688 research outputs found
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.
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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
Evolution of Nuro-Controllers for Trajectory Planning Applied to a Bipedal Walking Robot with a Tail
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
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