35 research outputs found
Stochastic Models on a Ring and Quadratic Algebras. The Three Species Diffusion Problem
The stationary state of a stochastic process on a ring can be expressed using
traces of monomials of an associative algebra defined by quadratic relations.
If one considers only exclusion processes one can restrict the type of algebras
and obtain recurrence relations for the traces. This is possible only if the
rates satisfy certain compatibility conditions. These conditions are derived
and the recurrence relations solved giving representations of the algebras.Comment: 12 pages, LaTeX, Sec. 3 extended, submitted to J.Phys.
Statistical Theory for the Kardar-Parisi-Zhang Equation in 1+1 Dimension
The Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimension dynamically develops
sharply connected valley structures within which the height derivative {\it is
not} continuous. There are two different regimes before and after creation of
the sharp valleys. We develop a statistical theory for the KPZ equation in 1+1
dimension driven with a random forcing which is white in time and Gaussian
correlated in space. A master equation is derived for the joint probability
density function of height difference and height gradient when the forcing correlation length is much smaller than
the system size and much bigger than the typical sharp valley width. In the
time scales before the creation of the sharp valleys we find the exact
generating function of and . Then we express the time
scale when the sharp valleys develop, in terms of the forcing characteristics.
In the stationary state, when the sharp valleys are fully developed, finite
size corrections to the scaling laws of the structure functions are also obtained.Comment: 50 Pages, 5 figure
Local Density Approximation for proton-neutron pairing correlations. I. Formalism
In the present study we generalize the self-consistent
Hartree-Fock-Bogoliubov (HFB) theory formulated in the coordinate space to the
case which incorporates an arbitrary mixing between protons and neutrons in the
particle-hole (p-h) and particle-particle (p-p or pairing) channels. We define
the HFB density matrices, discuss their spin-isospin structure, and construct
the most general energy density functional that is quadratic in local
densities. The consequences of the local gauge invariance are discussed and the
particular case of the Skyrme energy density functional is studied. By varying
the total energy with respect to the density matrices the self-consistent
one-body HFB Hamiltonian is obtained and the structure of the resulting mean
fields is shown. The consequences of the time-reversal symmetry, charge
invariance, and proton-neutron symmetry are summarized. The complete list of
expressions required to calculate total energy is presented.Comment: 22 RevTeX page
Extremal-point Densities of Interface Fluctuations
We introduce and investigate the stochastic dynamics of the density of local
extrema (minima and maxima) of non-equilibrium surface fluctuations. We give a
number of exact, analytic results for interface fluctuations described by
linear Langevin equations, and for on-lattice, solid-on-solid surface growth
models. We show that in spite of the non-universal character of the quantities
studied, their behavior against the variation of the microscopic length scales
can present generic features, characteristic to the macroscopic observables of
the system. The quantities investigated here present us with tools that give an
entirely un-orthodox approach to the dynamics of surface morphologies: a
statistical analysis from the short wavelength end of the Fourier decomposition
spectrum. In addition to surface growth applications, our results can be used
to solve the asymptotic scalability problem of massively parallel algorithms
for discrete event simulations, which are extensively used in Monte-Carlo type
simulations on parallel architectures.Comment: 30 pages, 5 ps figure