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We consider how the absence of thermalisation affects the classical Coulomb blockade regime in quantum dots. By solving the quantum kinetic equation in the experimentally accessible regime when the dot has two relevant occupation states, we calculate the current-voltage characteristics for arbitrary coupling to the leads. If the couplings are strongly asymmetric, we have found that the Coulomb staircase practically reduces to the first step independent of the charging energy when the latter is larger than the Fermi energy, while the standard thermalised results are recovered in the opposite case. If the couplings are of the same order, the absence of thermalisation has a new, striking signature - a robust additional peak in the differential conductance., Comment: 16 pages, 4 figures

In recent experiments on conductance of one-dimensional (1D) channels in ultra-clean samples, a diverse set of plateaus were found at fractions of the quantum of conductance in zero magnetic field. We consider a discrete model of strongly interacting electrons in a clean 1D system where the current between weak tunneling contacts is carried by fractionally charged solutions. While in the spinless case conductance remains unaffected by the interaction, as is typical for the strongly interacting clean 1D systems, we demonstrate that in the spinful case the peak conductance takes fractional values that depend on the filling factor of the 1D channel., Comment: 5 pages, 3 figures

We investigate non-equilibrium transport properties of a quantum dot in the Coulomb blockade regime under the condition of negligible inelastic scattering during the dwelling time of the electrons in the dot. Using the quantum kinetic equation we show that the absence of thermalization leads to a double-step in the distribution function of electrons on the dot, provided that it is symmetrically coupled to the leads. This drastically changes nonlinear transport through the dot resulting in an additional (compared to the thermalized case) jump in the conductance at voltages close to the charging energy, which could serve as an experimental manifestation of the absence of thermalization., Comment: 5 pages, 3 figures, and Supplemental material (4 pages); final version, as published (figures updated and revised discussion and supplemental material)

We investigate the Coulomb blockade in quantum dots asymmetrically coupled to the leads for an arbitrary voltage bias focusing on the regime where electrons do not thermalise during their dwell time in the dot. By solving the quantum kinetic equation, we show that the current-voltage characteristics are crucially dependent on the ratio of the Fermi energy to charging energy on the dot. In the standard regime when the Fermi energy is large, there is a Coulomb staircase which is practically the same as in the thermalised regime. In the opposite case of the large charging energy, we identify a new regime in which only one step is left in the staircase, and we anticipate experimental confirmation of this finding., Comment: 12 pages, 2 figures; final version, as published (typos corrected, introduction and section 4 contain revised arguments, results are unchanged)

In order to observe many-body localisation in electronic systems, decoupling from the lattice phonons is required, which is possible only in out-of-equilibrium systems. We show that such an electron-phonon decoupling may happen in suspended films and it manifests itself via a bistability in the electron temperature. By studying the electron-phonon cooling rate in disordered, suspended films with two-dimensional phonons, we derive the conditions needed for such a bistability, which can be observed experimentally through hysteretic jumps of several orders of magnitude in the nonlinear current-voltage characteristics. We demonstrate that such a regime is achievable in systems with an Arrhenius form of the equilibrium conductivity, while practically unreachable in materials with Mott or Efros-Shklovskii hopping., Comment: 8 pages, 4 figures

Quantum correlations between parts of a composite system most clearly reveal themselves through entanglement. Designing, maintaining, and controlling entangled systems is very demanding, which raises the stakes for understanding the efficacy of entanglement-free, yet quantum, correlations, exemplified by quantum discord. Discord is defined via conditional mutual entropies of parts of a composite system, and its direct measurement is hardly possible even via full tomographic characterization of the system state. Here we design a simple protocol to detect and quantify quantum discord in an unentangled bipartite system. Our protocol relies on a characteristic of discord that can be extracted from repeated direct measurements of certain correlations between subsystems of the bipartite system. The proposed protocol opens a way of extending experimental studies of discord to electronic systems but can also be implemented in quantum-optical systems., Comment: 10 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1901.11514

