Search results for " Statistical"

Molecular correlations in a supercooled liquid

1998

We present static and dynamic properties of molecular correlation functions S_{lmn,l'm'n'}(q,t) in a simulated supercooled liquid of water molecules, as a preliminary effort in the direction of solving the molecular mode coupling theory (MMCT) equations for supercooled molecular liquids. The temperature and time dependence of various molecular correlation functions, calculated from 250 ns long molecular dynamics simulations, show the characteristic patterns predicted by MMCT and shed light on the driving mechanism responsible for the slowing down of the molecular dynamics. We also discuss the symmetry properties of the molecular correlation functions which can be predicted on the basis of t…

Finite-size tests of hyperscaling.

1985

The possible form of hyperscaling violations in finite-size scaling theory is discussed. The implications for recent tests in Monte Carlo simulations of the d = 3 Ising model are examined, and new results for the d = 5 Ising model are presented.

Nonequilibrium statistical mechanics of dilute relativistic plasmas

2005

Statistical Mechanics of the Sine-Gordon Equation

1986

We give two fundamental methods for evaluation of classical free energies of all the integrable models admitting soliton solutions; the sine-Gordon equation is one example. Periodic boundary conditions impose integral equations for allowed phonon and soliton momenta. From these, generalized Bethe-Ansatz and functional-integration methods using action-angle variables follow. Results for free energies coincide, and coincide with those that we find by transfer-integral methods. Extension to the quantum case, and quantum Bethe Ansatz, on the lines to be reported elsewhere for the sinh-Gordon equation, is indicated.

Statistical quantities in particle collisions

1972

Abstract Statistical quantities for particle collisions are defined using the analogy between the phase-space integral in multiparticle collisions and that in relativistic quantum statistical mechanics. The analogs of thermodynamic quantities are computed for the uncorrelated jet model. A relativistic derivation for the mass spectrum of hadrons is given and thermodynamic quantities are calculated for a system with this spectrum.

The Usefulness of Lie Brackets: From Classical and Quantum Mechanics to Quantum Electrodynamics

2020

We know that in Hamiltonian systems a dynamic function f(q, p) develops in time according to

Quantum Solitons on Quantum Chaos: Coherent Structures, Anyons, and Statistical Mechanics

1991

This paper is concerned with the exact evaluation of functional integrals for the partition function Z (free energy F = -β -1 ln Z, β -1 = temperature) for integrable models like the quantum and classical sine-Gordon (s-G) models in 1+1 dimensions.1–12 These models have wide applications in physics and are generic (and important) in that sense. The classical s-G model in 1+1 dimensions $${\phi _{xx}} - {\phi _{tt}} = {m^2}\sin \phi$$ (1) (m > 0 is a “mass”) has soliton (kink, anti-kink and breather) solutions. In Refs 1–12 we have reported a general theory of ‘soliton statistical mechanics’ (soliton SM) in which the particle description can be seen in terms of ‘solitons’ and ‘phonons’. The …

Tensor Network Annealing Algorithm for Two-Dimensional Thermal States

2019

Tensor network methods have become a powerful class of tools to capture strongly correlated matter, but methods to capture the experimentally ubiquitous family of models at finite temperature beyond one spatial dimension are largely lacking. We introduce a tensor network algorithm able to simulate thermal states of two-dimensional quantum lattice systems in the thermodynamic limit. The method develops instances of projected entangled pair states and projected entangled pair operators for this purpose. It is the key feature of this algorithm to resemble the cooling down of the system from an infinite temperature state until it reaches the desired finite-temperature regime. As a benchmark we …

Quantum transport of non-interacting Fermi gas in an optical lattice combined with harmonic trapping

2004

We consider a non-interacting Fermi gas in a combined harmonic and periodic potential. We calculate the energy spectrum and simulate the motion of the gas after sudden replacement of the trap center. For different parameter regimes, the system presents dipole oscillations, damped oscillations around the replaced center, and localization. The behaviour is explained by the change of the energy spectrum from linear to quadratic.

Dynamical coexistence in moderately polydisperse hard-sphere glasses

2020

We perform extensive numerical simulations of a paradigmatic model glass former, the hard-sphere fluid with 10% polydispersity. We sample from the ensemble of trajectories with fixed observation time, whereby single trajectories are generated by event-driven molecular dynamics. We show that these trajectories can be characterized in terms of the local structure, and we find a dynamical-structural (active-inactive) phase transition between two dynamical phases: one dominated by liquidlike trajectories with a low degree of local order and one dominated by glassylike trajectories with a high degree of local order. We show that both phases coexist and are separated by a spatiotemporal interface…