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Sep 23, 2013
09/13

by
T. Ludwig; A. D. Mirlin

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We study the amplitude of mesoscopic Aharonov-Bohm oscillations in quasi-one-dimensional (Q1D) diffusive rings. We consider first the low-temperature limit of a fully coherent sample. The variance of oscillation harmonics is calculated as a function of the length of the leads attaching the ring to reservoirs. We further analyze the regime of relatively high temperatures, when the dephasing due to electron-electron interaction suppresses substantially the oscillations. We show that the dephasing...

Source: http://arxiv.org/abs/cond-mat/0312577v1

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36

Sep 23, 2013
09/13

by
T. Ludwig; A. D. Mirlin

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We study the effect of the electron-electron interaction on the amplitude of mesoscopic Aharonov-Bohm oscillations in quasi-one-dimensional (Q1D) diffusive rings. We show that the dephasing length L_phi^AB governing the damping factor exp(-2piR / L_phi^AB) of the oscillations is parametrically different from the common dephasing length for the Q1D geometry. This is due to the fact that the dephasing is governed by energy transfers determined by the ring circumference 2piR, making L_phi^AB...

Source: http://arxiv.org/abs/cond-mat/0312325v2

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33

Sep 22, 2013
09/13

by
A. D. Mirlin; F. Evers

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Critical fluctuations of wave functions and energy levels at the Anderson transition are studied for the family of the critical power-law random banded matrix ensembles. It is shown that the distribution functions of the inverse participation ratios (IPR) $P_q$ are scale-invariant at the critical point, with a power-law asymptotic tail. The IPR distribution, the multifractal spectrum and the level statistics are calculated analytically in the limits of weak and strong couplings, as well as...

Source: http://arxiv.org/abs/cond-mat/0003332v1

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33

Sep 17, 2013
09/13

by
A. D. Mirlin; P. Woelfle

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In a recent Letter, Taras-Semchuk and Efetov reconsider the problem of electron localization in a random magnetic field in two dimensions. They claim that due to the long-range nature of the vector potential correlations an additional term appears in the effective field theory ($\sigma$-model) of the problem, leading to delocalization at the one-loop level. This calls into question the results of earlier analytical studies, where the random magnetic field problem was mapped onto the...

Source: http://arxiv.org/abs/cond-mat/0007475v1

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65

Sep 22, 2013
09/13

by
F. Evers; A. D. Mirlin

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Statistics of the inverse participation ratio (IPR) at the critical point of the localization transition is studied numerically for the power-law random banded matrix model. It is shown that the IPR distribution function is scale-invariant, with a power-law asymptotic ``tail''. This scale invariance implies that the fractal dimensions $D_q$ are non-fluctuating quantities, contrary to a recent claim in the literature. A recently proposed relation between $D_2$ and the spectral compressibility...

Source: http://arxiv.org/abs/cond-mat/0001086v1

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131

Sep 18, 2013
09/13

by
F. Evers; A. D. Mirlin

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The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed. The term ``Anderson transition'' is understood in a broad sense, including both metal-insulator transitions and quantum-Hall-type transitions between phases with localized states. The emphasis is put on recent developments, which include: multifractality of critical wave functions, criticality in the power-law random banded matrix model, symmetry classification of disordered electronic...

Source: http://arxiv.org/abs/0707.4378v1

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32

Sep 20, 2013
09/13

by
A. D. Mirlin; P. Woelfle

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We calculate the magnetoresistivity of a two-dimensional electron gas in the presence of a periodic potential within classical transport theory, using realistic models of impurity scattering. The magnetooscillations induced by geometric resonance of the cyclotron orbits in the periodic grating, known as Weiss oscillations, are shown to be affected strongly by the small-angle scattering processes dominant in conventional semiconductor heterostructures. Our results are in full agreement with...

Source: http://arxiv.org/abs/cond-mat/9802288v2

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44

Sep 23, 2013
09/13

by
A. D. Mirlin; P. Woelfle

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We calculate the Altshuler-Aronov type quantum correction to the conductivity of $2d$ charge carriers in a random potential (or random magnetic field) coupled to a transverse gauge field. The gauge fields considered simulate the effect of the Coulomb interaction for the fractional quantum Hall state at half filling and for the $t-J$ model of high-$T_c$ superconducting compounds. We find an unusually large quantum correction varying linearly or quadratically with the logarithm of temperature, in...

