An analysis of the random lattice gas in the annealed limit is presented. The statistical mechanics of disordered lattice systems is briefly reviewed. For the case of the lattice gas with an arbitrary uniform interaction potential and random short-range interactions the annealed limit is discussed in detail. By identifying and extracting an entropy of mixing term, a correct physical expression ...

This paper studies an exchange economy with indivisibilities. Our main goal is to see if a price system can function well in an economy (e.g., an economy with complementary preferences) that does not have a Walrasian equilibrium. We study the price adjustment processes governed by the Euler iterative scheme. We show that in an economy that has a Walrasian equilibrium, our price adjustment proce...

A simple correlation energy functional for the uniform electron gas is derived based on the second-order Moller-Plesset perturbation theory. It can reproduce the known correlation functional in the high-density limit, while in the mid-density range maintaining a good agreement with the near-exact correlation energy of the uniform electron gas to within 2 × 10(-3) hartree. The correlation energy...

We construct and study a class of N particle supersymmetric Hamiltonians with nearest and next-nearest neighbor inverse-square interaction in one dimension. We show that solvable inhomogeneous XY models in an external non-uniform magnetic field can be obtained from these superHamiltonians in a particular limit decoupling the fermionic degrees of freedom from the kinematic ones. We further consi...

We analyze the phase diagram of uniform superfluidity for two-species fermion mixtures from the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation (BEC) limit as a function of the scattering parameter and population imbalance. We find at zero temperature that the phase diagram of population imbalance versus scattering parameter is asymmetric for unequal masses, having a larger stability re...

In nonintegrable Hamiltonian systems with mixed phase space and discrete symmetries, sequences of pitchfork bifurcations of periodic orbits pave the way from integrability to chaos. In extending the semiclassical trace formula for the spectral density, we develop a uniform approximation for the combined contribution of pitchfork bifurcation pairs. For a two-dimensional double-well potential and...

For natural integer n, let Dn denote the random variable taking the values log d for d dividing n with uniform probability 1/⌧(n). Then t 7! P(Dn 6 nt) (0 6 t 6 1) is an arithmetic process with respect to the uniform probability over the first N integers. It is known from previous works that this process converges to a limit law and that the same holds for various extensions. We investigate the...

Qualitative features of the mean-field theory of superconductivity in a strongly disordered system of fermions with short-range attraction are discussed. In this limit the effective theory at low energies is entirely bosonic, and I consider both the artificial infiniterange limit and the more realistic case of ”nearest-neighbor” hopping of bosons between the localized states. In the infinite-ra...

In Hamiltonian systems with mixed phase space and discrete symmetries, sequences of isochronous pitchfork bifurcations of periodic orbits pave the way from integrability to chaos. In extending the semiclassical trace formula for the spectral density, we develop a new codimension-two uniform approximation for the combined contribution of two successive pitchfork bifurcations. For a two-dimension...

We consider the two-dimensional uniformly frustrated XY model in the limit of small frustration, which is equivalent to anXY system, for instance a Josephson junction array, in a weak uniform magnetic field applied along a direction orthogonal to the lattice. We show that the uniform frustration (equivalently, the magnetic field) destabilizes the line of fixed points which characterize the crit...