Advances in cooling and trapping of atoms have enabled unprecedented experimental control of many-body quantum systems. This led to the observation of numerous quantum phenomena, important for fundamental science, indispensable for high-precision simulations of condensed-matter systems and promising for technological applications. However, transport measurements in neutral quantum gases are still in their infancy in contrast to the central role they play in electronics. In these lectures, after reviewing nascent experiments on quantum fermionic transport, I will focus on our theoretical prediction sand the possibility of experimental observations of qualitatively new phenomena in transport of ultracold bosons which do not have a direct counterpart in quantum electronic transport in condensed matter systems. The description of this transport is based on the Luttinger liquid (LL) theory. So in the first part of the lectures I will introduce main concepts of the LL based on the functional bosonisation approach., Comment: Lecture notes for 13th International School on Theoretical Physics "Symmetry and Structural Properties of Condensed Matter", Sep 2018, Rzesz\'ow, Poland

We revise a phase diagram for the sliding Luttinger liquid (SLL) of coupled one-dimensional quantum wires packed in two- or three-dimensional arrays. We analyse whether physically justifiable (reasonable) inter-wire interactions, i.e. either the screened Coulomb or "Coulomb-blockade" type interactions, stabilise the SLL phase. Calculating the scaling dimensions of the most relevant perturbations (the inter-wire single-particle hybridisation, charge-density wave, and superconducting inter-wire couplings), we find that their combination always destroys the SLL phase for the repulsive intra-wire interaction. However, suppressing the inter-wire tunnelling (when the charge-density wave is the only remaining perturbation), one can observe a stability region emerging due to the inter-wire interaction., Comment: 5 pages, 1 figure

We study the phase transition between conducting and insulating states taking place in disordered multi-channel Luttinger liquids with inter-channel interactions. We derive renormalisation group equations which are perturbative in disorder but nonperturbative in interaction. In the vicinity of the simultaneous phase transition in all channels, these equations become a set of coupled Berezinskii--Kosterlitz--Thouless equations, which we analyze within two models: an array of identical wires and a two-channel model with distinct channels. We show that a competition between disorder and interaction results in a variety of phases, expected to be observable at intermediate temperatures where the interaction and disorder are relevant but weak hybridization and the charge-density wave interaction may be ignored., Comment: 7 pages, 3 figures

We study the behaviour of ultracold bosonic gas in the critical region above the Bose-Einstein condensation in the presence of an artificial magnetic field, $B_\mathrm{art}$. We show that the condensate fluctuations above the critical temperature $T_c$ cause the fluctuational susceptibility, $\chi _\mathrm{fl}$, of a uniform gas to have a stronger power-law divergence than in an analogous superconducting system. Measuring such a divergence opens new ways of exploring critical properties of the ultracold gas and an opportunity of an accurate determination of $T_c$. We describe a method of measuring $\chi _\mathrm{fl}$ which requires a constant gradient in $B_\mathrm{art}$ and suggest a way of creating such a field in experiment., Comment: 5 pages, 3 figures, 5 pages of Supplement; the text is rewritten and rearranged, and the figures are modified

We study electronic transport in a Luttinger liquid (LL) with an embedded impurity, which is either a weak scatterer (WS) or a weak link (WL), when interacting electrons are coupled to one-dimensional massless bosons (e.g., acoustic phonons). We find that the duality relation, $\Delta_{ws}\Delta_{wl}=1 $, between scaling dimensions of the electron backscattering in the WS and WL limits, established for the standard LL, holds in the presence of the additional coupling for an arbitrary fixed strength of boson scattering from the impurity. This means that at low temperatures such a system remains either an ideal insulator or an ideal metal, regardless of the scattering strength. On the other hand, when fermion and boson scattering from the impurity are correlated, the system has a rich phase diagram that includes a metal-insulator transition at some intermediate values of the scattering., Comment: Final version, as published in PRL (including 2 pp. Supplemental material)