Source: http://arxiv.org/abs/cond-mat/9608003v2

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124

Jul 20, 2013
07/13

by
I. V. Gornyi; A. D. Mirlin

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We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth random potential, which allows us to apply the ballistic $\sigma$-model approach. We analyze conditions of applicability of the $\sigma$-model, emphasizing the role played by the single-particle mean free path and the Lyapunov exponent due to the random potential. In particular, we present a resolution of the puzzle of repetitions of periodic orbits counted...

Source: http://arxiv.org/abs/cond-mat/0107552v1

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67

Sep 18, 2013
09/13

by
Ya. M. Blanter; A. D. Mirlin

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Correlations of eigenfunctions, $\langle|\psi_k(r_1)|^2|\psi_l(r_2)|^2\rangle$, in a disordered system are investigated. We derive general formulae expressing these correlation functions in terms of the supermatrix sigma-model. In particular case of weak localization regime we find that the correlations of the same eigenfunction are proportional to $g^{-1}$ for large distances, while the correlations of two different eigenfunctions cross over from $g^{-1}$ behavior for $r_1=r_2$ to $g^{-2}$ one...

Source: http://arxiv.org/abs/cond-mat/9604139v2

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33

Sep 21, 2013
09/13

by
Ya. M. Blanter; A. D. Mirlin

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The weak localization correction and the mesoscopic fluctuations of the polarizability and the capacitance of a small disordered sample are studied systematically in 2D and 3D geometries. While the grand canonical ensemble calculation gives the positive magnetopolarizability, in the canonical ensemble (appropriate for isolated samples) the sign of the effect is reversed. The magnitude of mesoscopic fluctuations for a single sample exceeds considerably the value of the weak localization...

Source: http://arxiv.org/abs/cond-mat/9705250v2

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39

Sep 18, 2013
09/13

by
Ya. M. Blanter; A. D. Mirlin

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We calculate average magnetopolarizability of an isolated metallic sample at frequency $\omega$ comparable to the mean level spacing $\Delta$. The frequency dependence of the magnetopolarizability is described by a universal function of $\omega/\Delta$.

Source: http://arxiv.org/abs/cond-mat/0006420v1

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125

Sep 18, 2013
09/13

by
Ya. M. Blanter; A. D. Mirlin

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A rigorous microscopic calculation of the polarizability of disordered mesoscopic particles within the grand canonical ensemble is given in terms of the supersymmetry method. The phenomenological result of Gor'kov and Eliashberg is confirmed. Thus the underlying assumptions of their method are justified. This encourages application of RMT in the Gor'kov--Eliashberg style to more complicated situations.

Source: http://arxiv.org/abs/cond-mat/9509097v2

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48

Sep 18, 2013
09/13

by
I. V. Gornyi; A. D. Mirlin

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We study the interaction-induced quantum correction \delta\sigma_{\alpha\beta} to the conductivity tensor of electrons in two dimensions for arbitrary T\tau (where T is the temperature and \tau the transport scattering time), magnetic field, and type of disorder. A general theory is developed, allowing us to express \delta\sigma_{\alpha\beta} in terms of classical propagators (``ballistic diffusons''). The formalism is used to calculate the interaction contribution to the longitudinal and the...

Source: http://arxiv.org/abs/cond-mat/0306029v1

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2.0

Jun 29, 2018
06/18

by
K. S. Tikhonov; A. D. Mirlin

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We investigate analytically and numerically eigenfunction statistics in a disordered system on a finite Bethe lattice (Cayley tree). We show that the wave function amplitude at the root of a tree is distributed fractally in a large part of the delocalized phase. The fractal exponents are expressed in terms of the decay rate and the velocity in a problem of propagation of a front between unstable and stable phases. We demonstrate a crucial difference between a loopless Cayley tree and a locally...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1608.00331

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44

Sep 17, 2013
09/13

by
I. V. Gornyi; A. D. Mirlin

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We study interaction-induced quantum correction to the conductivity tensor of electrons in two dimensions for arbitrary T tau, where T is the temperature and tau the transport mean free time. A general formula is derived, expressing the correction in terms of classical propagators ("ballistic diffusons"). The formalism is used to calculate the interaction contribution to the magnetoresistance in a classically strong transverse field and smooth disorder in the whole range of...

