Calculation of quantum escape rates from a metastable well

The quantum-mechanical decay of a metastable state of a system coupled to a heat bath environment is studied. A functional integral method is presented allowing for the calculation of decay rates at finite temperatures and in the presence of dissipation. Analytical methods for high and intermediate temperatures are combined with an accurate numerical method for low temperatures where the system decays by quantum tunneling. Explicit results are given for a system with a cubic potential and frequency-independent damping.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Quantum tunneling of light particles in metals

The motion of a particle in a metallic crystal is studied for low temperatures where transitions between adjacent interstitial sites are caused by quantum tunneling. The influence of electrons and phonons on the hopping rate is taken into account by means of a functional integral method. The electronic influence may effectively be described by Ohmic damping which dominates the low temperature behavior of the defect motion. When subsequent tunneling transitions are statistically independent, the diffusion constant is found to obey a power law, D∼T^2K−1, where K depends on the defect-electron interaction. This power law is limited at low temperatures by the effects of phonon excitations. Near the transition between electron and phonon dominated behavior the diffusion constant has a minimum where the precise temperature dependence of the rate depends not only on phonon spectra but also on the processes limiting phonon lifetimes.     

Linear mobility for coherent quantum tunneling in a periodic potential

The dynamics of a quantum particle moving in a tight binding lattice and coupled to an ohmic heat bath is investigated. Imaginary-time functional integral methods are utilized to determine the self-energy of the velocity-velocity correlation function for weak damping and arbitrary temperatures. Recent results for the linear mobility atT=0 and high temperatures are confirmed and extended to intermediate temperatures. The dominant corrections to the zero temperature mobility are given in terms of a power law.On leave from Dipartimento di Fisica, CISM, Università di Genova Italy     

Semi-classical transport for predicting joule heating in carbon nanotubes

A method for predicting the joule heating using Monte Carlo simulation for the electron dynamics is proposed. The joule heating in (10,10) carbon nanotubes is computed. The full energy band is utilized; however the results show that for low temperatures only the lower subband is sufficient, while for temperatures above 900 K, it is important to include all the subbands. Results are compared with a quantum mechanical integral form which uses an approximation for the electron occupation probability. There is a quantitative agreement of the results; however saturation of the heat generated observed in the integral form is not observed.     

Anomaly of specific heat due to kinks

Finite temperature corrections to classical kink free energies for the sine-Gordon and ø⁴ chains are obtained analytically by means of the transfer integral method. These corrections reveal that kink excitations cause a Schottky-type anomaly of specific heat at low temperatures. The numerical results of Schneider and Stoll are explained qualitatively.     

Spin fluctuation theory of ferromagnetic metals

Ferromagnetic metals at finite temperatures are discussed using the functional integral method along the lines of the unifield spin fluctuation theory of Moriya and Takahashi. We develop a simple approach which makes use of only the density of states but still takes account of the nonlocal nature of the spin fluctuations with the aid of a single-site coherent potential approximation. The effect of the charge density fluctuation is also taken into account within the saddle point approximation. The results of numerical calculations for various model densities of states including those for bcc and fcc d-metals are presented. Particularly, the Curie temperatures and the Curie-Weiss magnetic susceptibilities for Fe, Co and Ni seem to be fairly well reproduced.     

Equivalence of the Two Results for the Free Energy of the Chiral Potts Model

The free energy of the chiral Potts model has been obtained in two ways. The first used only the star-triangle relation, symmetries, and invariances, and led to a system of equations that implicitly define the free energy, and from which the critical behavior can be obtained The second used the functional relations derived by Bazhanov and Stroganov, solving them to obtain the free energy explicitly as a double integral. Here we obtain, for the first time, a direct verification that the two results are identical at all temperatures.     

Effect of shape anisotropy on the phase diagram of the Gay-Berne fluid

We have used the density functional theory to study the effect of molecular elongation on the isotropic-nematic, isotropic-smectic A and nematic-smectic A phase transitions of a fluid of molecules interacting via the Gay-Berne intermolecular potential. We have considered a range of length-to-width parameter 3.0 ⩽ x₀ ⩽ 4.0 in steps of 0.2 at different densities and temperatures. Pair correlation functions needed as input information in density functional theory are calculated using the Percus-Yevick integral equation theory. Within the small range of elongation, the phase diagram shows significant changes. The fluid at low temperature is found to freeze directly from isotropic to smectic A phase for all the values of x₀ considered by us on increasing the density while the nematic phase stabilizes in between isotropic and smectic A phases only at high temperatures and densities. Both isotropic-nematic and nematic-smectic A transition density and pressure are found to decrease as we increase x₀. The phase diagram obtained is compared with computer simulation result of the same model potential and is found to be in good qualitative agreement.     

All-electron path integral Monte Carlo simulations of warm dense matter: application to water and carbon plasmas

We develop an all-electron path integral Monte Carlo method with free-particle nodes for warm dense matter and apply it to water and carbon plasmas. We thereby extend path integral Monte Carlo studies beyond hydrogen and helium to elements with core electrons. Path integral Monte Carlo results for pressures, internal energies, and pair-correlation functions compare well with density functional theory molecular dynamics calculations at temperatures of (2.5-7.5)×10(5) K, and both methods together form a coherent equation of state over a density-temperature range of 3-12 g/cm(3) and 10(4)-10(9) K.