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Classical Limit (classical + limit)

Distribution by Scientific Domains

Physics and Astronomy	44%

Selected Abstracts

Gauge-independent quantum dynamics on phase-space of charged scalar particles

FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 2-3 2003
S. Varró
On the basis of the Hamiltonian form of the Klein-Gordon equation of a charged scalar particle field introduced by Feshbach and Villars, the gauge-invariant 2×2 Wigner matrix has been constructed whose diagonal elements describe positive and negative charge densities and the off-diagonal elements correspond to cross-densities in phase-space. The system of coupled transport equations has been derived in case of interaction with an arbitrary external electromagnetic field. A gauge-independent generalization of the free particle representation due to Feshbach and Villars is given, and on the basis of it both the nonrelativistic and the classical limits of the general relativistic quantum Boltzmann-Vlasov equation(RQBVE) is discussed. In the non-relativistic limit (p/mc,0) the set of equations of motion decouple to two independent quantum transport equations describing the dynamics of oppositely charged positon and negaton densities separately. In the classical limit(,,0) two relativistic Boltzmann-Vlasov equations result for the diagonal positon and negaton densities. It is obtained that, though in the latter equations the Planck constant , is absent, the real part of the cross-density does not vanish. [source]

Superresolution planar diffraction tomography through evanescent fields,

INTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 1 2002
Sean K. Lehman
We consider the problem of noninvasively locating objects buried in a layered medium such as land mines in the ground or objects concealed in a wall. In such environments, the transmitter(s) and receiver(s) are frequently within the near-field region of the illuminating radiation. In these cases, the scattered evanescent field carries useful information on the scattering object. Conventional diffraction tomography techniques neglect, by their design, the evanescent field. Under near-field conditions, they treat it as noise as opposed to valid data. If correctly incorporated into a reconstruction algorithm, the evanescent field, which carries high spatial frequency information, can be used to achieve resolution beyond the classical limit of ,/2, or "superresolution." We build on the generalized holography theory presented by Langenberg to develop a planar diffraction tomography algorithm that incorporates evanescent field information to achieve superresolution. Our theory is based on a generalization of the Fourier transform, which allows for complex spatial frequencies in a manner similar to the Laplace transform. We specialize our model to the case of a two-dimensional multimonostatic, wideband imaging system, and derive an extended resolution reconstruction procedure. We implement and apply our reconstruction to two data sets collected using the Lawrence Livermore National Laboratory (LLNL) Micropower Impulse Radar (MIR). © 2002 John Wiley & Sons, Inc. Int J Imaging Syst Technol 12, 16,26, 2002 [source]

Discrete thermodynamics of chemical equilibria and classical limit in thermodynamic simulation

ISRAEL JOURNAL OF CHEMISTRY, Issue 3-4 2007
Boris Zilbergleyt
This article sets forth comprehensive basic concepts of the discrete thermodynamics of chemical equilibrium as balance between internal and external thermodynamic forces. Conditions of chemical equilibrium in the open chemical system are obtained in the form of a logistic map, containing only one new parameter that defines the chemical system's resistance to external impact and its deviation from thermodynamic equilibrium. Solutions to the basic map are bifurcation diagrams that have quite traditional shape but the diagram areas feature specific meanings for chemical systems and constitute the system's domain of states. The article is focused on two such areas: the area of "true" thermodynamic equilibrium and the area of open chemical equilibrium. The border between them represents the classical limit, a transition point between the classical and newly formulated equilibrium conditions. This limit also separates regions of the system ideality, typical for isolated classical systems, and non-ideality due to the limitations imposed on the open system from outside. Numerical examples illustrating the difference between results of classical and discrete thermodynamic simulation methods are presented. The article offers an analytical formula to find the classical limit, compares analytical results with these obtained by simulation, and shows the classical limit dependence upon the chemical reaction stoichiometry and robustness. [source]

Percolation model of hyperbranched polymerization

MACROMOLECULAR SYMPOSIA, Issue 1 2003
Henryk Galina
Abstract Computer simulations of the step-growth homopolymerization of an AB2 monomer have been carried out on a square lattice. No rearrangements of units were made between reaction events. Instead, the capture radius, i.e., the maximum distance between the randomly selected unit and its reaction partner was changed. The reaction was considered as controlled either by diffusion and local concentration fluctuations or by the law of mass action (classical limit). The size distribution of polymer species and the extent of cyclization reactions in the polymerization are discussed. [source]

Reduction of quantum fluctuations by anisotropy fields in Heisenberg ferro- and antiferromagnets

ANNALEN DER PHYSIK, Issue 10-11 2009
B. Vogt
Abstract The physical properties of quantum systems, which are described by the anisotropic Heisenberg model, are influenced by thermal as well as by quantum fluctuations. Such a quantum Heisenberg system can be profoundly changed towards a classical system by tuning two parameters, namely the total spin and the anisotropy field: Large easy-axis anisotropy fields, which drive the system towards the classical Ising model, as well as large spin quantum numbers suppress the quantum fluctuations and lead to a classical limit. We elucidate the incipience of this reduction of quantum fluctuations. In order to illustrate the resulting effects we determine the critical temperatures for ferro- and antiferromagnets and the ground state sublattice magnetization for antiferromagnets. The outcome depends on the dimension, the spin quantum number and the anisotropy field and is studied for a widespread range of these parameters. We compare the results obtained by: Classical Mean Field, Quantum Mean Field, Linear Spin Wave and Random Phase Approximation. Our findings are confirmed and quantitatively improved by numerical Quantum Monte Carlo simulations. The differences between the ferromagnet and antiferromagnet are investigated. We finally find a comprehensive picture of the classical trends and elucidate the suppression of quantum fluctuations in anisotropic spin systems. In particular, we find that the quantum fluctuations are extraordinarily sensitive to the presence of small anisotropy fields. This sensitivity can be quantified by introducing an "anisotropy susceptibility". [source]

Reduction of quantum fluctuations by anisotropy fields in Heisenberg ferro- and antiferromagnets

Semiclassical limit for the Schrödinger-Poisson equation in a crystal

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 7 2001
Philippe Bechouche
We give a mathematically rigorous theory for the limit from a weakly nonlinear Schrödinger equation with both periodic and nonperiodic potential to the semiclassical version of the Vlasov equation. To this end we perform simultaneously a classical limit (vanishing Planck constant) and a homogenization limit of the periodic structure (vanishing lattice length taken proportional to the Planck constant). We introduce a new variant of Wigner transforms, namely the "Wigner Bloch series" as an adaption of the Wigner series for density matrices related to two different "energy bands." Another essential tool are estimates on the commutators of the projectors into the Floquet subspaces ("band subspaces") and the multiplicative potential operator that destroy the invariance of these band subspaces under the periodic Hamiltonian. We assume the initial data to be concentrated in isolated bands but allow for band crossing of the other bands which is the generic situation in more than one space dimension. The nonperiodic potential is obtained from a coupling to the Poisson equation, i.e., we take into account the self-consistent Coulomb interaction. Our results hold also for the easier linear case where this potential is given. We hence give the first rigorous derivation of the (nonlinear) "semiclassical equations" of solid state physics widely used to describe the dynamics of electrons in semiconductors. © 2001 John Wiley & Sons, Inc. [source]