397 research outputs found
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
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 -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
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
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
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
Estimating errors reliably in Monte Carlo simulations of the Ehrenfest model
Using the Ehrenfest urn model we illustrate the subtleties of error
estimation in Monte Carlo simulations. We discuss how the smooth results of
correlated sampling in Markov chains can fool one's perception of the accuracy
of the data, and show (via numerical and analytical methods) how to obtain
reliable error estimates from correlated samples
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
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
Classical invariants and the quantization of chaotic systems
Long periodic orbits constitute a serious drawback in Gutzwiller's theory of
chaotic systems, and then it would be desirable that other classical
invariants, not suffering from the same problem, could be used in the
quantization of such systems. In this respect, we demonstrate how a suitable
dynamical analysis of chaotic quantum spectra unveils the fundamental role
played by classical invariant areas related to the stable and unstable
manifolds of short periodic orbits.Comment: 4 pages, 3 postscript figure
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