408 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
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 -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
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
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
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
Is the number of Photons a Classical Invariant?
We describe an apparent puzzle in classical electrodynamics and its
resolution. It is concerned with the Lorentz invariance of the classical analog
of the number of photons.Comment: Revised version, 3 figure
Circular Orbits in Einstein-Gauss-Bonnet Gravity
The stability under radial and vertical perturbations of circular orbits
associated to particles orbiting a spherically symmetric center of attraction
is study in the context of the n-dimensional: Newtonian theory of gravitation,
Einstein's general relativity, and Einstein-Gauss-Bonnet theory of gravitation.
The presence of a cosmological constant is also considered. We find that this
constant as well as the Gauss-Bonnet coupling constant are crucial to have
stability for .Comment: 11 pages, 4 figs, RevTex, Phys. Rev. D, in pres
Geometry, topology and dynamics of geodesic flows on noncompact polygonal surfaces
We establish the background for the study of geodesics on noncompact
polygonal surfaces. For illustration, we study the recurrence of geodesics on
-periodic polygonal surfaces. We prove, in particular, that almost all
geodesics on a topologically typical -periodic surface with boundary are
recurrent.Comment: 34 pages, 13 figures. To be published in V. V. Kozlov's Festschrif
Analysis of return distributions in the coherent noise model
The return distributions of the coherent noise model are studied for the
system size independent case. It is shown that, in this case, these
distributions are in the shape of q-Gaussians, which are the standard
distributions obtained in nonextensive statistical mechanics. Moreover, an
exact relation connecting the exponent of avalanche size distribution
and the q value of appropriate q-Gaussian has been obtained as q=(tau+2)/tau.
Making use of this relation one can easily determine the q parameter values of
the appropriate q-Gaussians a priori from one of the well-known exponents of
the system. Since the coherent noise model has the advantage of producing
different tau values by varying a model parameter \sigma, clear numerical
evidences on the validity of the proposed relation have been achieved for
different cases. Finally, the effect of the system size has also been analysed
and an analytical expression has been proposed, which is corroborated by the
numerical results.Comment: 14 pages, 3 fig
Adiabatic quantization of Andreev levels
We identify the time between Andreev reflections as a classical adiabatic
invariant in a ballistic chaotic cavity (Lyapunov exponent ), coupled
to a superconductor by an -mode point contact. Quantization of the
adiabatically invariant torus in phase space gives a discrete set of periods
, which in turn generate a ladder of excited states
. The largest quantized period is the
Ehrenfest time . Projection of the invariant torus
onto the coordinate plane shows that the wave functions inside the cavity are
squeezed to a transverse dimension , much below the width of
the point contact.Comment: 4 pages, 3 figure
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