Search results for "Matematica"
showing 10 items of 1637 documents
Quantum corrections to the Wigner crystal: A Hartree-Fock expansion
1993
The quantum corrections to the two-dimensional Wigner crystal, for filling \ensuremath{\nu}\ensuremath{\le}1/3, are discussed by using a Hartree-Fock expansion based on wave functions which are (i) related to one another by magnetic translations, (ii) orthonormal, and (iii) strongly localized. Such wave functions are constructed in terms of Gaussians that are localized at the sites of a triangular (Wigner) lattice and have a small overlap c. The ground-state energy per particle is calculated by an expansion in \ensuremath{\surd}\ensuremath{\nu} and in \ensuremath{\delta}\ensuremath{\equiv}${\mathit{c}}^{1/4}$, which is rapidly convergent and stable under the thermodynamical limit. In partic…
New structures in the theory of the laser model. II. Microscopic dynamics and a nonequilibrium entropy principle
1998
In a recent article, Alli and Sewell [J. Math. Phys. 36, 5598 (1995)] formulated a new version of the Dicke-Hepp-Lieb laser model in terms of quantum dynamical semigroups, and thereby extended the macroscopic picture of the model. In the present article, we complement that picture with a corresponding microscopic one, which carries the following new results. (a) The local microscopic dynamics of the model is piloted by the classical, macroscopic field, generated by the collective action of its components; (b) the global state of the system carries no correlations between its constituent atoms after transient effects have died out; and (c) in the latter situation, the state of the system at …
Phase transition in liquid 4HE by a mean field model
2013
In this work the transition of 4He at the lambda line in presence of a Cattaneo- Maxwell heat flux is studied. A hydrodynamical model is formulated, which chooses as fundamental fields the velocity, the temperature, the heat flux and a phase field function f, for which a time dependent Ginzburg-Landau equation is proposed. Using this model we are able to describe the phase transition and to obtain the pressure-temperature phase diagram which represents the transition, the thermodynamic restrictions and a maximum theorem for the phase field.
Some results on the dynamics and transition probabilities for non self-adjoint hamiltonians
2015
We discuss systematically several possible inequivalent ways to describe the dynamics and the transition probabilities of a quantum system when its hamiltonian is not self-adjoint. In order to simplify the treatment, we mainly restrict our analysis to finite dimensional Hilbert spaces. In particular, we propose some experiments which could discriminate between the various possibilities considered in the paper. An example taken from the literature is discussed in detail.
The Stochastic Limit of the Fröhlich Hamiltonian: Relations with the Quantum Hall Effect
2003
We propose a model of an approximatively two-dimensional electron gas in a uniform electric and magnetic field and interacting with a positive background through the Fröhlich Hamiltonian. We consider the stochastic limit of this model and we find the quantum Langevin equation and the generator of the master equation. This allows us to calculate the explicit form of the conductivity and the resistivity tensors and to deduce a fine tuning condition (FTC) between the electric and the magnetic fields. This condition shows that the x-component of the current is zero unless a certain quotient, involving the physical parameters, takes values in a finite set of physically meaningful rational number…
Waves Propagation in Turbulent Superfluid Helium in Presence of Combined Rotation and Counterflow
2010
A complete study of the propagation of waves (namely longitudinal density and temperature waves, longitudinal and transversal velocity waves and heat waves) in turbulent superfluid helium is made in three situations: a rotating frame, a thermal counterflow, and the simultaneous combination of thermal counterflow and rotation. Our analysis aims to obtain as much as possible information on the tangle of quantized vortices from the wave speed and attenuation factor of these different waves, depending on their relative direction of propagation with respect to the rotation vector.
Symmetry, winding number, and topological charge of vortex solitons in discrete-symmetry media
2009
[EN] We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schrodinger equation. We show that these solutions present a central phase singularity whose charge is restricted by symmetry arguments. Consequently, we demonstrate that the existence of high-charged discrete vortices is related to the presence of other off-axis phase singularities, whose positions and charges are also restricted by symmetry arguments. To illustrate our theoretical results, we offer two numerical examples of high-charged discrete vortices in photonic crystal fibers showing hexagonal discrete rotational invariance
Singular behavior of a vortex layer in the zero thickness limit
2017
The aim of this paper is to study the Euler dynamics of a 2D periodic layer of non uniform vorticity. We consider the zero thickness limit and we compare the Euler solution with the vortex sheet evolution predicted by the Birkhoff-Rott equation. The well known process of singularity formation in shape of the vortex sheet correlates with the appearance of several complex singularities in the Euler solution with the vortex layer datum. These singularities approach the real axis and are responsible for the roll-up process in the layer motion.
Nonstandard analysis in classical physics and quantum formal scattering
1988
After a rigorous introduction to hyperreal numbers, we give in terms of non standard analysis, (1) a Lagrangian statement of classical physics, and (2) a statement of formal quantum scattering. © 1988 Plenum Publishing Corporation.
Supersymmetric associated vector coherent states and generalized Landau levels arising from two-dimensional supersymmetry
2008
We describe a method for constructing vector coherent states for quantum supersymmetric partner Hamiltonians. The method is then applied to such partner Hamiltonians arising from a generalization of the fractional quantum Hall effect. Explicit examples are worked out.