We show that electron-phonon coupling strongly affects transport properties of the Luttinger liquid hybridized with a resonant level. Namely, this coupling significantly modifies the effective energy-dependent width of the resonant level in two different geometries, corresponding to the resonant or antiresonant transmission in the Fermi gas. This leads to a rich phase diagram for a metal-insulator transition induced by the hybridization with the resonant level., Comment: 6 pages, 3 figures

We study the influence of electron-phonon coupling on electron transport through a Luttinger liquid with an embedded weak scatterer or weak link. We derive the renormalization group (RG) equations which indicate that the directions of RG flows can change upon varying either the relative strength of the electron-electron and electron-phonon coupling or the ratio of Fermi to sound velocities. This results in the rich phase diagram with up to three fixed points: an unstable one with a finite value of conductance and two stable ones, corresponding to an ideal metal or insulator., Comment: 4 pages, 2 figures

We obtain the exact asymptotic result for the disorder-averaged probability distribution function for a random walk in a biased Sinai model and show that it is characterized by a creeping behavior of the displacement moments with time, ~ t^{\mu n} where \mu is dimensionless mean drift. We employ a method originated in quantum diffusion which is based on the exact mapping of the problem to an imaginary-time Schr\"{odinger} equation. For nonzero drift such an equation has an isolated lowest eigenvalue separated by a gap from quasi-continuous excited states, and the eigenstate corresponding to the former governs the long-time asymptotic behavior., Comment: 4 pages, 2 figures

The physics of quantum dots is succinctly depicted by the {\it Universal Hamiltonian}, where only zero mode interactions are included. In the case where the latter involve charging and isotropic spin-exchange terms, this would lead to a non-Abelian action. Here we address an Ising spin-exchange interaction, which leads to an Abelian action. The analysis of this simplified yet non-trivial model shed some light on a more general case of charge and spin entanglement. We present a calculation of the tunneling density of states and of the dynamic magnetic susceptibility. Our results are amenable to experimental study and may allow for an experimental determination of the exchange interaction strength., Comment: 11 pages, 7 figures

We have studied low-temperature properties of interacting electrons in a one-dimensional quantum wire (Luttinger liquid) side-hybridized with a single-level impurity. The hybridization induces a back-scattering of electrons in the wire which strongly affects its low energy properties. Using a one-loop renormalization group approach valid for a weak electron-electron interaction, we have calculated a transmission coefficient through the wire, $\mathcal{T}(\varepsilon)$, and a local density of states, $\nu(\varepsilon)$ at low energies $\varepsilon $. In particular, we have found that the antiresonance in $\mathcal{T}(\varepsilon)$ has a generalized Breit-Wigner shape with the effective width $\Gamma(\varepsilon)$ which diverges at the Fermi level., Comment: 4 pages, 1 figure; final version as published

In this lectures, we have described some essential features of loss of coherence by a qubit coupled to the environment. We have first presented well known semiclassical arguments that relate both decoherence and relaxation to the environmental noise. Then we have shown that models with pure decoherence (but no relaxation in qubit states) can be exactly solvable. As an example, we have treated in detail the model of fluctuating background charges which is believed to describe one of the most important channels for decoherence for the charge Josephson junction qubit. We have shown that the decoherence rate saturates at `high' temperatures while becoming linear in T at low temperatures and showing in all regimes a non-monotonic behaviour as a function of the coupling of the qubit to the fluctuating background charges. We have also considered, albeit only perturbatively, the qubit relaxation by the background charges and demonstrated that a quasi-linear behaviour of the spectral density of noise deduced from the measurements of the relaxation rate can be qualitatively explained., Comment: Lecture notes for International workshop on mesoscopic and nanoscopic systems, Kolkata, India, February 2006, to be published by Springer

