Biomedical subjects

Tomaz Prosen

Publications and source records attributed to Tomaz Prosen.

11 recordsLinked to original sources

PubMed2006

Nonequilibrium properties of the one-dimensional hard-point gas system.

We discuss the stability properties of a one-dimensional hard-point gas. We study the decay of the Loschmidt echo which describes the stability of the motion under system perturbations. We show a universal behavior in the echo decay which is intimately connected to the linear dynamical instability of the motion. In particular, in spite of such a weak instability, the asymptotic decay follows a simple exponential law.

Journal Article↗

PubMed2006

Verification of generic fidelity recovery in a dynamical system.

We study the time evolution of fidelity in a dynamical many-body system, namely, a kicked Ising model, modified to allow for a time-reversal invariance breaking. We find good agreement with the random matrix predictions in the realm of strong perturbations. In particular for the time-reversal symmetry breaking case the predicted revival at the Heisenberg time is clearly seen.

Journal Article↗

PubMed2005

Classical Loschmidt echo in chaotic many-body systems.

General theoretic approach to classical Loschmidt echoes in chaotic systems with many degrees of freedom is developed. For perturbations that affect essentially all degrees of freedom we find a doubly exponential decay with the rate determined by the largest Lyapunov exponent. The scaling of the decay rate on the perturbation strength depends on the continuity properties of the initial phase-space density.

Journal Article↗

PubMed2005

Universal decay of the classical Loschmidt echo of neutrally stable mixing dynamics.

We provide analytical and numerical evidence that the classical mixing systems, which lack exponential sensitivity on initial conditions, exhibit universal decay of the Loschmidt echo which turns out to be a function of a single scaled time variable delta(2/5)t, where delta is the strength of perturbation. The role of dynamical instability and entropy production is discussed.

Journal Article↗

PubMed2005

Quantum freeze of fidelity decay for chaotic dynamics.

We show that the mechanism of quantum freeze of fidelity decay for perturbations with a zero time average, recently discovered for a specific case of integrable dynamics [New J. Phys. 5, 109 (2003)], can be generalized to arbitrary quantum dynamics. We work out explicitly the case of a chaotic classical counterpart, for which we find semiclassical expressions for the value and the range of the plateau of fidelity. After the plateau ends, we find explicit expressions for the asymptotic decay, which can be exponential or Gaussian depending on the ratio of the Heisenberg time to the decay time. Arbitrary initial states can be considered; e.g., we discuss coherent states and random states.

Journal Article↗

PubMed2005

Normal and anomalous heat transport in one-dimensional classical lattices.

We present analytic and numerical results on several models of one-dimensional (1D) classical lattices with the goal of determining the origins of anomalous heat transport and the conditions for normal transport in these systems. Some of the recent results in the literature are reviewed and several original "toy" models are added that provide key elements to determine which dynamical properties are necessary and which are sufficient for certain types of heat transport. We demonstrate with numerical examples that chaos in the sense of positivity of Lyapunov exponents is neither necessary nor sufficient to guarantee normal transport in 1D lattices. Quite surprisingly, we find that in the absence of momentum conservation, even ergodicity of an isolated system is not necessary for the normal transport. Specifically, we demonstrate clearly the validity of the Fourier law in a pseudo-integrable particle chain.

Hot Temperature↗

PubMed2004

Fourier law in the alternate-mass hard-core potential chain.

We study energy transport in a one-dimensional model of elastically colliding particles with alternate masses m and M. In order to prevent total momentum conservation, we confine particles with mass M inside a cell of finite size. We provide convincing numerical evidence for the validity of Fourier law of heat conduction in spite of the lack of exponential dynamical instability. Comparison with previous results on similar models shows the relevance of the role played by total momentum conservation.

Journal Article↗

PubMed2004

Faster than Lyapunov decays of the classical Loschmidt echo.

We show that in the classical interaction picture the echo dynamics, namely, the composition of perturbed forward and unperturbed backward Hamiltonian evolution, can be treated as a time-dependent Hamiltonian system. For strongly chaotic (Anosov) systems we derive a cascade of exponential decays for the classical Loschmidt echo, starting with the leading Lyapunov exponent, followed by a sum of the two largest exponents, etc. In the loxodromic case a decay starts with the rate given as twice the largest Lyapunov exponent. For a class of perturbations of symplectic maps the echo dynamics exhibits a drift resulting in a superexponential decay of the Loschmidt echo.

Journal Article↗

PubMed2003

Anomalous heat conduction in a one-dimensional ideal gas.

We provide firm convincing evidence that the energy transport in a one-dimensional gas of elastically colliding free particles of unequal masses is anomalous, i.e., the Fourier law does not hold. Our conclusions are confirmed by a theoretical and numerical analysis based on a Green-Kubo-type approach specialized to momentum-conserving lattices.

Journal Article↗

PubMed2002

planck-->0 and classical-quantum correspondence in the kicked Harper model.

We investigate classical-quantum correspondence for the kicked Harper model for extremely small values of the Planck constant (planck). In the asymmetric case a pure quantum state shows a clear signature of classical diffusive as well as superdiffusive transitions asymptotically independent of planck. However, for the symmetric case, the planck independent behavior occurs only for the renormalized parameter (-)K=K/(2planck) with intriguing features such as a sharp transition from integrable to nonintegrable transport at (-)K=pi/2, a series of transitions at multiples of pi, and the periodicity of the transmission probability. We suggest that even as planck-->0, the quantum dynamics is influenced by cantori and additional features emerge in their absence.

Journal Article↗

PubMed2002

General relation between quantum ergodicity and fidelity of quantum dynamics.

A general relation is derived, which expresses the fidelity of quantum dynamics, measuring the stability of time evolution to small static variation in the Hamiltonian, in terms of ergodicity of an observable generating the perturbation as defined by its time correlation function. Fidelity for ergodic dynamics is predicted to decay exponentially on time scale proportional to delta(-2), delta approximately strength of perturbation, whereas faster, typically Gaussian decay on shorter time scale proportional delta(-1) is predicted for integrable, or generally nonergodic dynamics. This result needs the perturbation delta to be sufficiently small such that the fidelity decay time scale is larger than any (quantum) relaxation time, e.g., mixing time for mixing dynamics, or averaging time for nonergodic dynamics (or Ehrenfest time for wave packets in systems with chaotic classical limit). Our surprising predictions are demonstrated in a quantum Ising spin-(1/2) chain periodically kicked with a tilted magnetic field where we find finite parameter-space regions of nonergodic and nonintegrable motion in the thermodynamic limit.

Journal Article↗