Search results for "classical mechanics"
showing 10 items of 1211 documents
General restrictions for the relaxation constants of the polarization moments of the density matrix
1992
General inequalities for the relaxation constants of polarization moments are examined. Concrete numerical limitations for the values of these constants are obtained. In recent years it has been generally accepted to characterize the distribution of the angular momentum j of atomic as well as molecular states in the framework of the irreducible tensorial operators PG. The state is described by means of polarization moments p& which are the expansion coefficients of the angular momentum density matrix pm,,,, on the tensorial operators pz:
Towards a kinetic theory for fermions with quantum coherence
2008
A new density matrix and corresponding quantum kinetic equations are introduced for fermions undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). A central element in our derivation is finding new spectral solutions for the 2-point Green's functions written in the Wigner representation, that are carrying the information of the quantum coherence. Physically observable density matrix is then defined from the bare singular 2-point function by convoluting it with the extrenous information about the state of the system. The formalism is shown to reproduce familiar results from the Dirac equation approach, like Klein problem and nonlocal re…
Kinetic transport theory with quantum coherence
2008
We derive transport equations for fermions and bosons in spatially or temporally varying backgrounds with special symmetries, by use of the Schwinger-Keldysh formalism. In a noninteracting theory the coherence information is shown to be encoded in new singular shells for the 2-point function. Imposing this phase space structure to the interacting theory leads to a a self-consistent equation of motion for a physcial density matrix, including coherence and a well defined collision integral. The method is applied e.g. to demonstrate how an initially coherent out-of-equlibrium state approaches equlibrium through decoherence and thermalization.
Hard-sphere fluids in annular wedges: density distributions and depletion potentials.
2009
We analyze the density distribution and the adsorption of solvent hard spheres in an annular slit formed by two large solute spheres or a large solute and a wall at close distances by means of fundamental measure density functional theory, anisotropic integral equations and simulations. We find that the main features of the density distribution in the slit are described by an effective, two--dimensional system of disks in the vicinity of a central obstacle. For large solute--solvent size ratios, the resulting depletion force has a straightforward geometrical interpretation which gives a precise "colloidal" limit for the depletion interaction. For intermediate size ratios 5...10 and high sol…
Fluids of hard ellipsoids: Phase diagram including a nematic instability from Percus-Yevick theory
1999
An important aspect of molecular fluids is the relation between orientation and translation parts of the two-particle correlations. Especially the detailed knowledge of the influence of orientation correlations is needed to explain and calculate in detail the occurrence of a nematic phase. The simplest model system which shows both orientation and translation correlations is a system of hard ellipsoids. We investigate an isotropic fluid formed of hard ellipsoids with Percus-Yevick theory. Solving the Percus-Yevick equations self-consistently in the high density regime gives a clear criterion for a nematic instability. We calculate in detail the equilibrium phase diagram for a fluid of hard …
Devil’s vortex-lenses
2009
In this paper we present a new kind of vortex lenses in which the radial phase distribution is characterized by the "devil's staircase" function. The focusing properties of these fractal DOEs coined Devil's vortex-lenses are analytically studied and the influence of the topological charge is investigated. It is shown that under monochromatic illumination a vortex devil's lens give rise a focal volume containing a delimited chain of vortices that are axially distributed according to the self-similarity of the lens.
Experimental demonstration of hyperbolic patterns.
2008
We give experimental evidence of hyperbolic patterns in a nonlinear optical resonator. Such transverse patterns are a new kind of 2D dissipative structures, characterized by a distribution of the active modes along hyperbolas in the transverse wave-vector domain, in contrast with the usual (elliptic) patterns where the active modes distribute along rings. The hyperbolic character is realized by manipulating diffraction inside the optical resonator with cylindrical lenses. We also investigate theoretically hyperbolic patterns in corresponding Swift-Hohenberg models.
Inspirations for EO polymer design gained from modeling of chromophore poling by Langevin dynamics
2013
One of the possibilities to create organic molecular material for NLO applications are polymers with dispersed NLO active chromophores. These molecules must be acentrically ordered by applying an external electric poling field. The NLO efficiency depends on dipole moment, molecular hyperpolarizabilities, concentration of the chromophores and external poling field strength. Calculating, from first principles, the extent of the alignment and via this NLO efficiency has proven to be challenging. One approach to solve this problem is pure analytic statistical mechanics treatment, what could be enhanced by Monte Carlo ( MC ) statistical mechanical modelling. The chromophore molecules usually hav…
Quantum Walks with Multiple or Moving Marked Locations
2008
We study some properties of quantum walks on the plane. First, we discuss the behavior of quantum walks when moving marked locations are introduced. Second, we present an exceptional case, when quantum walk fails to find any of the marked locations.
Modulational instability and two-dimensional dynamical structures
2008
A process of nonlinear structure formation on a two-dimensional lattice is proposed. The basic model consists of a two-dimensional lattice equipped at each node with a molecule or dipole rotating in the lattice plane. The interactions involved in the model are reduced to a periodic lattice. Such a discrete system can be applied to the problem of molecule adsorption on a substrate crystal surface, for instance. The continuum approximation of the model leads to a 2-D sine-Gordon system including nonlinear couplings, which itself can be reduced to a 2-D nonlinear Schrodinger equation in the low amplitude limit. Spatio-temporal structure formation is investigated by means of numerical simulatio…