Source: http://arxiv.org/abs/cond-mat/0207557v2

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42

Sep 18, 2013
09/13

by
I. V. Gornyi; A. D. Mirlin

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We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth disorder. The conjecture of Gaussian fluctuations of wave functions put forward by Berry and generalized by Hortikar and Srednicki is proven to hold on sufficiently short distances, while it is found to be strongly violated on larger scales. This also resolves the conflict between the above conjecture and the wave function normalization. The method is further used...

Source: http://arxiv.org/abs/cond-mat/0105103v1

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37

Sep 19, 2013
09/13

by
A. D. Mirlin; F. Evers; A. Mildenberger

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The statistical properties of wave functions at the critical point of the spin quantum Hall transition are studied. The main emphasis is put onto determination of the spectrum of multifractal exponents $\Delta_q$ governing the scaling of moments $ \sim L^{-qd-\Delta_q}$ with the system size $L$ and the spatial decay of wave function correlations. Two- and three-point correlation functions are calculated analytically by means of mapping onto the classical percolation, yielding the values...

Source: http://arxiv.org/abs/cond-mat/0208451v1

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38

Sep 18, 2013
09/13

by
A. D. Mirlin; E. Tsitsishvili; P. Woelfle

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Commensurability oscillations in the magnetoresistivity of a two-dimensional electron gas in a two-dimensional lateral superlattice are studied in the framework of quasiclassical transport theory. It is assumed that the impurity scattering is of small-angle nature characteristic for currently fabricated high-mobility heterostructures. The shape of the modulation-induced magnetoresistivity $\Delta\rho_{xx}$ depends on the value of the parameter $\gamma\equiv \eta^2 ql/4$, where $\eta$ and $q$...

Source: http://arxiv.org/abs/cond-mat/0101242v1

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54

Sep 18, 2013
09/13

by
F. Evers; A. Mildenberger; A. D. Mirlin

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We investigate numerically the statistics of wavefunction amplitudes $\psi({\bf r})$ at the integer quantum Hall transition. It is demonstrated that in the limit of a large system size the distribution function of $|\psi|^2$ is log-normal, so that the multifractal spectrum $f(\alpha)$ is exactly parabolic. Our findings lend strong support to a recent conjecture for a critical theory of the quantum Hall transition.

Source: http://arxiv.org/abs/cond-mat/0105297v1

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32

Sep 21, 2013
09/13

by
F. Evers; A. Mildenberger; A. D. Mirlin

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Statistical properties of critical wave functions at the spin quantum Hall transition are studied both numerically and analytically (via mapping onto the classical percolation). It is shown that the index $\eta$ characterizing the decay of wave function correlations is equal to 1/4, at variance with the $r^{-1/2}$ decay of the diffusion propagator. The multifractality spectra of eigenfunctions and of two-point conductances are found to be close-to-parabolic, $\Delta_q\simeq q(1-q)/8$ and...

Source: http://arxiv.org/abs/cond-mat/0203134v1

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47

Sep 20, 2013
09/13

by
A. D. Mirlin; E. Altshuler; P. Woelfle

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We develop a quasiclassical method based on the path integral formalism, to study the influence of disorder on magnetooscillations of the density of states and conductivity. The treatment is appropriate for electron systems in the presence of a random potential with large correlation length or a random magnetic field, which are characterisitic features of various 2D electronic systems presently studied in experiment. In particular, we study the system of composite fermions in the fractional...

Source: http://arxiv.org/abs/cond-mat/9507081v1

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39

Sep 18, 2013
09/13

by
A. D. Mirlin; E. Tsitsishvili; P. Woelfle

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An analytical study of the low-field magnetoresistance of a two-dimensional electron gas subject to a weak periodic modulation is presented. We assume small-angle impurity scattering characteristic for high-mobility semiconductor heterostructures. It is shown that the condition for existence of the strong low-field magnetoresistance induced by so-called channeled orbits is $\eta^{3/2}ql\gg 1$, where $\eta$ and $q$ are the strength and the wave vector of the modulation, and $l$ is the transport...