We calculate the tunnelling density of states (TDoS) for a quantum dot in the Coulomb blockade regime, using a functional integral representation with allowing correctly for the charge quantisation. We show that in addition to the well-known gap in the TDoS in the Coulomb-blockade valleys, there is a suppression of the TDoS at the peaks. We show that such a suppression is necessary in order to get the correct result for the peak of the differential conductance through an almost close quantum dot., Comment: 6 pages, 2 figures

We have found an exact expression for the decoherence rate of a Josephson charge qubit coupled to fluctuating background charges. At low temperatures $T$ the decoherence rate ${\Gamma}$ is linear in $T$ while at high temperatures it saturates in agreement with a known classical solution which, however, reached at surprisingly high $T$. In contrast to the classical picture, impurity states spread in a wide interval of energies ($\gg T$) may essentially contribute to ${\Gamma}$., Comment: Both figures are changed to illustrate a more generic case of impurity states spread in wide interval of energies. Some changes have been made to the abstract and the introduction

The nonlinear sigma model (NLSM) epitomises a field-theoretical approach to (interacting) electrons in disordered media. These lectures are aimed at the audience who might have vaguely heard about its existence but know very little of what is that, even less so of why it should be used and next to nothing of how it can be applied. These what, why and mainly how are the subject of the present lectures. In the first part, after a short description of why to be bothered, the NLSM is derived from scratch in a relatively simple (but still rather mathematical) way for non-interacting electrons in the presence of disorder, and some illustration of its perturbative usage is given. In the second part it is generalised, not without some leap of faith, to include the Coulomb repulsion and superconducting pairing., Comment: 21 pages, 5 eps figures. To appear in "Proceedings of the International School of Physics "Enrico Fermi" Course CLI, edited by B. Altshuler and V. Tognetti, IOS Press, Amsterdam 2003

We use a functional integral formalism developed earlier for the pure Luttinger liquid (LL) to find an exact representation for the electron Green function of the LL in the presence of a single backscattering impurity. This allows us to reproduce results (well known from the bosonization techniques) for the suppression of the electron local density of states (LDoS) at the position of the impurity and for the Friedel oscillations at finite temperature. In addition, we have extracted from the exact representation an analytic dependence of LDoS on the distance from the impurity and shown how it crosses over to that for the pure LL., Comment: 7 pages, 1 LaTeX produced figure

We evaluate a typical value of higher order cumulants (irreducible moments) of conductance fluctuations that could be extracted from magneto-conductance measurements in a single sample when an external magnetic field is swept over an interval $B_0$. We find that the n-th cumulant has a sample-dependent random part $\pm \gN 2^{n/2}\sqrt{a_{n}B_{c}/B_{0}}$, where $\gN 2$ is the variance of conductance fluctuations, $B_{c}$ is a correlation field, and $a_{n}\sim n!$. This means that an apparent deviation of the conductance distribution from a Gaussian shape, manifested by non-vanishing higher cumulants, can be a spurious result of correlations of conductances at different values of the magnetic field., Comment: 4 pages, no figures, submitted to Phys. Rev. B

Mohanty and Webb [Phys. Rev. Lett. 88, 146601 (2002), cond-mat/0204298] claim that their data on conductance fluctuations in gold wires contradict the one-parameter scaling. We show that flaws in extracting values of the cumulants (irreducible moments) <> of the conductance distribution (for n=3,4) invalidate all the conclusions made there. The actual values of the cumulants determined by us from the published raw data contained in Ref. [Phys. Rev. Lett. 88, 146601 (2002)] are orders of magnitude smaller than those claimed. Moreover, the limited applicability of the ergodicity hypothesis makes the higher order cumulants extracted from magnetofingerprints statistically unreliable. Thus, the data of Ref. [Phys. Rev. Lett. 88, 146601 (2002)] do not warrant any statement on the violation or validity of the one-parameter scaling., Comment: This is a revised version, where a misprint has been corrected and an explicit footnote added, helping the interested reader to make a visual inspection of the data in the commented Letter by P. Mohanty and R.A. Webb, Phys. Rev. Lett. 88, 146601 (2002); cond-mat/0204298

