Extending a Hybrid Godunov Method for Radiation Hydrodynamics to Multiple Dimensions

This paper presents a hybrid Godunov method for three-dimensional radiation hydrodynamics. The multidimensional technique outlined in this paper is an extension of the one-dimensional method that was developed by Sekora & Stone 2009, 2010. The earlier one-dimensional technique was shown to preserve certain asymptotic limits and be uniformly well behaved from the photon free streaming (hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and to the strong equilibrium diffusion (hyperbolic) limit. This paper gives the algorithmic details for constructing a multidimensional method. A future paper will present numerical tests that demonstrate the robustness of the computational technique across a wide-range of parameter space.Comment: 25 page

Crossover from Non-Equilibrium to Equilibrium Behavior in the Time-Dependent Kondo Model

We investigate the equilibration of a Kondo model that is initially prepared in a non-equilibrium state towards its equilibrium behavior. Such initial non-equilibrium states can e.g. be realized in quantum dot experiments with time-dependent gate voltages. We evaluate the non-equilibrium spin-spin correlation function at the Toulouse point of the Kondo model exactly and analyze the crossover between non-equilibrium and equilibrium behavior as the non-equilibrium initial state evolves as a function of the waiting time for the first spin measurement. Using the flow equation method we extend these results to the experimentally relevant limit of small Kondo couplings.Comment: 4 pages, 2 figures; revised version contains added references and improved layout for figure

Rigorous results on the local equilibrium kinetics of a protein folding model

A local equilibrium approach for the kinetics of a simplified protein folding model, whose equilibrium thermodynamics is exactly solvable, was developed in [M. Zamparo and A. Pelizzola, Phys. Rev. Lett. 97, 068106 (2006)]. Important properties of this approach are (i) the free energy decreases with time, (ii) the exact equilibrium is recovered in the infinite time limit, (iii) the equilibration rate is an upper bound of the exact one and (iv) computational complexity is polynomial in the number of variables. Moreover, (v) this method is equivalent to another approximate approach to the kinetics: the path probability method. In this paper we give detailed rigorous proofs for the above results.Comment: 25 pages, RevTeX 4, to be published in JSTA

Stochastic Quantization for Complex Actions

We use the stochastic quantization method to study systems with complex valued path integral weights. We assume a Langevin equation with a memory kernel and Einstein's relations with colored noise. The equilibrium solution of this non-Markovian Langevin equation is analyzed. We show that for a large class of elliptic non-Hermitian operators acting on scalar functions on Euclidean space, which define different models in quantum field theory, converges to an equilibrium state in the asymptotic limit of the Markov parameter. Moreover, as we expected, we obtain the Schwinger functions of the theory

Refined Analytical Approximations to Limit Cycles for Non-Linear Multi-Degree-of-Freedom Systems

This paper presents analytical higher order approximations to limit cycles of an autonomous multi-degree-of-freedom system based on an integro-differential equation method for obtaining periodic solutions to nonlinear differential equations. The stability of the limit cycles obtained was then investigated using a method for carrying out Floquet analysis based on developments to extensions of the method for solving Hill's Determinant arising in analysing the Mathieu equation, which have previously been reported in the literature. The results of the Floquet analysis, together with the limit cycle predictions, have then been used to provide some estimates of points on the boundary of the domain of attraction of stable equilibrium points arising from a sub-critical Hopf bifurcation. This was achieved by producing a local approximation to the stable manifold of the unstable limit cycle that occurs. The integro-differential equation to be solved for the limit cycles involves no approximations. These only arise through the iterative approach adopted for its solution in which the first approximation is that which would be obtained from the harmonic balance method using only fundamental frequency terms. The higher order approximations are shown to give significantly improved predictions for the limit cycles for the cases considered. The Floquet analysis based approach to predicting the boundary of domains of attraction met with some success for conditions just following a sub-critical Hopf bifurcation. Although this study has focussed on cubic non-linearities, the method presented here could equally be used to refine limit cycle predictions for other non-linearity types.Peer reviewedFinal Accepted Versio

Inelastic quantum transport: the self-consistent Born approximation and correlated electron-ion dynamics

A dynamical method for inelastic transport simulations in nanostructures is compared with a steady-state method based on non-equilibrium Green's functions. A simplified form of the dynamical method produces, in the steady state in the weak-coupling limit, effective self-energies analogous to those in the Born Approximation due to electron-phonon coupling. The two methods are then compared numerically on a resonant system consisting of a linear trimer weakly embedded between metal electrodes. This system exhibits enhanced heating at high biases and long phonon equilibration times. Despite the differences in their formulation, the static and dynamical methods capture local current-induced heating and inelastic corrections to the current with good agreement over a wide range of conditions, except in the limit of very high vibrational excitations, where differences begin to emerge.Comment: 12 pages, 7 figure