Source: http://arxiv.org/abs/cond-mat/0012417v1

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23

Sep 22, 2013
09/13

by
A. Mildenberger; F. Evers; A. D. Mirlin

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The statistics of critical wave functions at the Anderson transition in three and four dimensions are studied numerically. The distribution of the inverse participation ratios (IPR) $P_q$ is shown to acquire a scale-invariant form in the limit of large system size. Multifractality spectra governing the scaling of the ensemble-averaged IPRs are determined. Conjectures concerning the IPR statistics and the multifractality at the Anderson transition in a high spatial dimensionality are formulated.

Source: http://arxiv.org/abs/cond-mat/0111081v1

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34

Jul 20, 2013
07/13

by
F. Evers; A. Mildenberger; A. D. Mirlin

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We present an ultra-high-precision numerical study of the spectrum of multifractal exponents $\Delta_q$ characterizing anomalous scaling of wave function moments $ $ at the quantum Hall transition. The result reads $\Delta_q = 2q(1-q)[b_0 + b_1(q-1/2)^2 + ...]$, with $b_0 = 0.1291\pm 0.0002$ and $b_1 = 0.0029\pm 0.0003$. The central finding is that the spectrum is not exactly parabolic, $b_1\ne 0$. This rules out a class of theories of Wess-Zumino-Witten type proposed recently as possible...

Source: http://arxiv.org/abs/0804.2334v1

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33

Sep 18, 2013
09/13

by
A. D. Mirlin; R. Pnini; B. Shapiro

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We study the intensity distribution function, P(I), for monochromatic waves propagating in quasi one-dimensional disordered medium, assuming that a point source and a point detector are embedded in the bulk of the medium. We find deviations from the Rayleigh statistics at moderately large I and a logarithmically-normal asymptotic behavior of P(I). When the radiation source and the detector are located close to the opposite edges of the sample (on a distance much less then the sample length), an...

Source: http://arxiv.org/abs/cond-mat/9803242v1

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48

Sep 18, 2013
09/13

by
Y. Adamov; I. V. Gornyi; A. D. Mirlin

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Motivated by recent experiments, we study the interaction corrections to the damping of magnetooscillations in a two-dimensional electron gas (2DEG). We identify leading contributions to the interaction-induced damping which are induced by corrections to the effective mass and quantum scattering time. The damping factor is calculated for Coulomb and short-range interaction in the whole range of temperatures, from the ballistic to the diffusive regime. It is shown that the dominant effect is...

Source: http://arxiv.org/abs/cond-mat/0509463v2

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37

Sep 22, 2013
09/13

by
I. V. Gornyi; A. D. Mirlin; P. Woelfle

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We study long-range correlations of equilibrium current densities in a two-dimensional mesoscopic system with the time reversal invariance broken by a random or homogeneous magnetic field. Our result is universal, i.e. it does not depend on the type (random potential or random magnetic field) or correlation length of disorder. This contradicts recent sigma-model calculations of Taras-Semchuk and Efetov (TS&E) for the current correlation function, as well as for the renormalization of the...

Source: http://arxiv.org/abs/cond-mat/0011208v1

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2.0

Jun 30, 2018
06/18

by
I. V. Protopopov; Yuval Gefen; A. D. Mirlin

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Electric and thermal transport properties of a $\nu=2/3$ fractional quantum Hall junction are analyzed. We investigate the evolution of the electric and thermal two-terminal conductances, $G$ and $G^Q$, with system size $L$ and temperature $T$. This is done both for the case of strong interaction between the 1 and 1/ 3 modes (when the low-temperature physics of the interacting segment of the device is controlled by the vicinity of the strong-disorder Kane-Fisher-Polchinski fixed point) and for...

