Table of contents

This letter examines the consequences of a recently proposed modification of the postulate of equal a priori probability in quantum statistical mechanics. This modification, called the quantum microcanonical postulate (QMP), asserts that for a system in microcanonical equilibrium all pure quantum states having the same energy expectation value are realized with equal probability. A simple model of a quantum system that obeys the QMP and that has a nondegenerate spectrum with equally spaced energy eigenvalues is studied. This model admits a closed-form expression for the density of states in terms of the energy eigenvalues. It is shown that in the limit as the number of energy levels approaches infinity, the expression for the density of states converges to a δ function centred at the intermediate value (E_max + E_min)/2 of the energy. Determining this limit requires an elaborate asymptotic study of an infinite sum whose terms alternate in sign.

Implementation of quantum logical gates for multilevel systems is demonstrated through decoherence control under the quantum adiabatic method using simple phase modulated laser pulses. We make use of selective population inversion and Hamiltonian evolution with time to achieve such goals robustly instead of the standard unitary transformation language.

We derive a generic expression for the generating function (GF) of the particle-number probability distribution (PNPD) for a simple reaction diffusion model that belongs to the directed percolation universality class. Starting with a single particle on a lattice, we show that the GF of the PNPD can be written as an infinite series of cumulants taken at zero momentum. This series can be summed up into a complete form at the level of a mean-field approximation. Using the renormalization group techniques, we determine logarithmic corrections for the GF at the upper critical dimension. We also find the critical scaling form for the PNPD and check its universality numerically in one dimension. The critical scaling function is found to be universal up to two non-universal metric factors.

Consider a homogeneous fluid membrane, or vesicle, described by the Helfrich–Canham energy, quadratic in the mean curvature. When the membrane is axially symmetric, this energy can be viewed as an 'action' describing the motion of a particle; the contours of equilibrium geometries are identified with particle trajectories. A novel Hamiltonian formulation of the problem is presented which exhibits the following two features: (i) the second derivatives appearing in the action through the mean curvature are accommodated in a natural phase space and (ii) the intrinsic freedom associated with the choice of evolution parameter along the contour is preserved. As a result, the phase space involves momenta conjugate not only to the particle position but also to its velocity, and there are constraints on the phase space variables. This formulation provides the groundwork for a field theoretical generalization to arbitrary configurations, with the particle replaced by a loop in space.

A criterion for the uniqueness of limit cycles for generalized Liénard-type system is established. Through a simple change of variable, three planar autonomous systems, which arise from the study of theoretical models for oscillating reactions, can be transformed into a better studied generalized Liénard-type system. As a result, the uniqueness of limit cycles of these systems is obtained.

A multi-parafermion basis of states for the parafermionic models is derived. Its generating function is constructed by elementary steps. It corresponds to the Andrews multiple sum which enumerates partitions whose parts separated by the distance k − 1 differ by at least 2. Two analogous bases are derived for graded parafermions; one of these entails a new expression for their fermionic characters.

In this paper, we extend the analysis of stationary states of a nonlinear model of a gas of pyramidal molecules (already discussed in the literature) by including a linear coupling to an external electromagnetic field. It is seen that this results in a shift of the bifurcation point and consequently allows, for appropriate values of Rabi frequency, stable localized stationary solutions below the critical pressure required in the absence of molecule–field coupling.

The coherent states are constructed for a charged particle in a uniform magnetic field based on coherent states for the circular motion which have recently been introduced by the authors.

The affine su(3) modular-invariant partition functions in 2D RCFT are associated with a set of generalized Coxeter graphs. These partition functions fall into two classes: the block-diagonal (Type I) and the non-block-diagonal (Type II) cases, associated, from spectral properties, with the subsets of subgroup and module graphs, respectively. We introduce a modular operator taking values on the set of vertices of the subgroup graphs. It allows us to easily obtain the associated Type I partition functions. We also show that all Type II partition functions are obtained by the action of suitable twists ϑ on the set of vertices of the subgroup graphs. These twists have to preserve the values of the modular operator .

There is a typographical error in equation (72) of this paper. Please see PDF for corrected version.