Search results for "quantum statistical mechanics"
showing 10 items of 41 documents
Instability of Equilibrium States for Coupled Heat Reservoirs at Different Temperatures
2007
Abstract We consider quantum systems consisting of a “small” system coupled to two reservoirs (called open systems). We show that such systems have no equilibrium states normal with respect to any state of the decoupled system in which the reservoirs are at different temperatures, provided that either the temperatures or the temperature difference divided by the product of the temperatures are not too small. Our proof involves an elaborate spectral analysis of a general class of generators of the dynamics of open quantum systems, including quantum Liouville operators (“positive temperature Hamiltonians”) which generate the dynamics of the systems under consideration.
Quantum and Classical Statistical Mechanics of the Integrable Models in 1 + 1 Dimensions
1990
In a short but remarkable paper Yang and Yang [1] showed that the free energy of a model system consisting of N bosons on a line with repulsive δ-function interactions was given by a set of coupled integral equations. The Yangs’ chosen model is in fact the repulsive version of the quantum Nonlinear Schrodinger (NLS) model. We have shown that with appropriate extensions and different dispersion relations and phase shifts similar formulae apply to ‘all’ of the integrable models quantum or classical. These models include the sine-Gordon (s-G) and sinh-Gordon (sinh-G) models, the two NLS models (attractive and repulsive), the Landau-Lifshitz (L-L’) model which includes all four previous models,…
Spatial quantum noise interferometry in expanding ultracold atom clouds
2005
It is ten years since the exotic form of matter known as a Bose–Einstein condensate was first created. It was the birth of ultra-low-temperature physics, and practitioners gathered last month in Banff, Canada, to celebrate and discuss the latest news, as Karen Fox reports. And this week a new development that could have a major impact in the field is announced. In the 1950s, Hanbury Brown and Twiss showed that it is possible to measure angular sizes of astronomical radio sources from correlations of signal intensities in independent detectors. ‘HBT interferometry’ later became a key technique in quantum optics, and now it has been harnessed to identify a quantum phase of ultracold bosonic a…
Quantum and classical integrability: new approaches in statistical mechanics
1991
Abstract The present status of the statistical mechanics (SM), quantum and classical, of integrable models is reviewed by reporting new results for their partition functions Z obtained for anyon type models in one space and one time (1 + 1) dimensions. The methods of functional integration developed already are extended further. Bose-Fermi equivalence and anyon descriptions are natural parts of the quantum theory and the anyon phase is quantised. The classical integrability is exploited throughout and both classical and quantum integrability theory are reviewed this way, and related to underlying algebraic structures - notably the Hopf algebras (“quantum groups”). A new “ q -boson” lattice …
Elastic Constants of Quantum Solids by Path Integral Simulations
2000
Two methods are proposed to evaluate the second-order elastic constants of quantum mechanically treated solids. One method is based on path-integral simulations in the (NVT) ensemble using an estimator for elastic constants. The other method is based on simulations in the (NpT) ensemble exploiting the relationship between strain fluctuations and elastic constants. The strengths and weaknesses of the methods are discussed thoroughly. We show how one can reduce statistical and systematic errors associated with so-called primitive estimators. The methods are then applied to solid argon at atmospheric pressures and solid helium 3 (hcp, fcc, and bcc) under varying pressures. Good agreement with …
Location- and observation time-dependent quantum-tunneling
2009
We investigate quantum tunneling in a translation invariant chain of particles. The particles interact harmonically with their nearest neighbors, except for one bond, which is anharmonic. It is described by a symmetric double well potential. In the first step, we show how the anharmonic coordinate can be separated from the normal modes. This yields a Lagrangian which has been used to study quantum dissipation. Elimination of the normal modes leads to a nonlocal action of Caldeira-Leggett type. If the anharmonic bond defect is in the bulk, one arrives at Ohmic damping, i.e. there is a transition of a delocalized bond state to a localized one if the elastic constant exceeds a critical value $…
Quantum effects on the herringbone ordering ofN2on graphite
1993
The effects of quantum fluctuations on the ``2-in'' herringbone ordering in a realistic model of 900 ${\mathrm{N}}_{2}$ molecules adsorbed in the (\ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 )R30\ifmmode^\circ\else\textdegree\fi{} structure on graphite are studied via path-integral Monte Carlo (PIMC) simulations. Quasiclassical and quasiharmonic calculations agree for high and low temperatures, respectively, but only PIMC gives satisfactory results over the entire temperature range. We can quantify the lowering of the transition temperature and the depression of the ground state order to 10% as compared to classical modeling.
The response field and the saddle points of quantum mechanical path integrals
2021
In quantum statistical mechanics, Moyal's equation governs the time evolution of Wigner functions and of more general Weyl symbols that represent the density matrix of arbitrary mixed states. A formal solution to Moyal's equation is given by Marinov's path integral. In this paper we demonstrate that this path integral can be regarded as the natural link between several conceptual, geometric, and dynamical issues in quantum mechanics. A unifying perspective is achieved by highlighting the pivotal role which the response field, one of the integration variables in Marinov's integral, plays for pure states even. The discussion focuses on how the integral's semiclassical approximation relates to…
Two-dimensional spectroscopy for the study of ion Coulomb crystals
2015
Ion Coulomb crystals are currently establishing themselves as a highly controllable test-bed for mesoscopic systems of statistical mechanics. The detailed experimental interrogation of the dynamics of these crystals however remains an experimental challenge. In this work, we show how to extend the concepts of multi-dimensional nonlinear spectroscopy to the study of the dynamics of ion Coulomb crystals. The scheme we present can be realized with state-of-the-art technology and gives direct access to the dynamics, revealing nonlinear couplings even in the presence of thermal excitations. We illustrate the advantages of our proposal showing how two-dimensional spectroscopy can be used to detec…
Semiquantum molecular dynamics simulation of thermal properties and heat transport in low-dimensional nanostructures
2012
We present a detailed description of the semi-quantum approach to the molecular dynamics simulation of stochastic dynamics of a system of interacting particles. Within this approach, the dynamics of the system is described with the use of classical Newtonian equations of motion in which the quantum effects are introduced through random Langevin-like forces with a specific power spectral density (the color noise). The color noise describes the interaction of the molecular system with the thermostat. We apply this technique to the simulation of the thermal properties of different low-dimensional nanostructures. Within this approach, we simulate the specific heat and heat transport in carbon n…