arXiv subjects

A. V. Andreev

Publications and source records attributed to A. V. Andreev.

97 records · Page 6Linked to original sources

arXiv1998

Adiabatic charge pumping in almost open dots

We consider adiabatic charge transport through an almost open quantum dot. We show that the charge transmitted in one cycle is quantized in the limit of vanishing temperature and one-electron mean level spacing in the dot. The explicit analytic expression for the pumped charge at finite temperature is obtained for spinless electrons. The pumped charge is produced by both non-dissipative and dissipative currents. The latter are responsible for the corrections to charge quantization which are expressed through the conductance of the system.

cond-mat.mes-hall↗

arXiv1996

Semiclassical Field Theory Approach to Quantum Chaos

We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the form of a functional supermatrix nonlinear $σ$-model where the effective action involves the evolution operator of the classical dynamics. Low-lying degrees of freedom of the field theory are shown to reflect the irreversible classical dynamics describing relaxation of phase space distributions. The validity of this approach is investigated over a wide range of energy scales. As well as recovering the universal long-time behavior characteristic of random matrix ensembles, this approach accounts correctly for the short-time limit yielding results which agree with the diagonal approximation of periodic orbit theory.

cond-mat↗

arXiv1996

Relations Between Quantum and Classical Spectral Determinants (Zeta-Functions)

We demonstrate that beyond the universal regime correlators of quantum spectral determinants $Δ(ε)=\det (ε-\hat{H})$ of chaotic systems, defined through an averaging over a wide energy interval, are determined by the underlying classical dynamics through the spectral determinant $1/Z(z)=\det (z- {\cal L})$, where $e^{-{\cal L}t}$ is the Perron-Frobenius operator. Application of these results to the Riemann zeta function, allows us to conjecture new relations satisfied by this function.

cond-mat↗

arXiv1996

Quantum Chaos, Irreversible Classical Dynamics and Random Matrix Theory

The Bohigas--Giannoni--Schmit conjecture stating that the statistical spectral properties of systems which are chaotic in their classical limit coincide with random matrix theory is proved. For this purpose a new semiclassical field theory for individual chaotic systems is constructed in the framework of the non--linear $σ$-model. The low lying modes are shown to be associated with the Perron--Frobenius spectrum of the underlying irreversible classical dynamics. It is shown that the existence of a gap in the Perron-Frobenius spectrum results in a RMT behavior. Moreover, our formalism offers a way of calculating system specific corrections beyond RMT.

cond-mat↗

arXiv1995

Sensitivity of quantum chaotic wavefunction intensities to changes in external perturbations

We examine the sensitivity of wavefunction intensities in chaotic quantum systems to small changes in an arbitrary external perturbation. A universal scaling is proposed for all three Dyson ensembles and a novel theoretical approach is used to determine exact expressions for systems which violate T-invariance. Analytical results are compared with numerical simulations of tight-binding Anderson Hamiltonians.

cond-mat↗

arXiv1995

Statistics of Oscillator Strengths in Chaotic Systems

The statistical description of oscillator strengths for systems like hydrogen in a magnetic field is developed by using the supermatrix nonlinear $σ$-model. The correlator of oscillator strengths is found to have a universal parametric and frequency dependence, and its analytical expression is given. This universal expression applies to quantum chaotic systems with the same generality as Wigner-Dyson statistics.

cond-mat↗

arXiv1995

Spectral Statistics Beyond Random Matrix Theory

Using a nonperturbative approach we examine the large frequency asymptotics of the two-point level density correlator in weakly disordered metallic grains. This allows us to study the behavior of the two-level structure factor close to the Heisenberg time. We find that the singularities (present for random matrix ensembles) are washed out in a grain with a finite conductance. The results are nonuniversal (they depend on the shape of the grain and on its conductance), though they suggest a generalization for any system with finite Heisenberg time.

cond-mat↗