arXiv subjects

Tsampikos Kottos

Publications and source records attributed to Tsampikos Kottos.

At least 127 records · Page 7Linked to original sources

arXiv2005

The twilight zone in the parametric evolution of eigenstates: beyond perturbation theory and semiclassics

Considering a quantized chaotic system, we analyze the evolution of its eigenstates as a result of varying a control parameter. As the induced perturbation becomes larger, there is a crossover from a perturbative to a non-perturbative regime, which is reflected in the structural changes of the local density of states. For the first time the {\em full} scenario is explored for a physical system: an Aharonov-Bohm cylindrical billiard. As we vary the magnetic flux, we discover an intermediate twilight regime where perturbative and semiclassical features co-exist. This is in contrast with the {\em simple} crossover from a Lorentzian to a semicircle line-shape which is found in random-matrix models.

cond-mat.mes-hall↗

arXiv2005

Quantum decay of an open chaotic system: a semiclassical approach

We study the quantum probability to survive in an open chaotic system in the framework of the van Vleck-Gutzwiller propagator and present the first such calculation that accounts for quantum interference effects. Specifically we calculate quantum deviations from the classical decay after the break time for both broken and preserved time-reversal symmetry. The source of these corrections is identified in interfering pairs of correlated classical trajectories. In our approach the quantized chaotic system is modelled by a quatum graph.

nlin.CD↗

arXiv2005

Quantum pumping: The charge transported due to a translation of a scatterer

The amount of charge which is pushed by a moving scatterer is $dQ = -G dX$, where $dX$ is the displacement of the scatterer. The question is what is $G$. Does it depend on the transmission $g_0$ of the scatterer? Does the answer depend on whether the system is open (with leads attached to reservoirs) or closed? In the latter case: what are the implications of having ``quantum chaos" and/or coupling to to the environment? The answers to these questions illuminate some fundamental aspects of the theory of quantum pumping. For the analysis we take a network (graph) as a model system, and use the Kubo formula approach.

cond-mat.mes-hall↗

arXiv2004

Current relaxation in nonlinear random media

We study the current relaxation of a wave packet in a nonlinear random sample coupled to the continuum and show that the survival probability decays as $P(t) \sim 1/t^α$. For intermediate times $t χ_{\rm cr}$ we find a universal decay with $α=2/3$ which is a signature of the {\it nonlinearity-induced delocalization}. Experimental evidence should be observable in coupled nonlinear optical waveguides.

cond-mat.dis-nn↗

arXiv2004

Signatures of Classical Diffusion in Quantum Fluctuations of 2D Chaotic Systems

We consider a two-dimensional (2D) generalization of the standard kicked-rotor (KR) and show that it is an excellent model for the study of 2D quantum systems with underlying diffusive classical dynamics. First we analyze the distribution of wavefunction intensities and compare them with the predictions derived in the framework of diffusive {\it disordered} samples. Next, we turn the closed system into an open one by constructing a scattering matrix. The distribution of the resonance widths ${\cal P}(Γ)$ and Wigner delay times ${\cal P}(τ_W)$ are investigated. The forms of these distributions are obtained for different symmetry classes and the traces of classical diffusive dynamics are identified. Our theoretical arguments are supported by extensive numerical calculations.

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↗

arXiv2004

Quantum Dissipation due to the Interaction with Chaos

We discuss the possibility of having "quantum dissipation" due to the interaction with chaotic degrees of freedom. We define the conditions that should be satisfied in order to have a dissipative effect similar to the one due to an interaction with a (many body) bath. We also compare with the case where the environment is modeled by a random matrix model. In case of interaction with "chaos" we observe a regime where the relaxation process is non-universal, and reflects the underlaying semiclassical dynamics. As an example we consider a two level system (spin) that interacts with a two dimensional anharmonic oscillator.

cond-mat.mes-hall↗

arXiv2003

Quantum Reversibility: Is there an Echo?

We study the possibility to undo the quantum mechanical evolution in a time reversal experiment. The naive expectation, as reflected in the common terminology ("Loschmidt echo"), is that maximum compensation results if the reversed dynamics extends to the same time as the forward evolution. We challenge this belief, and demonstrate that the time $t_r$ for maximum return probability is in general shorter. We find that $t_r$ depends on $lambda = eps_evol/eps_prep$, being the ratio of the error in setting the parameters (fields) for the time reversed evolution to the perturbation which is involved in the preparation process. Our results should be observable in spin-echo experiments where the dynamical irreversibility of quantum phases is measured.

