Search results for "Statistical"
showing 10 items of 4960 documents
Slow-light solitons
2007
We investigate propagation of slow-light solitons in atomic media described by the nonlinear � -model. Under a physical assumption, appropriate to the slow light propagation, we reduce the � -scheme to a simplified nonlinear model, which is also relevant to 2D dilatonic gravity. Exact solutions describing various regimes of stopping slow-light solitons can then be readily derived.
Surface free energy of the open XXZ spin-1/2 chain
2012
We study the boundary free energy of the XXZ spin-$\tf{1}{2}$ chain subject to diagonal boundary fields. We first show that the representation for its finite Trotter number approximant obtained by Bortz, Frahm and G\"{o}hmann is related to the partition function of the six-vertex model with reflecting ends. Building on the Tsuchiya determinant representation for the latter quantity we are able to take the infinite Trotter number limit. This yields a representation for the surface free energy which involves the solution of the non-linear integral equation that governs the thermodynamics of the XXZ spin-1/2 chain subject to periodic boundary conditions. We show that this integral representati…
Complete spectrum and scalar products for the open spin-1/2 XXZ quantum chains with non-diagonal boundary terms
2013
We use the quantum separation of variable (SOV) method to construct the eigenstates of the open XXZ chain with the most general boundary terms. The eigenstates in the inhomogeneous case are constructed in terms of solutions of a system of quadratic equations. This SOV representation permits us to compute scalar products and can be used to calculate form factors and correlation functions.
Monte Carlo study of asymmetric 2D XY model
1997
Employing the Polyakov-Susskind approximation in a field theoretical treatment, the t-J model for strongly correlated electrons in two dimensions has recently been shown to map effectively onto an asymmetric two-dimensional classical XY model. The critical temperature at which charge-spin separation occurs in the t-J model is determined by the location of the phase transitions of this effective model. Here we report results of Monte Carlo simulations which map out the complete phase diagram in the two-dimensional parameter space and also shed some light on the critical behaviour of the transitions.
Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from separation of variables
2014
28 pages; International audience; We solve the longstanding problem to define a functional characterization of the spectrum of the transfer matrix associated to the most general spin-1/2 representations of the 6-vertex reflection algebra for general inhomogeneous chains. The corresponding homogeneous limit reproduces the spectrum of the Hamiltonian of the spin-1/2 open XXZ and XXX quantum chains with the most general integrable boundaries. The spectrum is characterized by a second order finite difference functional equation of Baxter type with an inhomogeneous term which vanishes only for some special but yet interesting non-diagonal boundary conditions. This functional equation is shown to…
The distribution of velocities in an ensemble of accelerated particles on a surface
2016
An ensemble of particles diffusing with acceleration on a surface is considered as a 2D billiard system. The process of the finite-time diffusion of particles is studied using the balance equation. The probability distribution functions of the velocity and lifetime of particles are obtained analytically and by means of numerical simulations. A thermodynamic interpretation of the process is discussed. The effective temperature and entropy obey the relationship for an ideal gas.
Spatial decoherence in QED
2006
We consider the dynamics of a charged free particle, initially described by a coherent wave packet, interacting with an electromagnetic field characterized by the temperature T, considered as the environment. We have used dipole approximation neglecting the potential vector quadratic term in the minimal coupling Hamiltonian. This leads to the loss of coherence in the momentum representation, described by the decay of the off diagonal elements of the particle reduced density matrix, while the populations remain constant. Here we extend the analysis to the coordinate representation. We compute the particle reduced density matrix in this basis, analyzing in particular the mixing of various ef…
Dynamical block analysis in a non-equilibrium system
1991
Abstract We present molecular dynamics simulation results of quenches into the unstable region of a two-dimensional Lennard-Jones system. The evolution of the system from the non-equilibrium state into equilibrium was analyzed with a dynamical block analysis. This can lead to a new approach in the study of non-equilibrium phenomena. We show that with such an analysis one can obtain results on the dynamic evolution as the system evolves, consistent with those obtained from and analysis of the pair-distribution function, structure factor and excess energy. The simulations were carried out on the parallel computer of the condensed matter theory group at the University of Mainz.
Quantum graphs with mixed dynamics: the transport/diffusion case
2013
We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly nonlocal couplings at the boundary. We provide sufficient conditions for these to be governed by a contractive semigroup on a Hilbert space naturally associated with the system. We show that our setting is also adequate to discuss specific systems of diffusion equations with boundary delays.
On multi-scale percolation behaviour of the effective conductivity for the lattice model with interacting particles
2015
Recently, the effective medium approach using 2x2 basic cluster of model lattice sites to predict the conductivity of interacting droplets has been presented by Hattori et al. To make a step aside from pure applications, we have studied earlier a multi-scale percolation, employing any kxk basic cluster for non-interacting particles. Here, with interactions included, we examine in what way they alter the percolation threshold for any cluster case. We found that at a fixed length scale k the interaction reduces the range of shifts of the percolation threshold. To determine the critical concentrations, the simplified model is used. It diminishes the number of local conductivities into two main…