Search results for "Statistical physic"
showing 10 items of 1403 documents
Kohn-Sham Decomposition in Real-Time Time-Dependent Density-Functional Theory An Efficient Tool for Analyzing Plasmonic Excitations
2017
The real-time-propagation formulation of time-dependent density-functional theory (RT-TDDFT) is an efficient method for modeling the optical response of molecules and nanoparticles. Compared to the widely adopted linear-response TDDFT approaches based on, e.g., the Casida equations, RT-TDDFT appears, however, lacking efficient analysis methods. This applies in particular to a decomposition of the response in the basis of the underlying single-electron states. In this work, we overcome this limitation by developing an analysis method for obtaining the Kohn-Sham electron-hole decomposition in RT-TDDFT. We demonstrate the equivalence between the developed method and the Casida approach by a be…
Correspondence between generalized binomial field states and coherent atomic states
2008
We show that the N-photon generalized binomial states of electromagnetic field may be put in a bijective mapping with the coherent atomic states of N two-level atoms. We exploit this correspondence to simply obtain both known and new properties of the N-photon generalized binomial states. In particular, an over-complete basis of these binomial states and an orthonormal basis are obtained. Finally, the squeezing properties of generalized binomial state are analyzed.
Experimental Engineering of Arbitrary Qudit States with Discrete-Time Quantum Walks
2019
The capability to generate and manipulate quantum states in high-dimensional Hilbert spaces is a crucial step for the development of quantum technologies, from quantum communication to quantum computation. One-dimensional quantum walk dynamics represents a valid tool in the task of engineering arbitrary quantum states. Here we affirm such potential in a linear-optics platform that realizes discrete-time quantum walks in the orbital angular momentum degree of freedom of photons. Different classes of relevant qudit states in a six-dimensional space are prepared and measured, confirming the feasibility of the protocol. Our results represent a further investigation of quantum walk dynamics in p…
Inferring directionality of coupled dynamical systems using Gaussian process priors: Application on neurovascular systems
2022
Dynamical system theory has recently shown promise for uncovering causality and directionality in complex systems, particularly using the method of convergent cross mapping (CCM). In spite of its success in the literature, the presence of process noise raises concern about CCM's ability to uncover coupling direction. Furthermore, CCM's capacity to detect indirect causal links may be challenged in simulated unidrectionally coupled Rossler-Lorenz systems. To overcome these limitations, we propose a method that places a Gaussian process prior on a cross mapping function (named GP-CCM) to impose constraints on local state space neighborhood comparisons. Bayesian posterior likelihood and…
Assessing Transfer Entropy in cardiovascular and respiratory time series: A VARFI approach
2021
In the study of complex biomedical systems represented by multivariate stochastic processes, such as the cardiovascular and respiratory systems, an issue of great relevance is the description of the system dynamics spanning multiple temporal scales. Recently, the quantification of multiscale complexity based on linear parametric models, incorporating autoregressive coefficients and fractional integration, encompassing short term dynamics and long-range correlations, was extended to multivariate time series. Within this Vector AutoRegressive Fractionally Integrated (VARFI) framework formalized for Gaussian processes, in this work we propose to estimate the Transfer Entropy, or equivalently G…
The Poisson Point Process
2020
Poisson point processes can be used as a cornerstone in the construction of very different stochastic objects such as, for example, infinitely divisible distributions, Markov processes with complex dynamics, objects of stochastic geometry and so forth.
Thermodynamics: Classical Framework
2016
This chapter starts with a summary of the thermodynamic potentials and the relationships between them which are obtained from Legendre transformation. This is followed by an excursion to some important global properties of materials such as specific heat, expansion coefficients and others. The thermodynamic relations provide the basis for a discussion of continuous changes of state which are illustrated by the Joule-Thomson effect and the Van der Waals gas. These are models which are more realistic than the ideal gas. The discussion of Carnot cycles leads to and illustrates the second and third laws of thermodynamics. The chapter closes with a discussion of entropy as a concave function of …
On the autocorrelation function of Rice processes for unsymmetrical doppler power spectral densities
2010
In this paper, we derive an analytical expression for the ACF of Rice processes in the general case of unsymmetrical Doppler power spectral densities. This expression, which is obtained based on the multidimensional Gaussian distribution approach, is shown to cover the ACF of Rayleigh processes as a special case. Various numerical examples are presented to illustrate the impact of the channel parameters on the ACF. Computer simulations, considering the von Mises distribution for the angle of arrivals, are also performed to check the validity of the analytical result. Finally, the analysis of the covariance spectrum is addressed.
Non-linear systems under parametric alpha-stable LÉVY WHITE NOISES
2005
In this study stochastic analysis of nonlinear dynamical systems under a-stable, multiplicative white noise has been performed. Analysis has been conducted by means of the Ito rule extended to the case of α-stable noises. In this context the order of increments of Levy process has been evaluated and differential equations ruling the evolutions of statistical moments of either parametrically and external dynamical systems have been obtained. The extended Ito rule has also been used to yield the differential equation ruling the evolution of the characteristic function for parametrically excited dynamical systems. The Fourier transform of the characteristic function, namely the probability den…
Self-regulation mechanism of an ecosystem in a non-Gaussian fluctuation regime
1996
We study a dynamical model for an ecological network of many interacting species. We consider a Malthus-Verhulst type of self-regulation mechanism. In the framework of the mean field theory we study the nonlinear relaxation in three different cases: (a) towards the equilibrium state, (b) towards the absorbing barrier, (c) at the critical point. We obtain asymptotic behavior in all different cases for the time average of the process. The dynamical behavior of the system, in the limit of infinitely many interacting species, is investigated in the stability and instability conditions and theoretical results are compared with numerical simulations. \textcopyright{} 1996 The American Physical So…