arXiv subjects

Doron Cohen

Publications and source records attributed to Doron Cohen.

At least 145 records · Page 8Linked to original sources

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

Persistent currents in Moebius strips

Relation between the geometry of a two-dimensional sample and its equilibrium physical properties is exemplified here for a system of non-interacting electrons on a Moebius strip. Dispersion relation for a clean sample is derived and its persistent current under moderate disorder is elucidated, using statistical analysis pertinent to a single sample experiment. The flux periodicity is found to be distinct from that in a cylindrical sample, and the essential role of disorder in the ability to experimentally identify a Moebius strip is pointed out.

cond-mat.mes-hall↗

arXiv2002

Two-Step Enantio-selective Optical Switch

We present an optical "enantio-selective switch", that, in two steps, turns a ("racemic") mixture of left-handed and right-handed chiral molecules into the enantiomerically pure state of interest. The optical switch is composed of an "enantio-discriminator" and an "enantio-converter" acting in tandem. The method is robust, insensitive to decay processes, and does not require molecular preorientation. We demonstrate the method on the purification of a racemate of (transiently chiral) D$_2$S$_2$ molecules, performed on the nanosecond timescale.

quant-ph↗

arXiv2002

Quantum irreversibility, perturbation independent decay, and the parametric theory of the local density of states

The idea of perturbation independent decay (PID) has appeared in the context of survival-probability studies, and lately has emerged in the context of quantum irreversibility studies. In both cases the PID reflects the Lyapunov instability of the underlying semiclassical dynamics, and it can be distinguished from the Wigner-type decay that holds in the perturbative regime. The theory of the survival probability is manifestly related to the parametric theory of the local density of states (LDOS). In this Paper we demonstrate that in spite of the common "ideology", the physics of quantum irreversibility is {\em not} trivially related to the parametric theory of the LDOS. Rather, it is essential to take into account subtle cross correlations which are not captured by the LDOS alone.

quant-ph↗

arXiv2002

Stadium Billiard with Moving Walls

We study the evolution of the energy distribution for a stadium with moving walls. We consider one period driving cycle, which is characterized by an amplitude $A$ and wall velocity $V$. This evolving energy distribution has both "parametric" and "stochastic" components. The latter are important for the theory of quantum irreversibility and dissipation in driven mesoscopic devices (eg in the context of quantum computation). For extremely slow wall velocity $V$ the spreading mechanism is dominated by transitions between neighboring levels, while for larger (non-adiabatic) velocities the spreading mechanism has both perturbative and non-perturbative features. We present, for the first time, a numerical study which is aimed in identifying the latter features. A procedure is developed for the determination of the various $V$ regimes. The possible implications on linear response theory are discussed.

nlin.CD↗

arXiv2002

Quantum Chaos, Irreversibility, dissipation and dephasing

The main idea of "Quantum Chaos" studies is that Quantum Mechanics introduces two energy scales into the study of chaotic systems: One is obviously the mean level spacing $Δ\propto\hbar^d$, where $d$ is the dimensionality; The other is $Δ_b\propto\hbar$, which is known as the non-universal energy scale, or as the bandwidth, or as the Thouless energy. Associated with these two energy scales are two special quantum-mechanical (QM) regimes in the theory of driven system. These are the QM adiabatic regime, and the QM non-perturbative regime respectively. Otherwise Fermi golden rule applies, and linear response theory can be trusted. Demonstrations of this general idea, that had been published in 1999, have appeared in studies of wavepacket dynamics, survival probability, dissipation, quantum irreversibility, fidelity and dephasing.

quant-ph↗

arXiv2001

Dephasing due to the interaction with chaotic degrees of freedom

We consider the motion of a particle, taking into account its interaction with environmental degrees of freedom. The dephasing time is determined by the nature of the environment, and depends on the particle velocity. Our interest is in the case where the environment consists of few chaotic degrees of freedom. We obtain results for the dephasing time, and compare them with those of the effective-bath approach. The latter approach is based on the conjecture that the environment can be modelled as a collection of infinitely many harmonic oscillators. The work is related to studies of driven systems, quantum irreversibility, and fidelity. The specific model that we consider requires the solution of the problem of a particle-in-a-box with moving wall, whose 1D version is related to the Fermi acceleration problem.

