Journal of Statistical Physics

The aim of this paper is twofold. First, we shall derive the Fermi-Dirac (FD) and Bose-Einstein (BE) distributions from the classical Maxwell-Boltzmann (MB) distribution by introducing into the classical system the consequences of quantum mechanical indistinguishability in a direct and simple manner. Next, we go through a brief introduction to feedback systems and see how the FD and BE systems may be viewed as classical systems with appropriate feedback. We shall see that the resemblance to feedback systems is more than formal and that a feedback mechanism does exist in systems obeying quantum statistical mechanics.

For a system of hard spheres we prove the convergence of the second moment of the fluctuation field in the low-density limit. This extends a previous result by van Beijeren, Lanford, Lebowitz and Spohn(1) to nonequilibrium states.

We consider a nonlinear oscillator driven by random, Gaussian “noise.” The oscillator, which is damped and has linear and cubic terms in the restoring force, is often called the “Duffing Equation.” The Fourier transform of the response is expanded in a series in the coefficient of the nonlinear term. This series is then squared and averaged, and each term in the resulting response spectrum series is expressed in terms of the response spectrum of the linearized harmonic oscillator (i.e., without the cubic term). Since the forcing function is Gaussian, the linear solution is Gaussian. The terms in the series for the response spectrum are then regrouped so that common quantities can be factored out. This process leads to “consolidated equations” for the response spectrum and the “common factors.” These consolidated equations are truncated in various ways, and the corresponding solutions are compared with an analog computer experiment. This technique was proposed for turbulent flow by Kraichnan and followed up by Wyld, and has yielded some good results. The numerical results indicate that the truncated consolidated equations can provide a substantial improvement over some other methods used to solve this type of problem. The methods compared with it are (1) the traditional truncated parametric expansion, (2) statistical linearization, and (3) use of the joint-normal hypothesis to express the fourth and sixth moments in terms of the second.

We consider a system of trapped spinless bosons interacting with a repulsive potential and subject to rotation. In the limit of rapid rotation and small scattering length, we rigorously show that the ground state energy converges to that of a simplified model Hamiltonian with contact interaction projected onto the Lowest Landau Level. This effective Hamiltonian models the bosonic analogue of the Fractional Quantum Hall Effect (FQHE). For a fixed number of particles, we also prove convergence of states; in particular, in a certain regime we show convergence towards the bosonic Laughlin wavefunction. This is the first rigorous justification of the effective FQHE Hamiltonian for rapidly rotating Bose gases. We review previous results on this effective Hamiltonian and outline open problems.

We consider a gauge symmetric version of the p-spin glass model on a complete graph. The gauge symmetry guarantees the absence of replica symmetry breaking and allows to fully use the interpolation scheme of Guerra (Fields Inst. Commun. 30:161, 2001) to rigorously compute the free energy. In the case of pairwise interactions (p=2), where we have a gauge symmetric version of the Sherrington-Kirkpatrick model, we get the free energy and magnetization for all values of external parameters. Our analysis also works for even p≥4 except in a range of parameters surrounding the phase transition line, and for odd p≥3 in a more restricted region. We also obtain concentration estimates for the magnetization and overlap parameter that play a crucial role in the proofs for odd p and justify the absence of replica symmetry breaking. Our initial motivation for considering this model came from problems related to communication over a noisy channel, and is briefly explained.

When placed in suspension red blood cells adhere face-to-face and form long, cylindrical, and sometimes branched structures called rouleaux. We use methods developed in statistical mechanics to compute various statistical properties describing the size and shape of rouleaux in thermodynamic equilibrium. This leads to analytical expressions for (1) the average number of rouleaux consisting ofn cells and havingm branch points; (2) the average number of cells per rouleau; (3) the average number of branch points per rouleau; and (4) the number of rouleaux withn cells in a system containing a total ofN cells. We also derive asymptotic formulas that simplify these analytic expressions, and present numerical comparisons of the exact and asymptotic results.

The shape of (nano)islands is among significant factors of the catalytic activity of supported catalysts. A lattice model of the reshaping under reaction conditions is suggested and studied by means of kinetic Monte Carlo simulations. It is rooted in experimental findings and is simplified as far as possible to still demonstrate reversible compact—ramified shape transitions. This simple model with complex behavior demonstrates several reshaping regimes and is considered as a possible sub-network of more realistic networks of heterogeneous catalytic reactions.