The distribution $P_1$ of the first many-body excitation energy of a weakly and moderately interacting electron gas in a finite conductor (in the diffusive regime) is calculated. As the interaction is increased, $P_1$ crosses over from Wigner-Dyson to Poisson. We characterize this transition through the inverse participation ratio in Hilbert space, and examine its manifestation in a projected 2-dimensional space., Comment: 5 pages, 5 figures, corrected abstract posting

In these lectures, given at the NATO ASI at Windsor (2001), applications of the replicas nonlinear sigma model to disordered systems are reviewed. A particular attention is given to two sets of issues. First, obtaining non-perturbative results in the replica limit is discussed, using as examples (i) an oscillatory behaviour of the two-level correlation function and (ii) long-tail asymptotes of different mesoscopic distributions. Second, a new variant of the sigma model for interacting electrons in disordered normal and superconducting systems is presented, with demonstrating how to reduce it, under certain controlled approximations, to known ``phase-only'' actions, including that of the ``dirty bosons'' model., Comment: 25 pages, Proceedings of the NATO ASI "Field Theory of Strongly Correlated Fermions and Bosons in Low - Dimensional Disordered Systems", Windsor, August, 2001; to be published by Kluwer

We study the Anderson orthogonality catastrophe (AOC) in finite conductors with diffusive disorder. The disorder averaged logarithm of $\chi$, the overlap between the ground states before and after adding a static impurity, is found to depend nonmonotonically on the disorder. In two dimensions $<\ln\chi^{-1}> \propto \ln^2 N$ in the weak disorder limit, thus showing a stronger dependence on the number of electrons $N$ than in the canonical AOC. A very broad tail of the distribution of $\chi$, found numerically, is a signature of the importance of a few-level statistics at the Fermi energy., Comment: 4 pages, 3 figures

We modify a nonlinear sigma model (NLSM) for the description of a granulated disordered system in the presence of both the Coulomb repulsion and the Cooper pairing. We show that under certain controlled approximations this model is reduced to the Bose-Hubbard (or ``dirty-boson'') model with renormalized coupling constants. We obtain a more general effective action (which is still simpler than the full NLSM action) which can be applied in the region of parameters where the reduction to the Bose-Hubbard model is not justified. This action may lead to a different picture of the superconductor-insulator transition in 2D systems., Comment: 4 pages, revtex, no figures

We suggest a novel nonlinear $\sigma$-model for the description of disordered superconductors. The main distinction from existing models lies in the fact that the saddle point equation is solved non-perturbatively in the superconducting pairing field. It allows one to use the model both in the vicinity of the metal-superconductor transition and well below its critical temperature with full account for the self-consistency conditions. We show that the model reproduces a set of known results in different limiting cases, and apply it for a self-consistent description of the proximity effect at the superconductor-metal interface., Comment: Revised version, 8 pages, 1 fig., revtex; final version, as published, contains a few corrections in the summary

We present first results for the transmittance, T, through a 1D disordered system with an imaginary vector potential, ih, which provide a new analytical criterion for a delocalization transition in the model. It turns out that the position of the critical curve on the complex energy plane (i.e. the curve where an exponential decay of is changed by a power-law one) is different from that obtained previously from the complex energy spectra. Corresponding curves for or are also different. This happens because of different scales of the exponential decay of one-particle Green's functions (GF) defining the spectra and many-particle GF governing transport characteristics, and reflects higher-order correlations in localized eigenstates of the non-Hermitian model., Comment: 4 pages in RevTex, 1 eps figure included