cond-mat.mes-hall↗

arXiv2001

Failure of random matrix theory to correctly describe quantum dynamics

Consider a classically chaotic system which is described by a Hamiltonian H_0. At t=0 the Hamiltonian undergoes a sudden-change H_0 -> H. We consider the quantum-mechanical spreading of the evolving energy distribution, and argue that it cannot be analyzed using a random-matrix theory (RMT) approach. RMT can be trusted only to the extend that it gives trivial results that are implied by first-order perturbation theory. Non-perturbative effects are sensitive to the underlying classical dynamics, and therefore the hbar-->0 behavior for effective RMT models is strikingly different from the correct semiclassical limit.

cond-mat↗

arXiv2001

Parametric Evolution for a Deformed Cavity

We consider a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where (Q,P) describes a particle moving inside a cavity, and x controls a deformation of the boundary. The quantum-eigenstates of the system are |n(x)>. We describe how the parametric kernel P(n|m) = , also known as the local density of states, evolves as a function of x-x0. We illuminate the non-unitary nature of this parametric evolution, the emergence of non-perturbative features, the final non-universal saturation, and the limitations of random-wave considerations. The parametric evolution is demonstrated numerically for two distinct representative deformation processes.

nlin.CD↗

arXiv2000

Rate of energy absorption for a driven chaotic cavity

We consider the response of a chaotic cavity in d dimensions to periodic driving. We are motivated by older studies of one-body dissipation in nuclei, and also by anticipated mesoscopic applications. For calculating the rate of energy absorption due to time-dependent deformation of the confining potential, we introduce an improved version of the wall formula. Our formulation takes into account that a special class of deformations causes no heating in the zero-frequency limit. We also derive a mesoscopic version of the Drude formula, and explain that it can be regarded as a special example of our calculations. Specifically we consider a quantum dot driven by electro-motive force which is induced by a time-dependent homogeneous magnetic field.

nlin.CD↗

arXiv2000

Overview: Brownian Motion and Dephasing due to Dynamical Disorder

The motion of a particle under the influence of a dynamical disorder is described by the DLD model. One motivation is to understand the motion of an electron inside a metal; Another is to understand quantal Brownian motion. The overview is based on a research report for 1996-1998.

cond-mat.mes-hall↗

arXiv2000

Overview: Energy Absorption by Driven Mesoscopic Systems

There are three regimes in the theory of energy absorption: The adiabatic regime, the linear-response (Kubo) regime, and the non-perturbative regime. The mesoscopic Drude formula for electrical conductance, and the wall formula for friction, can be regarded as special cases of the general formulation of the dissipation problem. The overview is based on a research report for 1998-2000.

cond-mat.mes-hall↗

arXiv2000

Parametric dependent Hamiltonians, wavefunctions, random-matrix-theory, and quantal-classical correspondence

We study a classically chaotic system which is described by a Hamiltonian $H(Q,P;x)$ where $(Q,P)$ are the canonical coordinates of a particle in a 2D well, and $x$ is a parameter. By changing $x$ we can deform the `shape' of the well. The quantum-eigenstates of the system are $|n(x)>$. We analyze numerically how the parametric kernel $P(n|m)= | |^2$ evolves as a function of $x-x0$. This kernel, regarded as a function of $n-m$, characterizes the shape of the wavefunctions, and it also can be interpreted as the local density of states (LDOS). The kernel $P(n|m)$ has a well defined classical limit, and the study addresses the issue of quantum-classical correspondence (QCC). We distinguish between restricted QCC and detailed QCC. Both the perturbative and the non-perturbative regimes are explored. The limitations of the random-matrix-theory (RMT) approach are demonstrated.

nlin.CD↗

arXiv2000

Quantum-Mechanical Non-Perturbative Response of Driven Chaotic Mesoscopic Systems

