Probability assignment in a quantum statistical model

The evolution of a quantum system, appropriate to describe nano-magnets, can be mapped on a Markov process, continuous in $\beta$. The mapping implies a probability assignment that can be used to study the probability density (PDF) of the magnetization. This procedure is not the common way to assign probabilities, usually an assignment that is compatible with the von Neumann entropy is made. Making these two assignments for the same system and comparing both PDFs, we see that they differ numerically. In other words the assignments lead to different PDFs for the same observable within the same model for the dynamics of the system. Using the maximum entropy principle we show that the assignment resulting from the mapping on the Markov process makes less assumptions than the other one. Using a stochastic queue model that can be mapped on a quantum statistical model, we control both assignments on compatibility with the Gibbs procedure for systems in thermal equilibrium and argue that the assignment resulting from the mapping on the Markov process satisfies the compatibility requirements.Comment: 8 pages, 2 eps figures, presented at the 26-th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, 200

Comment on: rotational properties of trapped bosons

Based on the Hellman-Feynman theorem it is shown that the average square radius of a cloud of interacting bosons in a parabolic well can be derived from their free energy. As an application, the temperature dependence of the moment of inertia of non-interacting bosons in a parabolic trap is determined as a function of the number of bosons. Well below the critical condensation temperature, the Bose-Einstein statistics are found to substantially reduce the moment of inertia of this system, as compared to a gas of ``distinguishable'' particles in a parabolic well.Comment: Herewith we repost our paper cond-mat/9611090 (1996). It was published in Phys. Rev. A 55, 2453 (March 1997), three years before cond-mat/0003471 (2000) by Schneider and Wallis. Reposted by [email protected]

The center-of-mass response of confined systems

For confined systems of identical particles, either bosons or fermions, we argue that the parabolic nature of the confinement potential is a prerequisite for the non-dissipative character of the center of mass response to a uniform probe. For an excitation in a parabolic confining potential, the half width of the density response function depends nevertheless quantitatively on properties of the internal degrees of freedom, as is illustrated here for an ideal confined gas of identical particles with harmonic interparticle interactions.Comment: 4 pages REVTEX; accepted as Brief Communication in Phys. Rev.

Switching Boundary Conditions in the Many-Body Diffusion Algorithm

In this paper we show how the transposition, the basic operation of the permutation group, can be taken into account in a diffusion process of identical particles. Whereas in an earlier approach the method was applied to systems in which the potential is invariant under interchanging the Cartesian components of the particle coordinates, this condition on the potential is avoided here. In general, the potential introduces a switching of the boundary conditions of the walkers. These transitions modelled by a continuous-time Markov chain generate sample paths for the propagator as a Feynman-Kac functional. A few examples, including harmonic fermions with an anharmonic interaction, and the ground-state energy of ortho-helium are studied to elucidate the theoretical discussion and to illustrate the feasibility of a sign-problem-free implementation scheme for the recently developed many-body diffusion approach.Comment: 16 pages REVTEX + 6 postscript figures, submitted to Phys. Rev. E on Jan. 27, 199