quant-ph↗

arXiv2003

Non-perturbative response: chaos versus disorder

Quantized chaotic systems are generically characterized by two energy scales: the mean level spacing $Δ$, and the bandwidth $Δ_b\propto\hbar$. This implies that with respect to driving such systems have an adiabatic, a perturbative, and a non-perturbative regimes. A "strong" quantal non-perturbative response effect is found for {\em disordered} systems that are described by random matrix theory models. Is there a similar effect for quantized {\em chaotic} systems? Theoretical arguments cannot exclude the existence of a "weak" non-perturbative response effect, but our numerics demonstrate an unexpected degree of semiclassical correspondence.

cond-mat.mes-hall↗

arXiv2003

Scars on quantum networks ignore the Lyapunov exponent

We show that enhanced wavefunction localization due to the presence of short unstable orbits and strong scarring can rely on completely different mechanisms. Specifically we find that in quantum networks the shortest and most stable orbits do not support visible scars, although they are responsible for enhanced localization in the majority of the eigenstates. Scarring orbits are selected by a criterion which does not involve the classical Lyapunov exponent. We obtain predictions for the energies of visible scars and the distributions of scarring strengths and inverse participation ratios.

nlin.CD↗

arXiv2003

Quantum Irreversibility of Energy Spreading

The analysis of dissipation and dephasing in driven mesoscopic devices requires a distinction between two notions of quantum irreversibility. One ("Loschmidt echo") is related to "time reversal", while the other is related to "driving reversal". In the latter context the time of maximum return (compensation) should substitute the inappropriate notion of "echo" time. Non-perturbative features manifest themselves in the energy spreading process. This is demonstrated for the prototype random-matrix Wigner model, where the compensation time and the system response exhibit a non-universal scaling behavior.

cond-mat.mes-hall↗

arXiv2003

Statistical properties of resonance widths for open Quantum Graphs

We connect quantum compact graphs with infinite leads, and turn them into scattering systems. We derive an exact expression for the scattering matrix, and explain how it is related to the spectrum of the corresponding closed graph. The resulting expressions allow us to get a clear understanding of the phenomenon of resonance trapping due to over-critical coupling with the leads. Finally, we analyze the statistical properties of the resonance widths and compare our results with the predictions of Random Matrix Theory. Deviations appearing due to the dynamical nature of the system are pointed out and explained.

nlin.CD↗

arXiv2002

Quantum Graphs: A simple model for Chaotic Scattering

We connect quantum graphs with infinite leads, and turn them to scattering systems. We show that they display all the features which characterize quantum scattering systems with an underlying classical chaotic dynamics: typical poles, delay time and conductance distributions, Ericson fluctuations, and when considered statistically, the ensemble of scattering matrices reproduce quite well the predictions of appropriately defined Random Matrix ensembles. The underlying classical dynamics can be defined, and it provides important parameters which are needed for the quantum theory. In particular, we derive exact expressions for the scattering matrix, and an exact trace formula for the density of resonances, in terms of classical orbits, analogous to the semiclassical theory of chaotic scattering. We use this in order to investigate the origin of the connection between Random Matrix Theory and the underlying classical chaotic dynamics. Being an exact theory, and due to its relative simplicity, it offers new insights into this problem which is at the fore-front of the research in chaotic scattering and related fields.

nlin.CD↗

arXiv2002

Statistics of resonances and delay times: A criterion for Metal-Insulator transitions

We study the distributions of the normalized resonance widths ${\cal P} ({\tilde Γ})$ and delay times ${\cal P} ({\tilde τ})$ for $3$D disordered tight-binding systems at the metal-insulator transition (MIT) by attaching leads to the boundary sites. Both distributions are scale invariant, independent of the microscopic details of the random potential, and the number of channels. Theoretical considerations suggest the existence of a scaling theory for ${\cal P} ({\tilde Γ})$ in finite samples, and numerical calculations confirm this hypothesis. Based on this, we give a new criterion for the determination and analysis of the MIT.

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

Chaotic Scattering of Microwaves

In this paper we analyze a recent experiment conducted in an anechoic chamber, where the scattering of microwaves from an array of metallic cylinders was measured. This is a system which displays chaotic scattering in the short wave limit. The analysis of the experimental data is aimed at elucidating the effects of the underlying chaos. We describe a robust numerical method which provides the scattering matrix for any number of non overlapping reflecting cylinders. We use this method to calculate the scattering from one, two and three cylinders, and to compare the results in the numerical simulations with those obtained in the experiment. Both simulations and measurements validate the presented theory.

cond-mat↗

arXiv2001

Taming chaos by impurities in two-dimensional oscillator arrays

The effect of impurities in a two-dimensional lattice of coupled nonlinear chaotic oscillators and their ability to control the dynamical behavior of the system are studied. We show that a single impurity can produce synchronized spatio-temporal patterns, even though all oscillators and the impurity are chaotic when uncoupled. When a small number of impurities is arranged in a way, that the lattice is divided into two disjoint parts, synchronization is enforced even for small coupling. The synchronization is not affected as the size of the lattice increases, although the impurity concentration tends to zero.

nlin.CD↗