Topics: Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1703.02746

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41

Jul 20, 2013
07/13

by
D. B. Gutman; Yuval Gefen; A. D. Mirlin

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A one-dimensional system of interacting electrons out of equilibrium is studied in the framework of the Luttinger liquid model. We analyze several setups and develop a theory of tunneling into such systems. A remarkable property of the problem is the absence of relaxation in energy distribution functions of left- and right-movers, yet the presence of the finite dephasing rate due to electron-electron scattering, which smears zero-bias-anomaly singularities in the tunneling density of states.

Source: http://arxiv.org/abs/0804.4294v1

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6.0

Jun 28, 2018
06/18

by
J. Klier; I. V. Gornyi; A. D. Mirlin

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We explore theoretically the magnetoresistvity of three-dimensional Weyl and Dirac semimetals in transversal magnetic fields within two alternative models of disorder: (i) short-range impurities and (ii) charged (Coulomb) impurities. Impurity scattering is treated using the self-consistent Born approximation. We find that an unusual broadening of Landau levels leads to a variety of regimes of the resistivity scaling in the temperature-magnetic field plane. In particular, the magnetoresitance is...

Topics: Mesoscale and Nanoscale Physics, Condensed Matter

Source: http://arxiv.org/abs/1507.03481

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26

Sep 21, 2013
09/13

by
A. G. Aronov; A. D. Mirlin; P. Woelfle

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We consider a charged quantum particle in a random magnetic field with Gaussian, delta-correlated statistics. We show that although the single particle properties are peculiar, two particle quantities such as the diffusion constant can be calculated in perturbation theory. We map the problem onto a non-linear sigma-model for Q-matrices of unitary symmetry with renormalized diffusion coefficient for which all states are known to be localized in $d=2$ dimensions. Our results compare well with...

Source: http://arxiv.org/abs/cond-mat/9404070v1

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36

Sep 22, 2013
09/13

by
D. B. Gutman; Yuval Gefen; A. D. Mirlin

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We develop a bosonization technique for one-dimensional fermions out of equilibrium. The approach is used to study a quantum wire attached to two electrodes with arbitrary energy distributions. The non-equilibrium electron Green function is expressed in terms of functional determinants of a single-particle``counting'' operator with a time-dependent scattering phase. The result reveals an intrinsic relation of dephasing and energy redistribution in Luttinger-liquids to ``fractionalization'' of...

Source: http://arxiv.org/abs/0906.4076v1

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34

Sep 23, 2013
09/13

by
D. B. Gutman; Yuval Gefen; A. D. Mirlin

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We develop a theory of tunneling spectroscopy of interacting electrons in a non-equilibrium quantum wire coupled to reservoirs. The problem is modelled as an out-of-equilibrium Luttinger liquid with spatially dependent interaction. The interaction leads to the renormalization of the tunneling density of states, as well as to the redistribution of electrons over energies. Energy relaxation is controlled by plasmon scattering at the boundaries between regions with different interaction strength,...

Source: http://arxiv.org/abs/0903.3333v1

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31

Sep 22, 2013
09/13

by
D. B. Gutman; A. D. Mirlin; Yuval Gefen

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We propose an effective field theory describing the time dependent fluctuations of electrons in conducting systems, generalizing the well known kinetic theory of fluctuations. On several examples, we show its equivalence, (when quantum corrections are neglected) to a microscopic quantum mechanical non-linear $\sigma$-model theory. We apply then the theory to analyze the effects of strong electron-electron and electron-phonon scattering on the statistics of current fluctuations. We find that if...

Source: http://arxiv.org/abs/cond-mat/0403436v2

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63

Jul 20, 2013
07/13

by
T. Ludwig; Ya. M. Blanter; A. D. Mirlin

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We investigate the amplitude of mesoscopic fluctuations of the differential conductance of a metallic wire at arbitrary bias voltage V. For non-interacting electrons, the variance increases with V. The asymptotic large-V behavior is \sim V/V_c (where eV_c=D/L^2 is the Thouless energy), in agreement with the earlier prediction by Larkin and Khmelnitskii. We find, however, that this asymptotics has a very small numerical prefactor and sets in at very large V/V_c only, which strongly complicates...

