Search results for "Statistical Mechanic"
showing 10 items of 707 documents
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.
Determination of the stochastic evolution equation from noisy experimental data
2003
We have determined the coefficients of the Kardar-Parisi-Zhang equation as functions of coarse graining, which best describe the time evolution and spatial behavior observed for slow-combustion fronts in sheets of paper and magnetic flux fronts in a thin-film high-Tc superconductor. Reconstruction of the relevant equation of motion and its coefficients was mainly based on the inverse method proposed by Lam and Sander [Phys. Rev. Lett. 71, 561 (1993)]. The coefficient of the nonlinear term was also determined from the local slope-dependence of the front velocity.
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.
On the variational approach to Jastrow correlations in nuclei
1973
The variational equation determining the Jastrow correlation function is investigated with particular emphasis on the healing problem for both nuclear matter and finite nuclei. The consequences of several healing conditions are discussed. Furthermore, influences from the choice of the single particle basis and from long range correlations are studied and are found to be small in the short range region.
Two-particle correlations in 400 GeV proton-nucleus interactions
1980
Two-particle inclusive correlations are studied by means of the two-particle rapidity correlation function. The data for the analysis come from an exposure of emulsion plates to a 400 GeV proton beam at FNAL. Predominant short-range correlations among shower particles are found, but this does not allow to exclude some long-range correlation behaviour, in agreement with the results obtained in lower-energy experiments.
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.
Results of Three-Nucleon Calculations
1972
The motivation for studying the nonrelativistic three-body problem originates in the fact that three-particle collisions occur very frequently in many areas of physics a) atomic physics: the scattering of electrons, positrons and protons off hydrogen atoms b) nuclear physics: three-nucleon problem c) statistical mechanics: 3rd virial coefficient d) low-energy elementary particle physics: final-state interactions in three-body decays of hadrons.