arXiv subjects

Doron Cohen

Publications and source records attributed to Doron Cohen.

153 records · Page 9Linked to original sources

arXiv2000

Wavepacket dynamics in energy space, RMT and quantum-classical correspondence

We apply random-matrix-theory (RMT) to the analysis of evolution of wavepackets in energy space. We study the crossover from ballistic behavior to saturation, the possibility of having an intermediate diffusive behavior, and the feasibility of strong localization effect. Both theoretical considerations and numerical results are presented. Using quantal-classical correspondence (QCC) considerations we question the validity of the emerging dynamical picture. In particular we claim that the appearance of the intermediate diffusive behavior is possibly an artifact of the RMT strategy.

chao-dyn↗

arXiv1999

Non Perturbative Destruction of Localization in the Quantum Kicked Particle Problem

The angle coordinate of the Quantum Kicked Rotator problem is treated as if it were an extended coordinate. A new mechanism for destruction of coherence by noise is analyzed using both heuristic and formal approach. Its effectiveness constitutes a manifestation of long-range non-trivial dynamical correlations. Perturbation theory fails to quantify certain aspects of this effect. In the perturbative case, for sufficiently weak noise, the diffusion coefficient ${\cal D}$ is just proportional to the noise intensity $ν$. It is predicted that in some generic cases one may have a non-perturbative dependence ${\cal D}\proptoν^α$ with $0.35 < α< 0.38$ for arbitrarily weak noise. This work has been found relevant to the recently studied ionization of H-atoms by a microwave electric field in the presence of noise. Note added (a): Borgonovi and Shepelyansky have adopted this idea of non-perturbative transport, and have demonstrated that the same effect manifests itself in the tight-binding Anderson model with the same exponent $α$. Note added (b): The recent interest in the work reported here comes from the experimental work by the Austin group and by the Auckland group. In these experiment the QKP model is realized literally. However, the novel effect of non-perturbative transport, reported in this Letter, has not been tested yet.

chao-dyn↗

arXiv1999

Quantum dissipation due to the interaction with chaotic degrees-of-freedom and the correspondence principle

Both in atomic physics and in mesoscopic physics it is sometimes interesting to consider the energy time-dependence of a parametrically-driven chaotic system. We assume an Hamiltonian ${\cal H}(Q,P;x(t))$ where $x(t)=Vt$. The velocity $V$ is slow in the classical sense but not necessarily in the quantum-mechanical sense. The crossover (in time) from ballistic to diffusive energy-spreading is studied. The associated irreversible growth of the average energy has the meaning of dissipation. It is found that a dimensionless velocity $v_{PR}$ determines the nature of the dynamics, and controls the route towards quantal-classical correspondence (QCC). A perturbative regime and a non-perturbative semiclassical regime are distinguished.

cond-mat↗

arXiv1998

Dephasing at Low Temperatures

We discuss the significance and the calculation of dephasing at low temperatures. The particle is moving diffusively due to a static disorder configuration, while the interference between classical paths is suppressed due to the interaction with a dynamical environment. At high temperatures we may use the `white noise approximation' (WNA), while at low temperatures we distinguish the contribution of `zero point fluctuations' (ZPF) from the `thermal noise contribution' (TNC). We study the limitations of the above semiclassical approach and suggest the required modifications. In particular we find that the ZPF contribution becomes irrelevant for thermal motion.

cond-mat↗

arXiv1998

Quantal Brownian Motion - Dephasing and Dissipation

We analyze quantal Brownian motion in $d$ dimensions using the unified model for diffusion localization and dissipation, and Feynman-Vernon formalism. At high temperatures the propagator possess a Markovian property and we can write down an equivalent Master equation. Unlike the case of the Zwanzig-Caldeira-Leggett model, genuine quantum mechanical effects manifest themselves due to the disordered nature of the environment. Using Wigner picture of the dynamics we distinguish between two different mechanisms for destruction of coherence. The analysis of dephasing is extended to the low temperature regime by using a semiclassical strategy. Various results are derived for ballistic, chaotic, diffusive, both ergodic and non-ergodic motion. We also analyze loss of coherence at the limit of zero temperature and clarify the limitations of the semiclassical approach. The condition for having coherent effect due to scattering by low-frequency fluctuations is also pointed out. It is interesting that the dephasing rate can be either larger or smaller than the dissipation rate, depending on the physical circumstances.

