arXiv subjects

V. E. Kravtsov

Publications and source records attributed to V. E. Kravtsov.

At least 55 records · Page 3Linked to original sources

arXiv2004

Dynamic localization and Coulomb blockade in quantum dots under AC pumping

We study conductance through a quantum dot under Coulomb blockade conditions in the presence of an external periodic perturbation. The stationary state is determined by the balance between the heating of the dot electrons by the perturbation and cooling by electron exchange with the cold contacts. We show that Coulomb blockade peak can have a peculiar shape if heating is affected by dynamic localization, which can be an experimental signature of this effect.

cond-mat.mes-hall↗

arXiv2004

A super-Ohmic energy absorption in driven quantum chaotic systems

We consider energy absorption by driven chaotic systems of the symplectic symmetry class. According to our analytical perturbative calculation, at the initial stage of evolution the energy growth with time can be faster than linear. This appears to be an analog of weak anti-localization in disordered systems with spin-orbit interaction. Our analytical result is also confirmed by numerical calculations for the symplectic quantum kicked rotor.

cond-mat.mes-hall↗

arXiv2004

Energy absorption in time-dependent unitary random matrix ensembles: dynamic vs Anderson localization

We consider energy absorption in an externally driven complex system of noninteracting fermions with the chaotic underlying dynamics described by the unitary random matrices. In the absence of quantum interference the energy absorption rate W(t) can be calculated with the help of the linear-response Kubo formula. We calculate the leading two-loop interference correction to the semiclassical absorption rate for an arbitrary time dependence of the external perturbation. Based on the results for periodic perturbations, we make a conjecture that the dynamics of the periodically-driven random matrices can be mapped onto the one-dimensional Anderson model. We predict that in the regime of strong dynamic localization W(t) ln(t)/t^2 rather than decays exponentially.

cond-mat.mes-hall↗

arXiv2003

Dephasing and Dynamic Localization in Quantum Dots

The effects of dynamic localization in a solid-state system -- a quantum dot -- are considered. The theory of weak dynamic localization is developed for non-interacting electrons in a closed quantum dot under arbitrary time-dependent perturbation and its equivalence to the theory of weak Anderson localization is demonstrated. The dephasing due to inelastic electron scattering is shown to destroy the dynamic localization in a closed quantum dot leading to the classical energy absorption at times much greater than the inelastic scattering time. Finally a realistic case of a dot weakly connected to leads is studied and it is shown that the dynamic localization may lead to a drastic change of the shape of the Coulomb blockade peak in the dc conductance vs the gate voltage.

cond-mat.mes-hall↗

arXiv2003

Energy level statistics of a critical random matrix ensemble

We study level statistics of a critical random matrix ensemble of a power-law banded complex Hermitean matrices. We compute numerically the level compressibility via the level number variance and compare it with the analytical formula for the exactly solvable model of Moshe, Neuberger and Shapiro.

cond-mat.mes-hall↗

arXiv2002

Dynamic localization in quantum dots: analytical theory

We analyze the response of a complex quantum-mechanical system (e. g., a quantum dot) to a time-dependent perturbation. Assuming the dot energy spectrum and the perturbation to be described by the Gaussian Orthogonal Ensemble of random matrices we find the quantum corrections to the energy absorption rate as a function of dephasing time. If the perturbation is a sum of d harmonics with incommensurate frequencies, the quantum corrections behave similarly to those of conductivity for the d-dimensional Anderson model of the orthogonal symmetry class. For periodic perturbations, the leading quantum corrections are generically absent as in the systems of the unitary symmetry class. Exceptions are the harmonic perturbation and all other periodic perturbations that obey the generalized time-reversal condition (with an arbitrary time shift). Such cases fall into the quasi-1d orthogonal universality class.

cond-mat.mes-hall↗

arXiv2002

Aharonov-Bohm magnetization of mesoscopic rings caused by inelastic relaxation

The magnetization of a system of many mesoscopic rings under non-equilibrium conditions is considered. The corresponding disorder-averaged current in a ring is shown to be a sum of the `thermodynamic' and `kinetic' contributions both resulting from the electron-electron interaction. The thermodynamic part can be expressed through the diagonal matrix elements of the current operator in the basis of exact many-body eigenstates and is a generalization of the equilibrium persistent current. The novel kinetic part is present only out of equilibrium and is governed by the off-diagonal matrix elements. It has drastically different temperature and magnetic field behavior.

cond-mat.mes-hall↗

arXiv2002

Electron kinetics in isolated mesoscopic rings driven out of equilibrium

Kinetic theory of nonlinear current response to an external field is developed for mesoscopic normal metal rings threaded by a magnetic flux. General expressions for direct current (DC) are derived for a non-equilibrium regime. These expressions describe simultaneously a contribution to DC made by a non-equilibrium (external) field, as well as the contribution caused by interaction with intrinsic fields. Contributions of electron-electron and electron-phonon interactions to the direct current in a non-equilibrium systems are studied. The kinetic equation for electrons in a disordered metal ring is solved with taking into account the Coulomb and electron-phonon interactions. This gives an estimate of an overheating of the pumped electron system.

