582 research outputs found

### The Ehrenfest urn revisited: Playing the game on a realistic fluid model

The Ehrenfest urn process, also known as the dogs and fleas model, is
realistically simulated by molecular dynamics of the Lennard-Jones fluid. The
key variable is Delta z, i.e. the absolute value of the difference between the
number of particles in one half of the simulation box and in the other half.
This is a pure-jump stochastic process induced, under coarse graining, by the
deterministic time evolution of the atomic coordinates. We discuss the Markov
hypothesis by analyzing the statistical properties of the jumps and of the
waiting times between jumps. In the limit of a vanishing integration time-step,
the distribution of waiting times becomes closer to an exponential and,
therefore, the continuous-time jump stochastic process is Markovian. The random
variable Delta z behaves as a Markov chain and, in the gas phase, the observed
transition probabilities follow the predictions of the Ehrenfest theory.Comment: Accepted by Physical Review E on 4 May 200

### Coherent states and the classical-quantum limit considered from the point of view of entanglement

Three paradigms commonly used in classical, pre-quantum physics to describe
particles (that is: the material point, the test-particle and the diluted
particle (droplet model)) can be identified as limit-cases of a quantum regime
in which pairs of particles interact without getting entangled with each other.
This entanglement-free regime also provides a simplified model of what is
called in the decoherence approach "islands of classicality", that is,
preferred bases that would be selected through evolution by a Darwinist
mechanism that aims at optimising information. We show how, under very general
conditions, coherent states are natural candidates for classical pointer
states. This occurs essentially because, when a (supposedly bosonic) system
coherently exchanges only one quantum at a time with the (supposedly bosonic)
environment, coherent states of the system do not get entangled with the
environment, due to the bosonic symmetry.Comment: This is the definitive version of a paper entitled The
classical-quantum limit considered from the point of view of entanglement: a
survey (author T. Durt). The older version has been replaced by the
definitive on

### Non-analytic microscopic phase transitions and temperature oscillations in the microcanonical ensemble: An exactly solvable 1d-model for evaporation

We calculate exactly both the microcanonical and canonical thermodynamic
functions (TDFs) for a one-dimensional model system with piecewise constant
Lennard-Jones type pair interactions. In the case of an isolated $N$-particle
system, the microcanonical TDFs exhibit (N-1) singular (non-analytic)
microscopic phase transitions of the formal order N/2, separating N
energetically different evaporation (dissociation) states. In a suitably
designed evaporation experiment, these types of phase transitions should
manifest themselves in the form of pressure and temperature oscillations,
indicating cooling by evaporation. In the presence of a heat bath (thermostat),
such oscillations are absent, but the canonical heat capacity shows a
characteristic peak, indicating the temperature-induced dissociation of the
one-dimensional chain. The distribution of complex zeros (DOZ) of the canonical
partition may be used to identify different degrees of dissociation in the
canonical ensemble.Comment: version accepted for publication in PRE, minor additions in the text,
references adde

### Stabilisation of the lattice-Boltzmann method using the Ehrenfests' coarse-graining

The lattice-Boltzmann method (LBM) and its variants have emerged as
promising, computationally efficient and increasingly popular numerical methods
for modelling complex fluid flow. However, it is acknowledged that the method
can demonstrate numerical instabilities, e.g., in the vicinity of shocks. We
propose a simple and novel technique to stabilise the lattice-Boltzmann method
by monitoring the difference between microscopic and macroscopic entropy.
Populations are returned to their equilibrium states if a threshold value is
exceeded. We coin the name Ehrenfests' steps for this procedure in homage to
the vehicle that we use to introduce the procedure, namely, the Ehrenfests'
idea of coarse-graining. The one-dimensional shock tube for a compressible
isothermal fluid is a standard benchmark test for hydrodynamic codes. We
observe that, of all the LBMs considered in the numerical experiment with the
one-dimensional shock tube, only the method which includes Ehrenfests' steps is
capable of suppressing spurious post-shock oscillations.Comment: 4 pages, 9 figure

