It is challenging to compute the partition function (Q) for systems with enormous configurational spaces, such as fluids. Recently, we developed a Monte Carlo technique (an energy partitioning method) for computing Q [ J. Chem. Phys. 2011 , 135 , 174105 ]. In this paper, we use this approach to compute the partition function of a binary fluid mixture (carbon dioxide + methane); this...

[1] Phonon dispersions and vibrational density of states (VDoS) of Mg2SiO4 ringwoodite have been calculated by first principles as a function of pressure up to 30 GPa using density functional perturbation theory. The predicted zone center frequencies are in close correspondence with existing Raman and infrared experimental data. The pressure dependence of phonon frequencies is linear and agrees...

We present a quantum algorithm to prepare the thermal Gibbs state of interacting quantum systems. This algorithm sets a universal upper bound D(alpha) on the thermalization time of a quantum system, where D is the system's Hilbert space dimension and alpha < or = 1/2 is proportional to the Helmholtz free energy density. We also derive an algorithm to evaluate the partition function of a quantum...

Abstract. In this document we summarize a few supplementary results to the accompanying paper. We give a detailed proof of the bounds on the normalized total communicability obtained via quadrature rules (Theorem 3.1, section 3). We also derive the computational costs for the heuristics introduced. Moreover, this document contains the results of some numerical experiments performed on four smal...

Consider a sequence of N x N random nonnegative matrices in which each element depends on a vector u of parameters. The nth partial product is the random matrix formed by multiplying, from right to left, the first n of these random matrices in order. Under certain conditions, the elements of the nth partial product grow asymptotically exponentially as n increases, and the logarithms of the disc...

Using the Singwi–Tosi–Land–Sjolander theory, we have studied the many-body effects in the two-dimensional electron gas with arbitrary polarization at finite temperatures. We have calculated the structure factors, pair correlation functions, local-field factors and the Helmholtz free energy for different values of spin polarization, temperature and density parameter. We have shown that the spin ...

For spacetimes with timelike Killing fields, we introduce a “Fermi-WalkerKilling” coordinate system and use it to prove a Liouville Theorem for an appropriate volume element of phase space for a statistical mechanical system of particles. We derive an exact relativistic formula for the Helmholtz free energy of an ideal gas and compare it, for a class of spacetimes, to its Newtonian analog, deri...

We study global existence, uniqueness, and asymptotic behavior, as time tends to infinity, of weak solutions to the system of nonlinear thermoviscoelasticity. Various boundary conditions are considered. It is shown that for any initial data (u0 , v0 , %0) # L _W 1, _H 1 there is a unique global solution (u, v, %)=(deformation gradient, velocity, temperature) such that u # C([0, ], L ), v # C((0...

The self-referential (SR) method incorporating thermodynamic integration (TI) [Sweatman et al., J. Chem. Phys. 128, 064102 (2008)] is extended to treat systems of rigid linear bodies. The method is then applied to obtain the canonical ensemble Helmholtz free energy of the alpha-N(2) and plastic face centered cubic phases of systems of hard and Lennard-Jones dumbbells using Monte Carlo simulatio...

Abstract. We consider pairing in a two-component atomic Fermi gas, in a threedimensional optical lattice, when the components have unequal densities, i.e. the gas is polarized. We show that a superfluid where the translational symmetry is broken by a finite Cooper pair momentum, namely an FFLO-type state, minimizes the Helmholtz free energy of the system. We demonstrate that such a state is cle...