cond-mat↗

arXiv1998

Unified Model for The Study of Diffusion Localization and Dissipation

A new model that generalizes the study of quantum Brownian motion (BM) is constructed. We consider disordered environment that may be either static (quenched), noisy or dynamical. The Zwanzig-Caldeira-Leggett BM-model constitutes formally a special case where the disorder auto-correlation length is taken to be infinite. Alternatively, localization problem is obtained if the noise auto-correlation time is taken to be infinite. Also the general case of weak nonlinear coupling to thermal, possibly chaotic bath is handled by the same formalism. A general, Feynman-Vernon type path-integral expression for the propagator is introduced. Wigner transformed version of this expression is utilized in order to facilitate comparison with the classical limit. It is demonstrated that non-stochastic genuine quantal manifestations are associated with the new model. It is clarified that such effects are absent in the standard BM model, either the disorder or the chaotic nature of the bath are essential. Quantal correction to the classical diffusive behavior is found even in the limit of high temperatures. The suppression of interference due to dephasing is discussed, leading to the observation that due to the disorder the decay of coherence is exponential in time, and no longer depends on geometrical considerations. Fascinating non-Markovian effects due to time-correlated (colored) noise are explored. For this, a new strategy is developed in order to handle the integration over paths. This strategy is extended in order to demonstrate how localization comes out from the path integral expression.

chao-dyn↗

arXiv1997

Periodic Orbits, Breaktime and Localization

The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in the field of `Quantum Chaos'. Starting from the semiclassical trace formula, we formulate a quantal-classical duality relation that connects the spectral properties of the quantal spectrum to the statistical properties of lengths of periodic orbits. By identifying the classical correlation scale it is possible to extend the semiclassical theory of spectral statistics, in case of a complex systems, beyond the limitations that are implied by the diagonal approximation. We discuss the quantal dynamics of a particle in a disordered system. The various regimes are defined in terms of time-disorder `phase diagram'. As expected, the breaktime may be `disorder limited' rather than `volume limited', leading to localization if it is shorter than the ergodic time. Qualitative agreement with scaling theory of localization in one to three dimensions is demonstrated.

chao-dyn↗

arXiv1997

Quantal-Classical Duality and the Semiclassical Trace Formula

We consider Hamiltonian systems which can be described both classically and quantum mechanically. Trace formulas establish links between the energy spectra of the quantum description and the spectrum of actions of periodic orbits in the classical description. This duality is investigated in the present paper. The duality holds for chaotic as well as for integrable systems. For billiards the quantal spectrum (eigenvalues of the Helmholtz equation) and the classical spectrum (lengths of periodic orbits) are two manifestations of the billiard's boundary. The trace formula expresses this link as a Fourier transform relation between the corresponding spectral densities. It follows that the two-point statistics are also simply related. The universal correlations of the quantal spectrum are well known, consequently one can deduce the classical universal correlations. An explicit expression for the scale of the classical correlations is derived and interpreted. This allows a further extension of the formalism to the case of complex billiard systems, and in particular to the most interesting case of diffusive system. The concept of classical correlations allows a better understanding of the so-called diagonal approximation and its breakdown. It also paves the way towards a semiclassical theory that is capable of global description of spectral statistics beyond the breaktime. An illustrative application is the derivation of the disorder-limited breaktime in case of a disordered chain, thus obtaining a semiclassical theory for localization. A numerical study of classical correlations in the case of the 3D Sinai billiard is presented. We gain a direct understanding of specific statistical properties of the classical spectrum, as well as their semiclassical manifestation in the quantal spectrum.

chao-dyn↗

arXiv1997

Quantum Dissipation versus Classical Dissipation for Generalized Brownian Motion

We try to clarify what are the genuine quantal effects that are associated with generalized Brownian Motion (BM). All the quantal effects that are associated with the Zwanzig-Feynman-Vernon-Caldeira-Leggett model are (formally) a solution of the classical Langevin equation. Non-stochastic, genuine quantum mechanical effects, are found for a model that takes into account either the disordered or the chaotic nature of some environment.

chao-dyn↗