6,364 research outputs found
Effect of Noise on Patterns Formed by Growing Sandpiles
We consider patterns generated by adding large number of sand grains at a
single site in an abelian sandpile model with a periodic initial configuration,
and relaxing. The patterns show proportionate growth. We study the robustness
of these patterns against different types of noise, \textit{viz.}, randomness
in the point of addition, disorder in the initial periodic configuration, and
disorder in the connectivity of the underlying lattice. We find that the
patterns show a varying degree of robustness to addition of a small amount of
noise in each case. However, introducing stochasticity in the toppling rules
seems to destroy the asymptotic patterns completely, even for a weak noise. We
also discuss a variational formulation of the pattern selection problem in
growing abelian sandpiles.Comment: 15 pages,16 figure
Bosonization of non-relativistic fermions on a circle: Tomonaga's problem revisited
We use the recently developed tools for an exact bosonization of a finite
number of non-relativistic fermions to discuss the classic Tomonaga
problem. In the case of noninteracting fermions, the bosonized hamiltonian
naturally splits into an O piece and an O piece. We show that in the
large-N and low-energy limit, the O piece in the hamiltonian describes a
massless relativistic boson, while the O piece gives rise to cubic
self-interactions of the boson. At finite and high energies, the low-energy
effective description breaks down and the exact bosonized hamiltonian must be
used. We also comment on the connection between the Tomonaga problem and pure
Yang-Mills theory on a cylinder. In the dual context of baby universes and
multiple black holes in string theory, we point out that the O piece in
our bosonized hamiltonian provides a simple understanding of the origin of two
different kinds of nonperturbative O corrections to the black hole
partition function.Comment: latex, 28 pages, 5 epsf figure
Numerical Diagonalisation Study of the Trimer Deposition-Evaporation Model in One Dimension
We study the model of deposition-evaporation of trimers on a line recently
introduced by Barma, Grynberg and Stinchcombe. The stochastic matrix of the
model can be written in the form of the Hamiltonian of a quantum spin-1/2 chain
with three-spin couplings given by H= \sum\displaylimits_i [(1 -
\sigma_i^-\sigma_{i+1}^-\sigma_{i+2}^-) \sigma_i^+\sigma_{i+1}^+\sigma_{i+2}^+
+ h.c]. We study by exact numerical diagonalization of the variation of
the gap in the eigenvalue spectrum with the system size for rings of size up to
30. For the sector corresponding to the initial condition in which all sites
are empty, we find that the gap vanishes as where the gap exponent
is approximately . This model is equivalent to an interfacial
roughening model where the dynamical variables at each site are matrices. From
our estimate for the gap exponent we conclude that the model belongs to a new
universality class, distinct from that studied by Kardar, Parisi and Zhang.Comment: 11 pages, 2 figures (included
The Irreducible String and an Infinity of Additional Constants of Motion in a Deposition-Evaporation Model on a Line
We study a model of stochastic deposition-evaporation with recombination, of
three species of dimers on a line. This model is a generalization of the model
recently introduced by Barma {\it et. al.} (1993 {\it Phys. Rev. Lett.} {\bf
70} 1033) to states per site. It has an infinite number of constants
of motion, in addition to the infinity of conservation laws of the original
model which are encoded as the conservation of the irreducible string. We
determine the number of dynamically disconnected sectors and their sizes in
this model exactly. Using the additional symmetry we construct a class of exact
eigenvectors of the stochastic matrix. The autocorrelation function decays with
different powers of in different sectors. We find that the spatial
correlation function has an algebraic decay with exponent 3/2, in the sector
corresponding to the initial state in which all sites are in the same state.
The dynamical exponent is nontrivial in this sector, and we estimate it
numerically by exact diagonalization of the stochastic matrix for small sizes.
We find that in this case .Comment: Some minor errors in the first version has been correcte
Two simple models of classical heat pumps
Motivated by recent studies on models of particle and heat quantum pumps, we
study similar simple classical models and examine the possibility of heat
pumping. Unlike many of the usual ratchet models of molecular engines, the
models we study do not have particle transport. We consider a two-spin system
and a coupled oscillator system which exchange heat with multiple heat
reservoirs and which are acted upon by periodic forces. The simplicity of our
models allows accurate numerical and exact solutions and unambiguous
interpretation of results. We demonstrate that while both our models seem to be
built on similar principles, one is able to function as a heat pump (or engine)
while the other is not.Comment: 4 pages, 4 figure
Nonequilibrium Phase Transitions in a Driven Sandpile Model
We construct a driven sandpile slope model and study it by numerical
simulations in one dimension. The model is specified by a threshold slope
\sigma_c\/, a parameter \alpha\/, governing the local current-slope
relation (beyond threshold), and , the mean input current of sand.
A nonequilibrium phase diagram is obtained in the \alpha\, -\, j_{\rm in}\/
plane. We find an infinity of phases, characterized by different mean slopes
and separated by continuous or first-order boundaries, some of which we obtain
analytically. Extensions to two dimensions are discussed.Comment: 11 pages, RevTeX (preprint format), 4 figures available upon requs
Effect of phonon-phonon interactions on localization
We study the heat current J in a classical one-dimensional disordered chain
with on-site pinning and with ends connected to stochastic thermal reservoirs
at different temperatures. In the absence of anharmonicity all modes are
localized and there is a gap in the spectrum. Consequently J decays
exponentially with system size N. Using simulations we find that even a small
amount of anharmonicity leads to a J~1/N dependence, implying diffusive
transport of energy.Comment: 4 pages, 2 figures, Published versio
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