Molecular dynamics investigations on a quantum system in a thermostat

The model quantum system of fermions in a one dimensional harmonic oscillator potential is investigated by a molecular dynamics method at constant temperature. Although in quantum mechanics the equipartition theorem cannot be used like in the Nose-Hoover-thermostat it is possible to couple an additional degree of freedom to the system which acts as a thermometer and drives the system towards the desired temperature via complex time steps.Comment: 11 pages, 8 postscript figures, uses 'epsfig.sty'. Submitted to PHYSICA A. More information available at http://obelix.physik.uni-osnabrueck.de/~schnac

Bulk Properties of Anharmonic Chains in Strong Thermal Gradients: Non-Equilibrium ϕ4\phi^4 Theory

We study nonequilibrium properties of a one-dimensional lattice Hamiltonian with quartic interactions in strong thermal gradients. Nonequilibrium temperature profiles, T(x), are found to develop significant curvature and boundary jumps. From the determination of the bulk thermal conductivity, we develop a quantitative description of T(x) including the jumps.Comment: 14pp, 5 fig

Non-Equilibrium Statistical Mechanics of Classical Lattice ϕ4\phi^4 Field Theory

Classical $\phi^4$ theory in weak and strong thermal gradients is studied on the lattice in (1+1) dimensions. Classical $\phi^4$ theory in weak and strong thermal gradients is studied on the lattice in (1+1) dimensions. The steady state physics of the theory is investigated from first principles and classified into dynamical regimes. We derive the bulk properties associated with thermal transport, and explore in detail the non-equilibrium statistical mechanics of the theory as well as connections to equilibrium and irreversible thermodynamics. Linear response predictions are found to be valid for systems quite far from equilibrium and are seen to eventually break down simultaneously with local equilibrium.Comment: 28 pages, 20 fig

Global Demons in Field Theory : Critical Slowing Down in the Xy Model

We investigate the use of global demons, a `canonical dynamics', as an approach to simulating lattice regularized field theories. This deterministically chaotic dynamics is non-local and non-Hamiltonian, and preserves the canonical measure rather than $\delta(H-E)$. We apply this inexact dynamics to the 2D XY model, comparing to various implementations of hybrid Monte Carlo, focusing on critical exponents and critical slowing down. In addition, we discuss a scheme for making energy non-conserving dynamical algorithms exact without the use of a Metropolis hit.Comment: 23 pages text plus 12 figures [Submitted to Nuc. Phys. B, 7/92

Nose-Hoover dynamics for coherent states

The popular method of Nose and Hoover to create canonically distributed positions and momenta in classical molecular dynamics simulations is generalized to a genuine quantum system of infinite dimensionality. We show that for the quantum harmonic oscillator, the equations of motion in terms of coherent states can easily be modified in an analogous manner to mimic the coupling of the system to a thermal bath and create a quantum canonical ensemble. Possible applications to more complex systems, especially interacting Fermion systems, are proposed.Comment: 13 pages, 3 figure

Dynamical Symmetry Approach to Periodic Hamiltonians

We show that dynamical symmetry methods can be applied to Hamiltonians with periodic potentials. We construct dynamical symmetry Hamiltonians for the Scarf potential and its extensions using representations of su(1,1) and so(2,2). Energy bands and gaps are readily understood in terms of representation theory. We compute the transfer matrices and dispersion relations for these systems, and find that the complementary series plays a central role as well as non-unitary representations.Comment: 20 pages, 7 postscript figure