Source: http://arxiv.org/abs/cond-mat/0406063v2

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33

Sep 18, 2013
09/13

by
D. B. Gutman; Yuval Gefen; A. D. Mirlin

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We consider high order current cumulants in disordered systems out of equilibrium. They are interesting and reveal information which is not easily exposed by the traditional shot noise. Despite the fact that the dynamics of the electrons is classical, the standard kinetic theory of fluctuations needs to be modified to account for those cumulants. We perform a quantum-mechanical calculation using the Keldysh technique and analyze its relation to the quasi classical Boltzmann-Langevin scheme. We...

Source: http://arxiv.org/abs/cond-mat/0210076v1

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38

Sep 18, 2013
09/13

by
A. D. Mirlin; D. G. Polyakov; P. Woelfle

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We study transport in a smooth random magnetic field, with emphasis on composite fermions (CF) near half-filling of the Landau level. When either the amplitude of the magnetic field fluctuations or its mean value $\bar B$ is large enough, the transport is of percolating nature. While at $\bar{B}=0$ the percolation effects enhance the conductivity $\sigma_{xx}$, increasing $\bar B$ (which corresponds to moving away from half-filling for the CF problem) leads to a sharp falloff of $\sigma_{xx}$...

Source: http://arxiv.org/abs/cond-mat/9710135v1

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35

Sep 21, 2013
09/13

by
U. Briskot; I. A. Dmitriev; A. D. Mirlin

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The dynamic conductivity \sigma(\omega) of graphene in the presence of diagonal white noise disorder and quantizing magnetic field B is calculated. We obtain analytic expressions for \sigma(\omega) in various parametric regimes ranging from the quasiclassical Drude limit corresponding to strongly overlapping Landau levels (LLs) to the extreme quantum limit where the conductivity is determined by the optical selection rules of the clean graphene. The nonequidistant LL spectrum of graphene...

Source: http://arxiv.org/abs/1301.7246v1

70
70

Sep 23, 2013
09/13

by
D. B. Gutman; Y. Gefen; A. D. Mirlin

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We consider one dimensional potential trap that connects two reservoirs containing cold Bose atoms. The thermal current and single-particle bosonic Green functions are calculated under non-equilibrium conditions. The bosonic statistics leads to Luttinger liquid state with non-linear spectrum of collective modes. This results in suppression of thermal current at low temperatures and affects the single-particle Green functions.

Source: http://arxiv.org/abs/1111.4925v1

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30

Sep 18, 2013
09/13

by
Y. Adamov; I. V. Gornyi; A. D. Mirlin

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We investigate the sensitivity of a disordered system with diffractive scatterers to a weak external perturbation. Specifically, we calculate the fidelity M(t) (also called the Loschmidt echo) characterizing a return probability after a propagation for a time $t$ followed by a backward propagation governed by a slightly perturbed Hamiltonian. For short-range scatterers we perform a diagrammatic calculation showing that the fidelity decays first exponentially according to the golden rule, and...

Source: http://arxiv.org/abs/cond-mat/0212065v1

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51

Sep 18, 2013
09/13

by
D. B. Gutman; Yuval Gefen; A. D. Mirlin

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The non-equilibrium zero bias anomaly (ZBA) in the tunneling density of states of a diffusive metallic film is studied. An effective action describing virtual fluctuations out-of-equilibrium is derived. The singular behavior of the equilibrium ZBA is smoothed out by real processes of inelastic scattering.

Source: http://arxiv.org/abs/0704.0728v1

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32

Sep 19, 2013
09/13

by
D. B. Gutman; Yuval Gefen; A. D. Mirlin

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Non-equilibrium bosonization technique facilitates the solution of a number of important many-body problems out of equilibrium, including the Fermi-edge singularity, the tunneling spectroscopy and full counting statistics of interacting fermions forming a Luttinger liquid. We generalize the method to non-equilibrium hard-core bosons (Tonks-Girardeau gas) and establish interrelations between all these problems. The results can be expressed in terms of Fredholm determinants of Toeplitz type. We...

