arXiv subjects

A. Ossipov

Publications and source records attributed to A. Ossipov.

27 records · Page 2Linked to original sources

arXiv2005

Statistics of delay times in mesoscopic systems as a manifestation of eigenfunction fluctuations

We reveal a general explicit relation between the statistics of delay times in one-channel reflection from a mesoscopic sample of any spatial dimension and the statistics of the eigenfunction intensities in its closed counterpart. This opens a possibility to use experimentally measurable delay times as a sensitive probe of eigenfunction fluctuations. For the particular case of quasi-one dimensional geometry of the sample we use an alternative technique to derive the probability density of partial delay times for any number of open channels.

cond-mat.mes-hall↗

arXiv2005

Localization-delocalization transition in the quasi-one-dimensional ladder chain with correlated disorder

The generalization of the dimer model on a two-leg ladder is defined and investigated both, analytically and numerically. For the closed system we calculate the Landauer resistance analytically and found the presence of the point of delocalization at the band center which is confirmed by the numerical calculations of the Lyapunov exponent. We calculate also analytically the localization length index and present the numerical investigations of the density of states (DOS). For the open counterpart of this model the distribution of the Wigner delay times is calculated numerically. It is shown how the localization-delocalization transition manifest itself in the behavior of the distribution.

cond-mat.dis-nn↗

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

Superconductor-proximity effect in hybrid structures: Fractality versus Chaos

We study the proximity effect of a superconductor to a normal system with fractal spectrum. We find that there is no gap in the excitation spectrum, even in the case where the underlying classical dynamics of the normal system is chaotic. An analytical expression for the distribution of the smallest excitation eigenvalue $E_g$ of the hybrid structure is obtained.On small scales it decays algebraically as ${\cal P}(E_g)\sim E_g ^{-D_0}$, where $D_0$ is the fractal dimension of the spectrum of the normal system. Our theoretical predictions are verified by numerical calculations performed for various models.

cond-mat.mes-hall↗

arXiv2004

Fingerprints of classical diffusion in open 2D mesoscopic systems in the metallic regime

We investigate the distribution of the resonance widths ${\cal P}(Γ)$ and Wigner delay times ${\cal P}(τ_W)$ for scattering from two-dimensional systems in the diffusive regime. We obtain the forms of these distributions (log-normal for large $τ_W$ and small $Γ$, and power law in the opposite case) for different symmetry classes and show that they are determined by the underlying diffusive classical dynamics. Our theoretical arguments are supported by extensive numerical calculations.

cond-mat.mes-hall↗

arXiv2002

Signatures of Prelocalized States in Classically Chaotic Systems

We investigate the statistics of eigenfunction intensities ${\cal P}(|ψ|^2)$ in dynamical systems with classical chaotic diffusion. Our results contradict some recent theoretical considerations which challenge the applicability of field theoretical predictions, derived in a different framework for diffusive disordered samples. For two-dimensional systems, the tails of ${\cal P}(|ψ|^2)$ contradict the results of the optimal fluctuation method, but agree very well with the predictions of the non-linear $σ-$model.

cond-mat.mes-hall↗

arXiv2001

Quantum mechanical relaxation of open quasiperiodic systems

We study the time evolution of the survival probability $P(t)$ in open one-dimensional quasiperiodic tight-binding samples of size $L$, at critical conditions. We show that it decays algebraically as $P(t)\sim t^{-α}$ up to times $t^*\sim L^γ$, where $α= 1-D_0^E$, $γ=1/D_0^E$ and $D_0^E$ is the fractal dimension of the spectrum of the closed system. We verified these results for the Harper model at the metal-insulator transition and for Fibonacci lattices. Our predictions should be observable in propagation experiments with electrons or classical waves in quasiperiodic superlattices or dielectric multilayers.

cond-mat.mes-hall↗

arXiv2000

Statistics of resonances and of delay times in quasiperiodic Schr"odinger equations

We study the statistical distributions of the resonance widths ${\cal P} (Γ)$, and of delay times ${\cal P} (τ)$ in one dimensional quasi-periodic tight-binding systems with one open channel. Both quantities are found to decay algebraically as $Γ^{-α}$, and $τ^{-γ}$ on small and large scales respectively. The exponents $α$, and $γ$ are related to the fractal dimension $D_0^E$ of the spectrum of the closed system as $α=1+D_0^E$ and $γ=2-D_0^E$. Our results are verified for the Harper model at the metal-insulator transition and for Fibonacci lattices.

cond-mat.mes-hall↗

arXiv1999

Statistical properties of phases and delay times of the one-dimensional Anderson model with one open channel

We study the distribution of phases and of Wigner delay times for a one-dimensional Anderson model with one open channel. Our approach, based on classical Hamiltonian maps, allows us an analytical treatment. We find that the distribution of phases depends drastically on the parameter $σ_A = σ/sin k$ where $σ^2$ is the variance of the disorder distribution and $k$ the wavevector. It undergoes a transition from uniformity to singular behaviour as $σ_A$ increases. The distribution of delay times shows universal power law tails $~ 1/τ^2$, while the short time behaviour is $σ_A$- dependent.

cond-mat.dis-nn↗