Search results for "Statistical Mechanic"
showing 10 items of 707 documents
Geometric phase induced by a cyclically evolving squeezed vacuum reservoir
2006
We propose a new way to generate an observable geometric phase by means of a completely incoherent phenomenon. We show how to imprint a geometric phase to a system by "adiabatically" manipulating the environment with which it interacts. As a specific scheme we analyse a multilevel atom interacting with a broad-band squeezed vacuum bosonic bath. As the squeezing parameters are smoothly changed in time along a closed loop, the ground state of the system acquires a geometric phase. We propose also a scheme to measure such geometric phase by means of a suitable polarization detection.
Scattering lengths and universality in superdiffusive L\'evy materials
2012
We study the effects of scattering lengths on L\'evy walks in quenched one-dimensional random and fractal quasi-lattices, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling properties of the random-walk probability distribution, we show that the effect of the varying scattering length can be reabsorbed in the multiplicative coefficient of the scaling length. This leads to a superscaling behavior, where the dynamical exponents and also the scaling functions do not depend on the value of the scattering length. Within the scaling framework, we obtain an exact expression for the multiplicative coefficient as a function of the scattering length both in the a…
Disorder in molecular crystals justified with the help of statistical mechanics: a case of two enantiomer solid solutions
2019
An elegant statistical mechanics approach has been exploited in combination with accurate quantum chemical calculations to justify the disorder in two previously reported racemic solids. Generated canonical ensembles and performed lattice energy calculations show that the disorder in the studied systems of small organic enantiomer molecules can be modelled with great accuracy. Ensemble averages fully correspond to the disordered structure models repeatedly obtained in X-ray diffraction studies. The present work not only demonstrates that disorder and its extent in molecular crystals can be theoretically calculated, but also explains from a thermodynamic point of view the origins of the rare…
Levy targeting and the principle of detailed balance
2011
We investigate confining mechanisms for Lévy flights under premises of the principle of detailed balance. In this case, the master equation of the jump-type process admits a transformation to the Lévy-Schrödinger semigroup dynamics akin to a mapping of the Fokker-Planck equation into the generalized diffusion equation. This sets a correspondence between above two stochastic dynamical systems, within which we address a (stochastic) targeting problem for an arbitrary stability index μ ε (0,2) of symmetric Lévy drivers. Namely, given a probability density function, specify the semigroup potential, and thence the jump-type dynamics for which this PDF is actually a long-time asymptotic (target) …
Generalized Wiener Process and Kolmogorov's Equation for Diffusion induced by Non-Gaussian Noise Source
2005
We show that the increments of generalized Wiener process, useful to describe non-Gaussian white noise sources, have the properties of infinitely divisible random processes. Using functional approach and the new correlation formula for non-Gaussian white noise we derive directly from Langevin equation, with such a random source, the Kolmogorov's equation for Markovian non-Gaussian process. From this equation we obtain the Fokker-Planck equation for nonlinear system driven by white Gaussian noise, the Kolmogorov-Feller equation for discontinuous Markovian processes, and the fractional Fokker-Planck equation for anomalous diffusion. The stationary probability distributions for some simple cas…
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…
Path-wise versus kinetic modeling for equilibrating non-Langevin jump-type processes
2014
We discuss two independent methods of solution of a master equation whose biased jump transition rates account for long jumps of L\'{e}vy-stable type and nonetheless admit a Boltzmannian (thermal) equilibrium to arise in the large time asymptotics of a probability density function $\rho (x,t)$. Our main goal is to demonstrate a compatibility of a {\it direct} solution method (an explicit, albeit numerically assisted, integration of the master equation) with an {\it indirect} path-wise procedure, recently proposed in [Physica {\bf A 392}, 3485, (2013)] as a valid tool for a dynamical analysis of non-Langevin jump-type processes. The path-wise method heavily relies on an accumulation of large…
Non-Monotonic Concentration Dependence of the Electro-Phoretic Mobility of Charged Spheres in Realistic Salt Free Suspensions
2020
Using super-heterodyne Doppler velocimetry with multiple scattering correction, we extend the opti-cally accessible range of concentrations in experiments on colloidal electro-kinetics. We here meas-ured the electro-phoretic mobility and the DC conductivity of aqueous charged sphere suspensions covering about three orders of magnitude in particle concentrations and transmissions as low as 40%. The extended concentration range for the first time allows the demonstration of a non-monotonic con-centration dependence of the mobility for a single particle species. Our observations reconcile previ-ous experimental observations made on other species over restricted concentration ranges. We com-par…
Feigenbaum graphs: a complex network perspective of chaos
2011
The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map…
A Novel Wideband MIMO Car-to-Car Channel Model Based on a Geometrical Semi-Circular Tunnel Scattering Model
2016
In this paper, we present a wideband multiple-input multiple-output (MIMO) car-to-car (C2C) channel model based on a geometrical semi-circular tunnel (SCT) scattering model. From the geometrical SCT scattering model, a reference channel model is derived under the assumption of single-bounce scattering in line-of-sight (LOS) and non-LOS (NLOS) propagation environments. In the proposed reference channel model, it is assumed that an infinite number of scatterers are randomly distributed on the tunnel wall. Starting from the geometrical scattering model, the time-variant transfer function (TVTF) is derived, and its correlation properties in time, frequency, and space are studied. Expressions ar…