13 research outputs found
Stochastic Duality and Orthogonal Polynomials
For a series of Markov processes we prove stochastic duality relations with duality functions given by orthogonal polynomials. This means that expectations with respect to the original process (which evolves the variable of the orthogonal polynomial) can be studied via expectations with respect to the dual process (which evolves the index of the polynomial). The set of processes include interacting particle systems, such as the exclusion process, the inclusion process and independent random walkers, as well as interacting diffusions and redistribution models of Kipnis–Marchioro–Presutti type. Duality functions are given in terms of classical orthogonal polynomials, both of discrete and continuous variable, and the measure in the orthogonality relation coincides with the process stationary measure
A Symmetry Property of Momentum Distribution Functions in the Nonequilibrium Steady State of Lattice Thermal Conduction
We study a symmetry property of momentum distribution functions in the steady
state of heat conduction. When the equation of motion is symmetric under change
of signs for all dynamical variables, the distribution function is also
symmetric. This symmetry can be broken by introduction of an asymmetric term in
the interaction potential or the on-site potential, or employing the thermal
walls as heat reservoirs. We numerically find differences of behavior of the
models with and without the on-site potential.Comment: 13 pages. submitted to JPS
Controlling the energy flow in nonlinear lattices: a model for a thermal rectifier
We address the problem of heat conduction in 1-D nonlinear chains; we show
that, acting on the parameter which controls the strength of the on site
potential inside a segment of the chain, we induce a transition from conducting
to insulating behavior in the whole system. Quite remarkably, the same
transition can be observed by increasing the temperatures of the thermal baths
at both ends of the chain by the same amount. The control of heat conduction by
nonlinearity opens the possibility to propose new devices such as a thermal
rectifier.Comment: 4 pages with figures included. Phys. Rev. Lett., to be published
(Ref. [10] corrected
Heat transport by lattice and spin excitations in the spin chain compounds SrCuO_2 and Sr_2CuO_3
We present the results of measurements of the thermal conductivity of the
quasi one-dimensional spin S=1/2 chain compound SrCuO_2 in the temperature
range between 0.4 and 300 K along the directions parallel and perpendicular to
the chains. An anomalously enhanced thermal conductivity is observed along the
chains. The analysis of the present data and a comparison with analogous recent
results for Sr_2CuO_3 and other similar materials demonstrates that this
behavior is generic for cuprates with copper-oxygen chains and strong
intrachain interactions. The observed anomalies are attributed to the
one-dimensional energy transport by spin excitations (spinons), limited by the
interaction between spin and lattice excitations. The energy transport along
the spin chains has a non-diffusive character, in agreement with theoretical
predictions for integrable models.Comment: 12 pages (RevTeX), 8 figure
FPU model: Boundary Jumps, Fourier's Law and Scaling
We examine the interplay of surface and volume effects in systems undergoing
heat flow. In particular, we compute the thermal conductivity in the FPU
model as a function of temperature and lattice size, and scaling
arguments are used to provide analytic guidance. From this we show that
boundary temperature jumps can be quantitatively understood, and that they play
an important role in determining the dynamics of the system, relating soliton
dynamics, kinetic theory and Fourier transport.Comment: 5pages, 5 figure