Source: http://arxiv.org/abs/1010.5645v1

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74

Sep 17, 2013
09/13

by
D. B. Gutman; Yuval Gefen; A. D. Mirlin

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Non-equilibrium bosonization technique is used to study current fluctuations of interacting electrons in a single-channel quantum wire representing a Luttinger liquid (LL) conductor. An exact expression for the full counting statistics of the transmitted charge is derived. It is given by Fredholm determinant of the counting operator with a time dependent scattering phase. The result has a form of counting statistics of non-interacting particles with fractional charges, induced by scattering off...

Source: http://arxiv.org/abs/1003.5433v1

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42

Sep 18, 2013
09/13

by
I. A. Dmitriev; A. D. Mirlin; D. G. Polyakov

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We develop a systematic theory of microwave-induced oscillations in magnetoresistivity of a 2D electron gas in the vicinity of fractional harmonics of the cyclotron resonance, observed in recent experiments. We show that in the limit of well-separated Landau levels the effect is dominated by a change of the distribution function induced by multiphoton processes. At moderate magnetic field, a single-photon mechanism originating from the microwave-induced sidebands in the density of states of...

Source: http://arxiv.org/abs/0707.0990v2

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3.0

Jun 30, 2018
06/18

by
I. V. Protopopov; D. B. Gutman; A. D. Mirlin

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We explore the life time of excitations in a dispersive Luttinger liquid. We perform a bosonization supplemented by a sequence of unitary transformations that allows us to treat the problem in terms of weakly interacting quasiparticles. The relaxation described by the resulting Hamiltonian is analyzed by bosonic and (after a refermionization) by fermionic perturbation theory. We show that the the fermionic and bosonic formulations of the problem exhibit a remarkable strong-weak-coupling...

Topics: Mesoscale and Nanoscale Physics, Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1404.0178

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4.0

Jun 29, 2018
06/18

by
K. S. Tikhonov; A. D. Mirlin; M. A. Skvortsov

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A numerical study of Anderson transition on random regular graphs (RRG) with diagonal disorder is performed. The problem can be described as a tight-binding model on a lattice with N sites that is locally a tree with constant connectivity. In certain sense, the RRG ensemble can be seen as infinite-dimensional ($d\to\infty$) cousin of Anderson model in d dimensions. We focus on the delocalized side of the transition and stress the importance of finite-size effects. We show that the data can be...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1604.05353

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34

Sep 17, 2013
09/13

by
I. A. Dmitriev; A. D. Mirlin; D. G. Polyakov

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We develop a systematic theory of microwave-induced oscillations in magnetoresistivity of a 2D electron gas in the vicinity of fractional harmonics of the cyclotron resonance, observed in recent experiments. We show that in the limit of well-separated Landau levels the effect is dominated by the multiphoton inelastic mechanism. At moderate magnetic field, two single-photon mechanisms become important. One of them is due to resonant series of multiple single-photon transitions, while the other...

Source: http://arxiv.org/abs/0711.4249v1

2
2.0

Jun 28, 2018
06/18

by
I. V. Gornyi; A. D. Mirlin; D. G. Polyakov

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We revisit the problem of quantum localization of many-body states in a quantum dot and the associated problem of relaxation of an excited state in a finite correlated electron system. We determine the localization threshold for the eigenstates in Fock space. We argue that the localization-delocalization transition (which manifests itself, e.g., in the statistics of many-body energy levels) becomes sharp in the limit of a large dimensionless conductance (or, equivalently, in the limit of weak...

Topics: Strongly Correlated Electrons, Mesoscale and Nanoscale Physics, Condensed Matter

Source: http://arxiv.org/abs/1512.01807

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30

Sep 23, 2013
09/13

by
I. V. Protopopov; D. B. Gutman; A. D. Mirlin

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We study interaction-induced correlations in Luttinger liquid with multiple Fermi edges. Many-particle correlation functions are expressed in terms of Fredholm determinants ${\rm det}(1+\hat{A}\hat{B})$, where $A(\epsilon)$ and $B(t)$ have multiple discontinuities in energy and time spaces. Such determinants are a generalization of Toeplitz determinants with Fisher-Hartwig singularities. We propose a general asymptotic formula for this class of determinants and provide analytical and numerical...

Source: http://arxiv.org/abs/1212.0708v1