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 The older version has been replaced by the definitive on

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

Quantum mechanical virial theorem in systems with translational and rotational symmetry

Generalized virial theorem for quantum mechanical nonrelativistic and relativistic systems with translational and rotational symmetry is derived in the form of the commutator between the generator of dilations G and the Hamiltonian H. If the conditions of translational and rotational symmetry together with the additional conditions of the theorem are satisfied, the matrix elements of the commutator [G, H] are equal to zero on the subspace of the Hilbert space. Normalized simultaneous eigenvectors of the particular set of commuting operators which contains H, J^{2}, J_{z} and additional operators form an orthonormal basis in this subspace. It is expected that the theorem is relevant for a large number of quantum mechanical N-particle systems with translational and rotational symmetry.Comment: 24 pages, accepted for publication in International Journal of Theoretical Physic

Exact Solution for the Time Evolution of Network Rewiring Models

We consider the rewiring of a bipartite graph using a mixture of random and preferential attachment. The full mean field equations for the degree distribution and its generating function are given. The exact solution of these equations for all finite parameter values at any time is found in terms of standard functions. It is demonstrated that these solutions are an excellent fit to numerical simulations of the model. We discuss the relationship between our model and several others in the literature including examples of Urn, Backgammon, and Balls-in-Boxes models, the Watts and Strogatz rewiring problem and some models of zero range processes. Our model is also equivalent to those used in various applications including cultural transmission, family name and gene frequencies, glasses, and wealth distributions. Finally some Voter models and an example of a Minority game also show features described by our model.Comment: This version contains a few footnotes not in published Phys.Rev.E versio

Quantitative conditions do not guarantee the validity of the adiabatic approximation

In this letter, we point out that the widely used quantitative conditions in the adiabatic theorem are insufficient in that they do not guarantee the validity of the adiabatic approximation. We also reexamine the inconsistency issue raised by Marzlin and Sanders (Phys. Rev. Lett. 93, 160408, 2004) and elucidate the underlying cause.Comment: corrected typos. Eq. (32) is corrected. No other change

Entropy of Classical Histories

We consider a number of proposals for the entropy of sets of classical coarse-grained histories based on the procedures of Jaynes, and prove a series of inequalities relating these measures. We then examine these as a function of the coarse-graining for various classical systems, and show explicitly that the entropy is minimized by the finest-grained description of a set of histories. We propose an extension of the second law of thermodynamics to the entropy of histories. We briefly discuss the implications for decoherent or consistent history formulations of quantum mechanics.Comment: 35 pages RevTeX 3.0 + 5 figures (postscript). Minor corrections and typos. To appear in Physical Review

Stationary Distribution and Eigenvalues for a de Bruijn Process

We define a de Bruijn process with parameters n and L as a certain continuous-time Markov chain on the de Bruijn graph with words of length L over an n-letter alphabet as vertices. We determine explicitly its steady state distribution and its characteristic polynomial, which turns out to decompose into linear factors. In addition, we examine the stationary state of two specializations in detail. In the first one, the de Bruijn-Bernoulli process, this is a product measure. In the second one, the Skin-deep de Bruin process, the distribution has constant density but nontrivial correlation functions. The two point correlation function is determined using generating function techniques.Comment: Dedicated to Herb Wilf on the occasion of his 80th birthda

Effects of Large-Scale Convection on p-mode Frequencies

We describe an approach for finding the eigenfrequencies of solar acoustic modes (p modes) in a convective envelope in the WKB limit. This approximation restricts us to examining the effects of fluid motions which are large compared to the mode wavelength, but allows us to treat the three-dimensional mode as a localized ray. The method of adiabatic switching is then used to investigate the frequency shifts resulting from simple perturbations to a polytropic model of the convection zone as well as from two basic models of a convective cell. We find that although solely depth-dependent perturbations can give frequency shifts which are first order in the strength of the perturbation, models of convective cells generate downward frequency shifts which are second order in the perturbation strength. These results may have implications for resolving the differences between eigenfrequencies derived from solar models and those found from helioseismic observations.Comment: 27 pages + 6 figures; accepted for publication in Ap

An Adiabatic Theorem without a Gap Condition

The basic adiabatic theorems of classical and quantum mechanics are over-viewed and an adiabatic theorem in quantum mechanics without a gap condition is described.Comment: Talk at QMath 7, Prague, 1998. 10 pages, 7 figure

On time's arrow in Ehrenfest models with reversible deterministic dynamics

We introduce a deterministic, time-reversible version of the Ehrenfest urn model. The distribution of first-passage times from equilibrium to non-equilibrium states and vice versa is calculated. We find that average times for transition to non-equilibrium always scale exponentially with the system size, whereas the time scale for relaxation to equilibrium depends on microscopic dynamics. To illustrate this, we also look at deterministic and stochastic versions of the Ehrenfest model with a distribution of microscopic relaxation times.Comment: 6 pages, 7 figures, revte