37,863 research outputs found
Particle Systems with Stochastic Passing
We study a system of particles moving on a line in the same direction.
Passing is allowed and when a fast particle overtakes a slow particle, it
acquires a new velocity drawn from a distribution P_0(v), while the slow
particle remains unaffected. We show that the system reaches a steady state if
P_0(v) vanishes at its lower cutoff; otherwise, the system evolves
indefinitely.Comment: 5 pages, 5 figure
Information propagation for interacting particle systems
We show that excitations of interacting quantum particles in lattice models
always propagate with a finite speed of sound. Our argument is simple yet
general and shows that by focusing on the physically relevant observables one
can generally expect a bounded speed of information propagation. The argument
applies equally to quantum spins, bosons such as in the Bose-Hubbard model,
fermions, anyons, and general mixtures thereof, on arbitrary lattices of any
dimension. It also pertains to dissipative dynamics on the lattice, and
generalizes to the continuum for quantum fields. Our result can be seen as a
meaningful analogue of the Lieb-Robinson bound for strongly correlated models.Comment: 4 pages, 1 figure, minor change
Renormalization approach to many-particle systems
This paper presents a renormalization approach to many-particle systems. By
starting from a bare Hamiltonian with an
unperturbed part and a perturbation ,we define an
effective Hamiltonian which has a band-diagonal shape with respect to the
eigenbasis of . This means that all transition matrix elements are
suppressed which have energy differences larger than a given cutoff
that is smaller than the cutoff of the original Hamiltonian. This
property resembles a recent flow equation approach on the basis of continuous
unitary transformations. For demonstration of the method we discuss an exact
solvable model, as well as the Anderson-lattice model where the well-known
quasiparticle behavior of heavy fermions is derived.Comment: 11 pages, final version, to be published in Phys. Rev.
Trimmed trees and embedded particle systems
In a supercritical branching particle system, the trimmed tree consists of
those particles which have descendants at all times. We develop this concept in
the superprocess setting. For a class of continuous superprocesses with Feller
underlying motion on compact spaces, we identify the trimmed tree, which turns
out to be a binary splitting particle system with a new underlying motion that
is a compensated h-transform of the old one. We show how trimmed trees may be
estimated from above by embedded binary branching particle systems.Comment: Published by the Institute of Mathematical Statistics
(http://www.imstat.org) in the Annals of Probability
(http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000009
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