### Drifting diffusion on a circle as continuous limit of a multiurn Ehrenfest model

We study the continuous limit of a multibox Erhenfest urn model proposed
before by the authors. The evolution of the resulting continuous system is
governed by a differential equation, which describes a diffusion process on a
circle with a nonzero drifting velocity. The short time behavior of this
diffusion process is obtained directly by solving the equation, while the long
time behavior is derived using the Poisson summation formula. They reproduce
the previous results in the large $M$ (number of boxes) limit. We also discuss
the connection between this diffusion equation and the Schr$\ddot{\rm o}$dinger
equation of some quantum mechanical problems.Comment: 4 pages prevtex4 file, 1 eps figur

### Microscopic chaos from Brownian motion?

A recent experiment on Brownian motion has been interpreted to exhibit direct
evidence for microscopic chaos. In this note we demonstrate that virtually
identical results can be obtained numerically using a manifestly
microscopically nonchaotic system.Comment: 3 pages, 1 figure, Comment on P. Gaspard et al, Nature vol 394, 865
(1998); rewritten in a more popular styl

### Einstein's quantum theory of the monatomic ideal gas: non-statistical arguments for a new statistics

In this article, we analyze the third of three papers, in which Einstein
presented his quantum theory of the ideal gas of 1924-1925. Although it failed
to attract the attention of Einstein's contemporaries and although also today
very few commentators refer to it, we argue for its significance in the context
of Einstein's quantum researches. It contains an attempt to extend and exhaust
the characterization of the monatomic ideal gas without appealing to
combinatorics. Its ambiguities illustrate Einstein's confusion with his initial
success in extending Bose's results and in realizing the consequences of what
later became to be called Bose-Einstein statistics. We discuss Einstein's
motivation for writing a non-combinatorial paper, partly in response to
criticism by his friend Ehrenfest, and we paraphrase its content. Its arguments
are based on Einstein's belief in the complete analogy between the
thermodynamics of light quanta and of material particles and invoke
considerations of adiabatic transformations as well as of dimensional analysis.
These techniques were well-known to Einstein from earlier work on Wien's
displacement law, Planck's radiation theory, and the specific heat of solids.
We also investigate the possible role of Ehrenfest in the gestation of the
theory.Comment: 57 pp

### Adiabatic Fidelity for Atom-Molecule Conversion in a Nonlinear Three-Level \Lambda-system

We investigate the dynamics of the population transfer for atom-molecule
three-level $\Lambda$-system on stimulated Raman adiabatic passage(STIRAP). We
find that the adiabatic fidelity for the coherent population trapping(CPT)
state or dark state, as the function of the adiabatic parameter, approaches to
unit in a power law. The power exponent however is much less than the
prediction of linear adiabatic theorem. We further discuss how to achieve
higher adiabatic fidelity for the dark state through optimizing the external
parameters of STIRAP. Our discussions are helpful to gain higher atom-molecule
conversion yield in practical experiments.Comment: 4 pages, 5 figure

### Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics

It is shown how to resolve the apparent contradiction between the macroscopic
approach of phase space and the validity of the uncertainty relations. The main
notions of statistical mechanics are re-interpreted in a quantum-mechanical
way, the ergodic theorem and the H-theorem are formulated and proven (without
"assumptions of disorder"), followed by a discussion of the physical meaning of
the mathematical conditions characterizing their domain of validity.Comment: English translation by Roderich Tumulka of J. von Neumann: Beweis des
Ergodensatzes und des H-Theorems. 41 pages LaTeX, no figures; v2: typos
corrected. See also the accompanying commentary by S. Goldstein, J. L.
Lebowitz, R. Tumulka, N. Zanghi, arXiv:1003.212

### Charged Particles and the Electro-Magnetic Field in Non-Inertial Frames of Minkowski Spacetime: II. Applications: Rotating Frames, Sagnac Effect, Faraday Rotation, Wrap-up Effect

We apply the theory of non-inertial frames in Minkowski space-time, developed
in the previous paper, to various relevant physical systems. We give the 3+1
description without coordinate-singularities of the rotating disk and the
Sagnac effect, with added comments on pulsar magnetosphere and on a
relativistic extension of the Earth-fixed coordinate system. Then we study
properties of Maxwell equations in non-inertial frames like the wrap-up effect
and the Faraday rotation in astrophysics.Comment: This paper and the second one are an adaptation of arXiv 0812.3057
for publication on Int.J.Geom. Methods in Modern Phys. 36

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