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 The older version has been replaced by the definitive on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