condensate function is not realized in @xmath243 ( in @xmath243 it is odd in @xmath242 but not in frequency ) , this odd ( in @xmath241 ) triplet component does exist in the system considered here , although under special conditions described above .    as it was mentioned in the introduction , experimental data are still controversial . it has been established in an experiment @xcite that the conductance of the ferromagnet does not change below @xmath3 and all changes in @xmath143 are due to changes of the s / f interface resistance @xmath35 . however , in other experiments @xmath35 was negligibly small @xcite . the mechanism suggested in our work may explain the long - range effects observed in the experiments @xcite . at the same time , the result of the experiment @xcite is not necessarily at odds with our findings . the inhomogeneity of the magnetic moment at the interface , which is the crucial ingredient of our theory , is not a phenomenon under control in these experiments . one can easily imagine that such inhomogeneity existed in the structures studied in refs . @xcite but was absent in those of ref . the magnetic inhomogeneity near the interface may have different origins . anyway , a more careful study of the possibility of a rotating magnetic moment should be performed to clarify this question . we have analyzed the conductance variation @xmath244 of the f / s mesoscopic structure in the dirty limit when the condition @xmath245 is satisfied . first , neglecting the proximity effect we have shown that below @xmath3 the conductance variation @xmath246 is negative and its magnitude increases with increasing the difference between the conductances for spin up and down . the change of the conductance is related to changes in the boundary conditions at the f / s interface . below @xmath3 one of the boundary conditions requires the spin current to be zero . the formulas for the conductance remain valid even if inelastic scattering ( not spin flip ) processes are taken into account . we also studied how the proximity effect affects the conductance for an arbitrary transparency of the f / s interface . the account for the condensate penetration ( the proximity effect ) leads to an increase of the conductance near @xmath3 . this is possible , however , only if the exchange energy @xmath26 is not too large : the parameter @xmath247 should not be large , where @xmath141 is the exchange energy in units of the thouless energy @xmath248 and @xmath153 is the ratio of the f / s interface resistance in the normal state to the resistance of the f wire . if the parameter @xmath247 is large , the conductance @xmath90 decreases with decreasing temperature and becomes very small at low @xmath147 this behavior is related to a strong suppression of the andreev reflection processes that determine the conductance at low @xmath11 by the exchange field . it is important to note that we neglected the inverse proximity effect , that is , suppression of superconductivity in s. in the case of large @xmath141 one has to take into account this effect and calculate a deviation of the green s functions in the superconductor from their bulk values . it turns out that in the case of a large exchange energy @xmath249 the energy gap in the superconductor may be suppressed and the dos @xmath250 is not zero even at @xmath95@xmath251 . in this case the quasiparticle conductance is not zero and the charge transfer is possible through the f / s interface at low energies @xmath252 the conversion of the quasiparticle current into the current of cooper pairs is realized in the superconductor over the coherence length @xmath253 ( at low energies ) .    at last , we have calculated the conductance of a f / s structure in which the magnetization is non - homogeneous near the f / s interface . it was shown that , in this case , a triplet component arises alongside with the singlet one . this triplet component in another systems ( he@xmath254 , high @xmath3 superconductors etc ) was studied in several papers @xcite ; it is odd in matsubara frequencies ( the so called odd superconductivity ) and even in momentum space ( in the main approximation in the parameter ( @xmath255 ) ) . the triplet component penetrates into the f wire over a large distance of the order @xmath256 and leads to a positive conductance variation . the singlet component penetrates over much shorter length of the order @xmath257 and leads to a negligible contribution to the conductance . it would be interesting to realize experimentally the situation that we analyzed in the last section and to observe the triplet component not in an exotic system but in an ordinary f / s structure . here we show how the boundary conditions for the distribution functions @xmath258 can be derived from matching conditions for the quasiclassical green functions , where @xmath259 is the distribution function of electrons and @xmath260 is the distribution functions of holes ( having in mind a superconductor , it is better to speak about electron- and hole - like excitations ) . we use the boundary conditions for the quasiclassical matrix green functions @xmath261 the matrix elements of which consist of the retarded ( advanced ) green s functions @xmath262 and the keldysh green s function @xmath263 the last matrix is expressed in terms of the matrix distribution function @xmath264 @xmath265 , where the matrix @xmath266 can be represented in the form : @xmath267 the first function @xmath268 determines the order parameter in the superconductor and is equal @xmath269 the second function @xmath270 determines the electrical or spin current and equals @xmath271 the matching condition at the f(n)/s interface for the 4@xmath2724 matrix green function has the form @xcite      where @xmath274 is the f / s interface resistance ( in the normal state ) normalized to the resistance of the f wire @xmath275 the physical meaning of eq.(a1 ) is simple . if we take the keldysh ( the element ( 12 ) ) of eq.(a1 ) , multiply it by @xmath276 and calculate the trace , we obtain the current at a given energy @xmath95 . if we integrate over energies , we obtain on the left side the usual expression for the current      where @xmath278 is the dos in the normal state . on the right hand side we obtain the current at a given energy which is well known in the tunnel hamiltonian method . we take the keldysh component of eq . ( a1 ) , multiply it by @xmath276 and @xmath279 and calculate the trace . we obtain thus the equations                    the symbol \{ ... }@xmath289 stands for @xmath290 . in the case under consideration @xmath291 @xmath292 and @xmath293 @xmath294so that @xmath295 . we are interested in the states with subgap energies ( low temperatures ) @xmath296 for these states one has @xmath297 and @xmath298 therefore we obtain that @xmath299 and  @xmath300 but @xmath301 one can show that at any non - zero @xmath153 the functions @xmath302 and @xmath303 are not zero and we find from eqs.(a3-a4 )                                                                                              v. i. falko , a. f. volkov , and c. j. lambert , phys . b * 60 * , 15394 ( 1999 ) ; v. i. falko , a. f. volkov , and c. j. lambert , jetp lett . * 69 * , 532 ( 1999 ) ; f.taddei , j.h.jefferson . and c.j.lambert , phys.rev.lett . * 82 * , 4938 ( 1999 ) . fig.3 : the dependence of the conductance variation @xmath310 , for different values of the exchange field @xmath311 . here @xmath312 , @xmath313 and @xmath315 . the solid , dashed and dotted lines correspond to @xmath316 , @xmath317 and @xmath318 respectively . fig.5 : spatial dependence of the singlet ( dashed line ) and the triplet ( solid line ) components of @xmath171 in the f wire for different values of @xmath319 . here @xmath320 , @xmath321 and @xmath322 . @xmath323 is the thouless energy .
we calculate the conductance of a superconductor / ferromagnet ( s / f ) mesoscopic structure in the dirty limit . 
 first we assume that the ferromagnet exhibits a homogeneous magnetization and consider the case that the penetration of the condensate into the f wire is negligible and the case in which the proximity effect is taken into account . 
 it is shown that if the exchange field is large enough , the conductance below the critical temperature @xmath0 , is always smaller than the conductance in the normal state . 
 at last , we calculate the conductance for a f / s structure with a local inhomogeneity of the magnetization in the ferromagnet . 
 we demonstrate that a triplet component of the condensate is induced in the f wire.this leads to a increase of the conductance below @xmath0 
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