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.Comment: 8 pages, 2 figures. To be published in Phys. Rev. E. This detailed version includes discussion of quantum irreversibilit

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.Comment: 36-page lecture notes of the course in Varenna school, Session CXLIII "New Directions in Quantum Chaos", Italy (July 1999

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.Comment: ~4 pages, no figure

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 $\nu$. It is predicted that in some generic cases one may have a non-perturbative dependence ${\cal D}\propto\nu^{\alpha}$ with $0.35 < \alpha < 0.38$ 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 $\alpha$. 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.Comment: 4 pages, 1 figure. Written in 1991. Notes added 1999. New interest due to recent experiment

EPR, Bell, Schrodinger's cat, and the Monty Hall Paradox

The purpose of this manuscript is to provide a short pedagogical explanation why "quantum collapse" is not a metaphysical event, by pointing out the analogy with a "classical collapse" which is associated with the Monty Hall Paradox.Comment: 6 page

Stability and stabilization of unstable condensates

It is possible to condense a macroscopic number of bosons into a single mode. Adding interactions the question arises whether the condensate is stable. For repulsive interaction the answer is positive with regard to the ground-state, but what about a condensation in an excited mode? We discuss some results that have been obtained for a 2-mode bosonic Josephson junction, and for a 3-mode minimal-model of a superfluid circuit. Additionally we mention the possibility to stabilize an unstable condensate by introducing periodic or noisy driving into the system: this is due to the Kapitza and the Zeno effects.Comment: 7 pages, 6 figure

Temporal quantum fluctuations in the fringe-visibility of atom interferometers with interacting Bose-Einstein condensate

We formulate a semiclassical approach to study the dynamics of coherence loss and revival in a Bose-Josephson dimer. The phase-space structure of the bi-modal system in the Rabi, Josephson, and Fock interaction regimes, is reviewed and the prescription for its WKB quantization is specified. The local density of states (LDOS) is then deduced for any given preparation from its semiclassical projection onto the WKB eigenstates. The LDOS and the non-linear variation of its level-spacing are employed to construct the time evolution of the initial preparation and study the temporal fluctuations of interferometric fringe visibility. The qualitative behavior and characteristic timescales of these fluctuations are set by the pertinent participation number, quantifying the spectral content of the preparation. We employ this methodology to study the Josephson-regime coherence dynamics of several initial state preparations, including a Twin-Fock state and three different coherent states that we denote as 'Zero', 'Pi', and 'Edge' (the latter two are both on-separatrix preparations, while the Zero is the standard ground sate preparation). We find a remarkable agreement between the semiclassical predictions and numerical simulations of the full quantum dynamics. Consequently, a characteristic distinct behavior is implied for each of the different preparations.Comment: 11 pages, 8 figures; Progress in Optical science and Photonics, Vol. 1: Spontaneous Symmetry Breaking, Self-trapping, and Josephson Oscillations (Springer, New York, 2013), Ed. B. A. Malome

Quantum transport and counting statistics in closed systems

A current can be induced in a closed device by changing control parameters. The amount $Q$ of particles that are transported via a path of motion, is characterized by its expectation value $$, and by its variance $Var(Q)$. We show that quantum mechanics invalidates some common conceptions about this statistics. We first consider the process of a double path crossing, which is the prototype example for counting statistics in multiple path non-trivial geometry. We find out that contrary to the common expectation, this process does not lead to partition noise. Then we analyze a full stirring cycle that consists of a sequence of two Landau-Zener crossings. We find out that quite generally counting statistics and occupation statistics become unrelated, and that quantum interference affects them in different ways.Comment: 9 pages, 2 figures. Proceedings of FQMT conference (Prague, 2008

The relaxation rate of a stochastic spreading process in a closed ring

The relaxation process of a diffusive ring becomes under-damped if the bias (so called affinity) exceeds a critical threshold value, aka delocalization transition. This is related to the spectral properties of the pertinent stochastic kernel. We find the dependence of the relaxation rate on the affinity and on the length of the ring. Additionally we study the implications of introducing a weak-link into the circuit, and illuminate some subtleties that arise while taking the continuum limit of the discrete model.Comment: 10 pages, 6 figure, improved versio

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.Comment: 7 pages, 5 figures, long detailed versio