cond-mat.mes-hall↗

arXiv2001

Time-reversal symmetry breaking by ac field: Effect of commensurability in the frequency domain

It is shown that the variance of the linear dc conductance fluctuations in an open quantum dot under a high-frequency ac pumping depends significantly on the spectral content of the ac field. For a sufficiently strong ac field the dc conductance fluctuations are much stronger for the periodic pumping than in the case of the noise ac field of the same intensity. The reduction factor r in a static magnetic field takes the universal value of 2 only for the white-noise pumping. In general r may deviate from 2 thus signalling on the time-reversal symmetry breaking by the ac field. For the bi-harmonic ac field of the form A(t)=A_{0} [cos(ω_{1} t)+cos(ω_{2} t)] we predict the enchancement of effects of T-symmetry breaking at commensurate frequencies ω_{2}/ω_{1}=P/Q. In the high-temperature limit there is also the parity effect: the enchancement is only present if either P or Q is even.

cond-mat.mes-hall↗

arXiv2001

Conductance fluctuations in a quantum dot under almost periodic ac pumping

It is shown that the variance of the linear dc conductance fluctuations in an open quantum dot under a high-frequency ac pumping depends significantly on the spectral content of the ac field. For a sufficiently strong ac field $γτ_ϕ<< 1$, where $1/τ_ϕ$ is the dephasing rate induced by ac noise and $γ$ is the electron escape rate, the dc conductance fluctuations are much stronger for the harmonic pumping than in the case of the noise ac field of the same intensity. The reduction factor $r$ in a static magnetic field takes the universal value of 2 only for the white--noise pumping. For the strictly harmonic pumping $A(t)=A_{0}\cosωt$ of sufficiently large intensity the variance is almost insensitive to the static magnetic field $r-1= 2\sqrt{τ_ϕγ} << 1$. For the quasi-periodic ac field of the form $A(t)=A_{0} [\cos(ω_{1} t)+\cos(ω_{2} t)]$ with $ω_{1,2} >> γ$ and $γτ_ϕ << 1$ we predict the novel effect of enchancement of conductance fluctuations at commensurate frequencies $ω_{2}/ω_{1}=P/Q$.

cond-mat.mes-hall↗

arXiv2001

Limits of the dynamical approach to non-linear response of mesoscopic systems

We have considered the nonlinear response of mesoscopic systems of non-interacting electrons to the time-dependent external field. In this consideration the inelastic processes have been neglected and the electron thermalization occurs due to the electron exchange with the reservoirs. We have demonstrated that the diagrammatic technique based on the method of analytical continuation or on the Keldysh formalism is capable to describe the heating automatically. The corresponding diagrams contain a novel element, {\it the loose diffuson}. We have shown the equivalence of such a diagrammatic technique to the solution to the kinetic equation for the electron energy distribution function. We have identified two classes of problems with different behavior under ac pumping. In one class of problems (persistent current fluctuations, Kubo conductance) the observable depends on the electron energy distribution renormalized by heating. In another class of problems (Landauer conductance) the observable is insensitive to heating and depends on the temperature of electron reservoirs. As examples of such problems we have considered in detail the persistent current fluctuations under ac pumping and two types of conductance measurements (Landauer conductance and Kubo conductance) that behave differently under ac pumping.

cond-mat.mes-hall↗

arXiv2000

Energy level dynamics in systems with weakly multifractal eigenstates: equivalence to 1D correlated fermions

It is shown that the parametric spectral statistics in the critical random matrix ensemble with multifractal eigenvector statistics are identical to the statistics of correlated 1D fermions at finite temperatures. For weak multifractality the effective temperature of fictitious 1D fermions is proportional to (1-d_{n})/n, where d_{n} is the fractal dimension found from the n-th moment of inverse participation ratio. For large energy and parameter separations the fictitious fermions are described by the Luttinger liquid model which follows from the Calogero-Sutherland model. The low-temperature asymptotic form of the two-point equal-parameter spectral correlation function is found for all energy separations and its relevance for the low temperature equal-time density correlations in the Calogero-Sutherland model is conjectured.

cond-mat.mes-hall↗

arXiv1999

On the relationship between the noise-induced persistent current and dephasing rate