We show that for all the three standard symmetry classes (unitary, orthogonal and symplectic), the conventional replica nonlinear sigma model gives the correct non-perturbative result for the two-level correlation functions R_2(\omega) of electrons in disordered metals in the limit of large \omega. In this limit, non-perturbative oscillatory contributions arise from a degenerate saddle-point manifold within this sigma model which corresponds to the replica-symmetry breaking. Moreover, we demonstrate that in the unitary case the very same results can be extracted from the well known exact integral representation for R_2(\omega)., Comment: 9 pages, no figures, RevTex

We attempt to systematically derive perturbative quantum corrections to the Berry diagonal approximation of the two-level correlation function (TLCF) for chaotic systems. To this end, we develop a ``weak diagonal approximation'' based on a recent description of the first weak localisation correction to conductance in terms of the Gutzwiller trace formula. This semiclassical method is tested by using it to derive the weak localisation corrections to the TLCF for a semiclassically disordered system. Unfortunately the method is unable to correctly reproduce the ``Hikami boxes'' (the relatively small regions where classical paths are glued together by quantum processes). This results in the method failing to reproduce the well known weak localisation expansion. It so happens that for the first order correction it merely produces the wrong prefactor. However for the second order correction, it is unable to reproduce certain contributions, and leads to a result which is of a different form to the standard one., Comment: 23 pages in Latex (with IOP style files), 3 eps figures included, to be a symposium paper in a Topical Issue of Waves in Random Media, 1999

We show that the perturbative expansion of the two-level correlation function, $R(\omega)$, in disordered conductors can be understood semiclassically in terms of self-intersecting particle trajectories. This requires the extension of the standard diagonal approximation to include pairs of paths which are non-identical but have almost identical action. The number of diagrams thus produced is much smaller than in a standard field-theoretical approach. We show that such a simplification occurs because $R(\omega)$ has a natural representation as the second derivative of free energy $F(\omega)$. We calculate $R(\omega)$ to 3-loop order, and verify a one-parameter scaling hypothesis for it in 2d. We discuss the possibility of applying our ``weak diagonal approximation'' to generic chaotic systems., Comment: 9 pages in REVTeX two-column format including 4 figures; submitted to Phys.Rev.B

We consider the distribution of conductance fluctuations in disordered quantum dots with single channel leads. Using a perturbative diagrammatic approach, valid for continuous level spectra, we describe dephasing due to processes within the dot by considering two different contributions to the level broadening, thus satisfying particle number conservation. Instead of a completely non-Gaussian distribution, which occurs for zero dephasing, we find for strong dephasing that the distribution is mainly Gaussian with non-universal variance and non-Gaussian tails., Comment: 11 pages in REVTeX two-column format; 6 eps figures included; submitted to Phys. Rev. B

The conductance distribution of metallic mesoscopic systems is considered. The variance of this distribution describes the universal conductance fluctuations, yielding a Gaussian distribution of the conductance. We calculate diagrammatically the third cumulant of this distribution, the leading deviation from the Gaussian. We confirm random matrix theory calculations that the leading contribution in quasi-one dimension vanishes. However, in quasi two dimensions the third cumulant is negative, whereas in three dimensions it is positive., Comment: 9 pages, Revtex, with eps figures,to appear in Phys Rev B

We consider a distribution of conductance fluctuations in quantum dots with single channel leads and continuous level spectra and we demonstrate that it has a distinctly non-Gaussian shape and strong dependence on time-reversal symmetry, in contrast to an almost Gaussian distribution of conductances in a disordered metallic sample connected to a reservoir by broad multi-channel leads. In the absence of time-reversal symmetry, our results obtained within the diagrammatic approach coincide with those derived within non-perturbative techniques. In addition, we show that the distribution has lognormal tails for weak disorder, similar to the case of broad leads, and that it becomes almost lognormal as the amount of disorder is increased towards the Anderson transition., Comment: 14 pages in the ReVTeX preprint format, including 5 postscript figures; to be published in J.Phys.:Cond.Mat., 1996

