Fourier's Law in a Quantum Spin Chain and the Onset of Quantum Chaos

We study heat transport in a nonequilibrium steady state of a quantum interacting spin chain. We provide clear numerical evidence of the validity of Fourier law. The regime of normal conductivity is shown to set in at the transition to quantum chaos.Comment: 4 pages, 5 figures, RevTe

On general relation between quantum ergodicity and fidelity of quantum dynamics

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) where delta is the strength of perturbation, whereas faster, typically gaussian decay on shorter time scale proportional to delta^(-1) is predicted for integrable, or generally non-ergodic dynamics. This surprising result is demonstrated in quantum Ising spin-1/2 chain periodically kicked with a tilted magnetic field where we find finite parameter-space regions of non-ergodic and non-integrable motion in thermodynamic limit.Comment: Slightly revised version, 4.5 RevTeX pages, 2 figure

High order non-unitary split-step decomposition of unitary operators

We propose a high order numerical decomposition of exponentials of hermitean operators in terms of a product of exponentials of simple terms, following an idea which has been pioneered by M. Suzuki, however implementing it for complex coefficients. We outline a convenient fourth order formula which can be written compactly for arbitrary number of noncommuting terms in the Hamiltonian and which is superiour to the optimal formula with real coefficients, both in complexity and accuracy. We show asymptotic stability of our method for sufficiently small time step and demonstrate its efficiency and accuracy in different numerical models.Comment: 10 pages, 4 figures (5 eps files) Submitted to J. of Phys. A: Math. Ge

Exact solution for a diffusive nonequilibrium steady state of an open quantum chain

We calculate a nonequilibrium steady state of a quantum XX chain in the presence of dephasing and driving due to baths at chain ends. The obtained state is exact in the limit of weak driving while the expressions for one- and two-point correlations are exact for an arbitrary driving strength. In the steady state the magnetization profile and the spin current display diffusive behavior. Spin-spin correlation function on the other hand has long-range correlations which though decay to zero in either the thermodynamical limit or for equilibrium driving. At zero dephasing a nonequilibrium phase transition occurs from a ballistic transport having short-range correlations to a diffusive transport with long-range correlations.Comment: 5 page

Berry-Robnik level statistics in a smooth billiard system

Berry-Robnik level spacing distribution is demonstrated clearly in a generic quantized plane billiard for the first time. However, this ultimate semi-classical distribution is found to be valid only for extremely small semi-classical parameter (effective Planck's constant) where the assumption of statistical independence of regular and irregular levels is achieved. For sufficiently larger semiclassical parameter we find (fractional power-law) level repulsion with phenomenological Brody distribution providing an adequate global fit.Comment: 10 pages in LaTeX with 4 eps figures include

Chaotic dynamics in superconducting nanocircuits

The quantum kicked rotator can be realized in a periodically driven superconducting nanocircuit. A study of the fidelity allows the experimental investigation of exponential instability of quantum motion inside the Ehrenfest time scale, chaotic diffusion and quantum dynamical localization. The role of noise and the experimental setup to measure the fidelity is discussed as well.Comment: 4 pages, 4 figure

Controlling the energy flow in nonlinear lattices: a model for a thermal rectifier

We address the problem of heat conduction in 1-D nonlinear chains; we show that, acting on the parameter which controls the strength of the on site potential inside a segment of the chain, we induce a transition from conducting to insulating behavior in the whole system. Quite remarkably, the same transition can be observed by increasing the temperatures of the thermal baths at both ends of the chain by the same amount. The control of heat conduction by nonlinearity opens the possibility to propose new devices such as a thermal rectifier.Comment: 4 pages with figures included. Phys. Rev. Lett., to be published (Ref. [10] corrected

Regular and Irregular States in Generic Systems

In this work we present the results of a numerical and semiclassical analysis of high lying states in a Hamiltonian system, whose classical mechanics is of a generic, mixed type, where the energy surface is split into regions of regular and chaotic motion. As predicted by the principle of uniform semiclassical condensation (PUSC), when the effective $\hbar$ tends to 0, each state can be classified as regular or irregular. We were able to semiclassically reproduce individual regular states by the EBK torus quantization, for which we devise a new approach, while for the irregular ones we found the semiclassical prediction of their autocorrelation function, in a good agreement with numerics. We also looked at the low lying states to better understand the onset of semiclassical behaviour.Comment: 25 pages, 14 figures (as .GIF files), high quality figures available upon reques

Decay of the classical Loschmidt echo in integrable systems

We study both analytically and numerically the decay of fidelity of classical motion for integrable systems. We find that the decay can exhibit two qualitatively different behaviors, namely an algebraic decay, that is due to the perturbation of the shape of the tori, or a ballistic decay, that is associated with perturbing the frequencies of the tori. The type of decay depends on initial conditions and on the shape of the perturbation but, for small enough perturbations, not on its size. We demonstrate numerically this general behavior for the cases of the twist map, the rectangular billiard, and the kicked rotor in the almost integrable regime.Comment: 8 pages, 3 figures, revte