In 1992, Goulden and Jackson found a beautiful determinantal expression for the immanant of a matrix. This paper proves the same result combinatori-ally.

This article concerns the time-dependent Hartree-Fock (TDHF) approximation of single-particle dynamics in systems of interacting fermions. We find that the TDHF approximation is accurate when there are sufficiently many particles and the initial manyparticle state is any Gibbs equilibrium state for noninteracting fermions (with Slater determinants as a special example). Assuming a bounded two-p...

The wavefunction ψ for a system of N electrons under the time-independent, non-relativistic, multiparticle Schrödinger equation with the Born-Oppenheimer approximation is an antisymmetric function of N variables, each of the form γ = (r, σ) = ((x, y, z), σ) where σ ∈ {−1/2, 1/2} is the spin variable. A natural way to approximate ψ is as the antisymmetrization of a sum of products of functions o...

Abstract We investigate analytically the fermionic fluctuation determinant at finite temperatures in the minimal standard model, including all operators up to dimension 6 and all contributions to the effective potential to all orders in the high T expansion, to 1 loop. We apply the results to find corrections to the Sphaleron erasure rate in the broken phase. We conclude that the analytic treat...

In previous work [11] the authors found integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice Z. The dynamics are uniquely determined once the initial state is specified. In this note we restrict our attention to the case of step initial condition with particles at the positive integers Z+ and consider the distribution function for the mth ...

We propose a new method to investigate the thermal properties of QCD with a small chemical potential (µ). The derivatives of the phase transition point with respect to µ are computed for 2 flavors of p4-improved staggered fermions. We moreover comment on the complex phase of the fermion determinant in finite-density QCD.

We find that the fermion determinant is not generally positive in a class of lattice actions recently constructed by Cohen et al. [hep-lat/0307012]; these are actions that contain an exact lattice supersymmetry and have as their target (continuum) theory (4,4) 2-dimensional super-Yang-Mills. We discuss the implications of this finding for lattice simulations and give some preliminary results fo...

Let μ denote a symmetric probability measure on [−1, 1] and let (pn) be the corresponding orthogonal polynomials normalized such that pn(1) = 1. We prove that the normalized Turán determinant ∆n(x)/(1−x), where ∆n = pn−pn−1pn+1, is a Turán determinant of order n− 1 for orthogonal polynomials with respect to (1− x2)dμ(x). We use this to prove lower and upper bounds for the normalized Turán deter...

Let D(n) be the maximal determinant for n × n {±1}-matrices, and R(n) = D(n)/n be the ratio of D(n) to the Hadamard upper bound. Using the probabilistic method, we prove new lower bounds on D(n) and R(n) in terms of the distance d to the nearest (smaller) Hadamard matrix, defined by d = n − h, where h is the order of a Hadamard matrix and h is maximal subject to h ≤ n. The lower bounds on R(n) ...

A new algorithm is presented for the sparse representation and evaluation of Slater determinants in the quantum Monte Carlo (QMC) method. The approach, combined with the use of localized orbitals in a Slater-type orbital basis set, significantly extends the size molecule that can be treated with the QMC method. Application of the algorithm to systems containing up to 390 electrons confirms that...