We use a random walk in the ensemble of impurity configurations to generate a Brownian motion model for energy levels in disordered conductors. Treating arc-length along the random walk as fictitous time, the resulting Langevin equation relates spectral statistics to eigenfunction correlations. Solving this equation at energy scales large compared with the mean level spacing, we obtain the spectral form factor, and its parametric dependence., Comment: 4 pages in REVTeX format including 1 postscript figure; to be published in Phys. Rev. Letters, 1996

We establish a new approach to calculating spectral statistics in disordered conductors, by considering how energy levels move in response to changes in the impurity potential. We use this fictitious dynamics to calculate the spectral form factor in two ways. First, describing the dynamics using a Fokker-Planck equation, we make a physically motivated decoupling, obtaining the spectral correlations in terms of the quantum return probability. Second, from an identity which we derive between two- and three-particle correlation functions, we make a mathematically controlled decoupling to obtain the same result. We also calculate weak localization corrections to this result, and show for two dimensional systems (which are of most interest) that corrections vanish to three-loop order., Comment: 35 pages in REVTeX format including 10 postscript figures; to be published in a special issue (on Topics in Mesoscopic Physics) of the Journal of Mathematical Physics, October 1996

We use the semiclassical approach combined with the scaling results for the diffusion coefficient to consider the two-level correlation function $R(\varepsilon)$ for a disordered electron system in the crossover region, characterized by the appearance of a macroscopic correlation or localization length, $\xi$, that diverges at the metal-insulator transition. We show new critical statistics, characterized by a nontrivial asymptotic behavior of $R(\varepsilon)$, to emerge on both sides of the transition at higher energies, and to expand to all energies larger than mean level spacing when $\xi$ exceeds the system size., Comment: 4 pages,1 figure, in self-ectracting uuencoded gz-compressed file to be published in Phys. Rev. Letters; REVTeX source file is available upon request

We consider the two-level correlation function in two-dimensional disordered systems. In the non-ergodic diffusive regime, at energy $\epsilon>E_{c}$ ($E_{c}$ is the Thouless energy), it is shown to be completely determined by the weak localization effects, thus being extremely sensitive to time-reversal and spin symmetry breaking: it decreases drastically in the presence of magnetic field or magnetic impurities and changes its sign in the presence of a spin-orbit interaction. In contrast to this, the variance of the levels number fluctuations is shown to be almost unaffected by the weak localization effects., Comment: 4 pages, 2 figures, in self-ectracting uuencoded file, submitted to Phys. Rev. Letters

It is shown that the characteristics of the mesoscopic fluctuations in the conventional quantum-diffusion model and the model of the non-coherent (`classical') diffusion in media with long-range correlated disorder are quite similar in the weak-disorder limit. The relative values of the variance and of the high-order moments of the fluctuations in one model are obtained from those in another one by substituting a proper weak-disorder parameter. As behaviour of the ensemble-averaged diffusion coefficient is quite different in these models, it suggests that the mesoscopic properties, including a possible universality in the distribution functions, could be independent of the behaviour of the averaged quantities., Comment: 17 pages, REVTeX, no figures, to be published in NATO ASI series

Using the conventional scaling approach as well as the renormalization group analysis in $d=2+\epsilon$ dimensions, we calculate the localization length $\xi(B)$ in the presence of a magnetic field $B$. For the quasi 1D case the results are consistent with a universal increase of $\xi(B)$ by a numerical factor when the magnetic field is in the range $\ell\ll{\ell_{\!{_H}}}\alt\xi(0)$, $\ell$ is the mean free path, ${\ell_{\!{_H}}}$ is the magnetic length $\sqrt{\hbar c/eB}$. However, for $d\ge 2$ where the magnetic field does cause delocalization there is no universal relation between $\xi(B)$ and $\xi(0)$. The effect of spin-orbit interaction is briefly considered as well., Comment: 4 pages, revtex, no figures; to be published in Europhysics Letters