AC noise in disordered conductors causes both dephasing of the electron wave functions and a DC current around a mesoscopic ring. We demonstrate that the dephasing rate tau_ϕ^{-1} in long wires and the DC current, induced by the same noise and averaged over an ensemble of small rings are connected. The ensemble-averaged h/2e flux harmonic of the current and the dephasing rate caused by the same uniform in space high frequency AC field are related in a remarkably simple way: tau_ϕ=C e. Here e is an electron charge, and the constant C depends on the Dyson symmetry class. For a pure potential disorder the current is diamagnetic C = -(4/π) and in the presence of strong spin-orbit scattering it is paramagnetic C =(2/π). The relationship seems to agree reasonably with experiments. This suggests that the two puzzles: anomalously large persistent current [L.P.Levy et al., Phys.Rev.Lett., v.64, 2074 (1990)] and the low-temperature saturation of the dephasing [P.Mohanty et al., Phys.Rev.Lett., v.78, 3366 (1997)] may have a common solution.

cond-mat.mes-hall↗

arXiv1999

Topological universality of level dynamics in quasi-one-dimensional disordered conductors

Nonperturbative, in inverse Thouless conductance 1/g, corrections to distributions of level velocities and level curvatures in quasi-one-dimensional disordered conductors with a topology of a ring subject to a constant vector potential are studied within the framework of the instanton approximation of nonlinear sigma-model. It is demonstrated that a global character of the perturbation reveals the universal features of the level dynamics. The universality shows up in the form of weak topological oscillations of the magnitude ~ exp(-g) covering the main bodies of the densities of level velocities and level curvatures. The period of discovered universal oscillations does not depend on microscopic parameters of conductor, and is only determined by the global symmetries of the Hamiltonian before and after the perturbation was applied. We predict the period of topological oscillations to be 4/(pi)^2 for the distribution function of level curvatures in orthogonal symmetry class, and 3^(1/2)/(pi) for the distribution of level velocities in unitary and symplectic symmetry classes.

cond-mat.mes-hall↗

arXiv1998

Level statistics inside the core of a superconductive vortex

Microscopic theory of the type of Efetov's supermatrix sigma-model is constructed for the low-lying electron states in a mixed superconductive-normal system with disorder. The developed technique is used for the study of the localized states in the core of a vortex in a moderately clean superconductor (1/Δ<< τ<< 1/ω_0 = E_F/Δ^2). At sufficiently low energies E << ω_{Th}, the energy level statistics is described by the "zero-dimensional" limit of this supermatrix theory, with the effective "Thouless energy" ω_{Th} \sim (ω_0/τ)^{1/2}. Within this energy range the result for the density of states is equivalent to that obtained within Altland-Zirnbauer random matrix model of class C. Nonzero modes of the sigma-model increase the mean interlevel distance ω_0 by the relative amount of the order of [2\ln(1/ω_0τ)]^{-1}.

cond-mat.mes-hall↗

arXiv1997

Level Curvature Distribution and the Structure of Eigenfunctions in Disordered Systems

The level curvature distribution function is studied both analytically and numerically for the case of T-breaking perturbations over the orthogonal ensemble. The leading correction to the shape of the curvature distribution beyond the random matrix theory is calculated using the nonlinear supersymmetric sigma-model and compared to numerical simulations on the Anderson model. It is predicted analytically and confirmed numerically that the sign of the correction is different for T-breaking perturbations caused by a constant vector-potential equivalent to a phase twist in the boundary conditions, and those caused by a random magnetic field. In the former case it is shown using a nonperturbative approach that quasi-localized states in weakly disordered systems can cause the curvature distribution to be nonanalytic. In $2d$ systems the distribution function $P(K)$ has a branching point at K=0 that is related to the multifractality of the wave functions and thus should be a generic feature of all critical eigenstates. A relationship between the branching power and the multifractality exponent $d_{2}$ is suggested. Evidence of the branch-cut singularity is found in numerical simulations in $2d$ systems and at the Anderson transition point in $3d$ systems.

cond-mat.mes-hall↗

arXiv1997

On a Connection Between Nonlinear Response to an External Field and Equilibrium Properties of Systems with Interaction: Comment on cond-mat/9711226 by Kopietz and Voelker

We demonstrate the danger of a naive identification of kinetic coefficients in the free-electron response expansion in powers of an external electric field and coefficients in the expansion of the corresponding equilibrium quantity in powers of the fluctuating intrinsic electric field. A particular example of the direct current generation by an AC electric field in a mesoscopic system of non-interacting electrons vs. the Fock contribution to the equilibrium persistent current in a system of interacting electrons is considered.

cond-mat↗

arXiv1997

New Class of Random Matrix Ensembles with Multifractal Eigenvectors

Three recently suggested random matrix ensembles (RME) are linked together by an exact mapping and plausible conjections. Since it is known that in one of these ensembles the eigenvector statistics is multifractal, we argue that all three ensembles belong to a new class of critical RME with multifractal eigenfunction statistics and a universal critical spectral statitics. The generic form of the two-level correlation function for weak and extremely strong multifractality is suggested. Applications to the spectral statistics at the Anderson transition and for certain systems on the border of chaos and integrability is discussed.

cond-mat↗