Consider a time-dependent Hamiltonian $H(Q,P;x(t))$ with periodic driving $x(t)=A\sin(Ωt)$. It is assumed that the classical dynamics is chaotic, and that its power-spectrum extends over some frequency range $|ω|<ω_{cl}$. Both classical and quantum-mechanical (QM) linear response theory (LRT) predict a relatively large response for $Ω<ω_{cl}$, and a relatively small response otherwise, independently of the driving amplitude $A$. We define a non-perturbative regime in the $(Ω,A)$ space, where LRT fails, and demonstrate this failure numerically. For $A>A_{prt}$, where $A_{prt}\propto\hbar$, the system may have a relatively strong response for $Ω>ω_{cl}$, and the shape of the response function becomes $A$ dependent.

cond-mat↗

arXiv2000

Chaos, Dissipation and Quantal Brownian Motion

Energy absorption by driven chaotic systems, the theory of energy spreading and quantal Brownian motion are considered. In particular we discuss the theory of a classical particle that interacts with quantal chaotic degrees of freedom, and try to relate it to the problem of quantal particle that interacts with an effective harmonic bath.

chao-dyn↗

arXiv2000

Deformations and dilations of chaotic billiards, dissipation rate, and quasi-orthogonality of the boundary wavefunctions

We consider chaotic billiards in d dimensions, and study the matrix elements M_{nm} corresponding to general deformations of the boundary. We analyze the dependence of |M_{nm}|^2 on ω= (E_n-E_m)/\hbar using semiclassical considerations. This relates to an estimate of the energy dissipation rate when the deformation is periodic at frequency ω. We show that for dilations and translations of the boundary, |M_{nm}|^2 vanishes like ω^4 as ω-> 0, for rotations like ω^2, whereas for generic deformations it goes to a constant. Such special cases lead to quasi-orthogonality of the eigenstates on the boundary.

nlin.CD↗

arXiv2000

Chaos and energy spreading for time-Dependent Hamiltonians, and the various Regimes in the theory of Quantum Dissipation

We make the first steps towards a generic theory for energy spreading and quantum dissipation. The Wall formula for the calculation of friction in nuclear physics and the Drude formula for the calculation of conductivity in mesoscopic physics can be regarded as two special results of the general formulation. We assume a time-dependent Hamiltonian $H(Q,P;x(t))$ with $x(t)=Vt$, where $V$ is slow in a classical sense. The rate-of-change $V$ is not necessarily slow in the quantum-mechanical sense. Dissipation means an irreversible systematic growth of the (average) energy. It is associated with the stochastic spreading of energy across levels. The latter can be characterized by a transition probability kernel $P_t(n|m)$ where $n$ and $m$ are level indices. This kernel is the main object of the present study. In the classical limit, due to the (assumed) chaotic nature of the dynamics, the second moment of $P_t(n|m)$ exhibits a crossover from ballistic to diffusive behavior. We define the $V$ regimes where either perturbation theory or semiclassical considerations are applicable in order to establish this crossover in the quantal case. In the limit $\hbar\to 0$ perturbation theory does not apply but semiclassical considerations can be used in order to argue that there is detailed correspondence, during the crossover time. In the perturbative regime there is a lack of such correspondence. Namely, $P_t(n|m)$ is characterized by a perturbative core-tail structure that persists during the crossover time. In spite of this lack of (detailed) correspondence there may be still a restricted correspondence as far as the second-moment is concerned. Such restricted correspondence is essential in order to establish the universal fluctuation-dissipation relation.

cond-mat↗

arXiv2000

Unification of perturbation theory, RMT and semiclassical considerations in the study of parametrically-dependent eigenstates

We consider a classically chaotic system that is described by an Hamiltonian $H(Q,P;x)$ where x is a constant parameter. Our main interest is in the case of a gas-particle inside a cavity, where $x$ controls a deformation of the boundary or the position of a `piston'. The quantum-eigenstates of the system are $|n(x)>$. We describe how the parametric kernel $P(n|m)=| |^2$ evolves as a function of $δx = (x-x_0)$. We explore both the perturbative and the non-perturbative regimes, and discuss the capabilities and the limitations of semiclassical as well as of random-waves and random-matrix-theory (RMT) considerations.

chao-dyn↗