Quantum and classical echoes in scattering systems described by simple Smale horseshoes

We explore the quantum scattering of systems classically described by binary and other low order Smale horseshoes, in a stage of development where the stable island associated with the inner periodic orbit is large, but chaos around this island is well developed. For short incoming pulses we find periodic echoes modulating an exponential decay over many periods. The period is directly related to the development stage of the horseshoe. We exemplify our studies with a one-dimensional system periodically kicked in time and we mention possible experiments.Comment: 7 pages with 6 reduced quality figures! Please contact the authors ([email protected]) for an original good quality pre-prin

Memory Effects in Nonequilibrium Transport for Deterministic Hamiltonian Systems

We consider nonequilibrium transport in a simple chain of identical mechanical cells in which particles move around. In each cell, there is a rotating disc, with which these particles interact, and this is the only interaction in the model. It was shown in \cite{eckmann-young} that when the cells are weakly coupled, to a good approximation, the jump rates of particles and the energy-exchange rates from cell to cell follow linear profiles. Here, we refine that study by analyzing higher-order effects which are induced by the presence of external gradients for situations in which memory effects, typical of Hamiltonian dynamics, cannot be neglected. For the steady state we propose a set of balance equations for the particle number and energy in terms of the reflection probabilities of the cell and solve it phenomenologically. Using this approximate theory we explain how these asymmetries affect various aspects of heat and particle transport in systems of the general type described above and obtain in the infinite volume limit the deviation from the theory in \cite{eckmann-young} to first-order. We verify our assumptions with extensive numerical simulations.Comment: Several change

Reconstructing Fourier's law from disorder in quantum wires

The theory of open quantum systems is used to study the local temperature and heat currents in metallic nanowires connected to leads at different temperatures. We show that for ballistic wires the local temperature is almost uniform along the wire and Fourier's law is invalid. By gradually increasing disorder, a uniform temperature gradient ensues inside the wire and the thermal current linearly relates to this local temperature gradient, in agreement with Fourier's law. Finally, we demonstrate that while disorder is responsible for the onset of Fourier's law, the non-equilibrium energy distribution function is determined solely by the heat baths

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

Optimal estimates of the diffusion coefficient of a single Brownian trajectory

Modern developments in microscopy and image processing are revolutionizing areas of physics, chemistry and biology as nanoscale objects can be tracked with unprecedented accuracy. The goal of single particle tracking is to determine the interaction between the particle and its environment. The price paid for having a direct visualization of a single particle is a consequent lack of statistics. Here we address the optimal way of extracting diffusion constants from single trajectories for pure Brownian motion. It is shown that the maximum likelihood estimator is much more efficient than the commonly used least squares estimate. Furthermore we investigate the effect of disorder on the distribution of estimated diffusion constants and show that it increases the probability of observing estimates much smaller than the true (average) value.Comment: 8 pages, 5 figure

Third quantization: a general method to solve master equations for quadratic open Fermi systems

The Lindblad master equation for an arbitrary quadratic system of n fermions is solved explicitly in terms of diagonalization of a 4n x 4n matrix, provided that all Lindblad bath operators are linear in the fermionic variables. The method is applied to the explicit construction of non-equilibrium steady states and the calculation of asymptotic relaxation rates in the far from equilibrium problem of heat and spin transport in a nearest neighbor Heisenberg XY spin 1/2 chain in a transverse magnetic field.Comment: 24 pages, with 8 eps figures - few minor corrections to the published version, e.g. anti-symmetrizing the matrix given by eq. (27

Cause of the fragile-to-strong transition observed in water confined in C-S-H gel

In this study, the rotational dynamics of hydration water confined in calcium-silicate-hydrate (C-S-H) gel with a water content of 22 wt.% was studied by broadband dielectric spectroscopy in broad temperature (110-300 K) and frequency (10(-1)-10(8) Hz) ranges. The C-S-H gel was used as a 3D confining system for investigating the possible existence of a fragile-to-strong transition for water around 220 K. Such transition was observed at 220 K in a previous study [Y. Zhang, M. Lagi, F. Ridi, E. Fratini, P. Baglioni, E. Mamontov and S. H. Chen, J. Phys.: Condens. Matter 20, 502101 (2008)] on a similar system, and it was there associated with a hidden critical point of bulk water. However, based on the experimental results presented here, there is no sign of a fragile-to-strong transition for water confined in C-S-H gel. Instead, the fragile-to-strong transition can be explained by a merging of two different relaxation processes at about 220 K. (C) 2013 AIP Publishing LLC

Density dynamics from current auto-correlations at finite time- and length-scales

We consider the increase of the spatial variance of some inhomogeneous, non-equilibrium density (particles, energy, etc.) in a periodic quantum system of condensed matter-type. This is done for a certain class of initial quantum states which is supported by static linear response and typicality arguments. We directly relate the broadening to some current auto-correlation function at finite times. Our result is not limited to diffusive behavior, however, in that case it yields a generalized Einstein relation. These findings facilitate the approximation of diffusion constants/conductivities on the basis of current auto-correlation functions at finite times for finite systems. Pursuing this, we quantitatively confirm the magnetization diffusion constant in a spin chain which was recently found from non-equilibrium bath scenarios.Comment: 4 pages, 1 figure, accepted for publication in Europhys. Let