5,082 research outputs found
Spontaneous Breaking of Translational Invariance in One-Dimensional Stationary States on a Ring
We consider a model in which positive and negative particles diffuse in an
asymmetric, CP-invariant way on a ring. The positive particles hop clockwise,
the negative counterclockwise and oppositely-charged adjacent particles may
swap positions. Monte-Carlo simulations and analytic calculations suggest that
the model has three phases; a "pure" phase in which one has three pinned blocks
of only positive, negative particles and vacancies, and in which translational
invariance is spontaneously broken, a "mixed" phase with a non-vanishing
current in which the three blocks are positive, negative and neutral, and a
disordered phase without blocks.Comment: 7 pages, LaTeX, needs epsf.st
Yang-Lee Theory for a Nonequilibrium Phase Transition
To analyze phase transitions in a nonequilibrium system we study its grand
canonical partition function as a function of complex fugacity. Real and
positive roots of the partition function mark phase transitions. This behavior,
first found by Yang and Lee under general conditions for equilibrium systems,
can also be applied to nonequilibrium phase transitions. We consider a
one-dimensional diffusion model with periodic boundary conditions. Depending on
the diffusion rates, we find real and positive roots and can distinguish two
regions of analyticity, which can identified with two different phases. In a
region of the parameter space both of these phases coexist. The condensation
point can be computed with high accuracy.Comment: 4 pages, accepted for publication in Phys.Rev.Let
Experimental verification of the Heisenberg uncertainty principle for hot fullerene molecules
The Heisenberg uncertainty principle for material objects is an essential
corner stone of quantum mechanics and clearly visualizes the wave nature of
matter. Here we report a demonstration of the Heisenberg uncertainty principle
for the most massive, complex and hottest single object so far, the fullerene
molecule C70 at a temperature of 900 K. We find a good quantitative agreement
with the theoretical expectation: dx * dp = h, where dx is the width of the
restricting slit, dp is the momentum transfer required to deflect the fullerene
to the first interference minimum and h is Planck's quantum of action.Comment: 4 pages, 4 figure
Symmetry breaking and phase coexistence in a driven diffusive two-channel system
We consider classical hard-core particles moving on two parallel chains in
the same direction. An interaction between the channels is included via the
hopping rates. For a ring, the stationary state has a product form. For the
case of coupling to two reservoirs, it is investigated analytically and
numerically. In addition to the known one-channel phases, two new regions are
found, in particular the one, where the total density is fixed, but the filling
of the individual chains changes back and forth, with a preference for strongly
different densities. The corresponding probability distribution is determined
and shown to have an universal form. The phase diagram and general aspects of
the problem are discussed.Comment: 12 pages, 10 figures, to appear in Phys.Rev.
Universality of Long-Range Correlations in Expansion-Randomization Systems
We study the stochastic dynamics of sequences evolving by single site
mutations, segmental duplications, deletions, and random insertions. These
processes are relevant for the evolution of genomic DNA. They define a
universality class of non-equilibrium 1D expansion-randomization systems with
generic stationary long-range correlations in a regime of growing sequence
length. We obtain explicitly the two-point correlation function of the sequence
composition and the distribution function of the composition bias in sequences
of finite length. The characteristic exponent of these quantities is
determined by the ratio of two effective rates, which are explicitly calculated
for several specific sequence evolution dynamics of the universality class.
Depending on the value of , we find two different scaling regimes, which
are distinguished by the detectability of the initial composition bias. All
analytic results are accurately verified by numerical simulations. We also
discuss the non-stationary build-up and decay of correlations, as well as more
complex evolutionary scenarios, where the rates of the processes vary in time.
Our findings provide a possible example for the emergence of universality in
molecular biology.Comment: 23 pages, 15 figure
One-Dimensional Partially Asymmetric Simple Exclusion Process on a Ring with a Defect Particle
The effect of a moving defect particle for the one-dimensional partially
asymmetric simple exclusion process on a ring is considered. The current of the
ordinary particles, the speed of the defect particle and the density profile of
the ordinary particles are calculated exactly. The phase diagram for the
correlation length is identified. As a byproduct, the average and the variance
of the particle density of the one-dimensional partially asymmetric simple
exclusion process with open boundaries are also computed.Comment: 23 pages, 1 figur
Symmetry breaking through a sequence of transitions in a driven diffusive system
In this work we study a two species driven diffusive system with open
boundaries that exhibits spontaneous symmetry breaking in one dimension. In a
symmetry broken state the currents of the two species are not equal, although
the dynamics is symmetric. A mean field theory predicts a sequence of two
transitions from a strongly symmetry broken state through an intermediate
symmetry broken state to a symmetric state. However, a recent numerical study
has questioned the existence of the intermediate state and instead suggested a
single discontinuous transition. In this work we present an extensive numerical
study that supports the existence of the intermediate phase but shows that this
phase and the transition to the symmetric phase are qualitatively different
from the mean-field predictions.Comment: 19 pages, 12 figure
Exact solution and asymptotic behaviour of the asymmetric simple exclusion process on a ring
In this paper, we study an exact solution of the asymmetric simple exclusion
process on a periodic lattice of finite sites with two typical updates, i.e.,
random and parallel. Then, we find that the explicit formulas for the partition
function and the average velocity are expressed by the Gauss hypergeometric
function. In order to obtain these results, we effectively exploit the
recursion formula for the partition function for the zero-range process. The
zero-range process corresponds to the asymmetric simple exclusion process if
one chooses the relevant hop rates of particles, and the recursion gives the
partition function, in principle, for any finite system size. Moreover, we
reveal the asymptotic behaviour of the average velocity in the thermodynamic
limit, expanding the formula as a series in system size.Comment: 10 page
Yang-Lee zeroes for an urn model for the separation of sand
We apply the Yang-Lee theory of phase transitions to an urn model of
separation of sand. The effective partition function of this nonequilibrium
system can be expressed as a polynomial of the size-dependent effective
fugacity . Numerical calculations show that in the thermodynamic limit, the
zeros of the effective partition function are located on the unit circle in the
complex -plane. In the complex plane of the actual control parameter certain
roots converge to the transition point of the model. Thus the Yang-Lee theory
can be applied to a wider class of nonequilibrium systems than those considered
previously.Comment: 4 pages, 3 eps figures include
On Matrix Product States for Periodic Boundary Conditions
The possibility of a matrix product representation for eigenstates with
energy and momentum zero of a general m-state quantum spin Hamiltonian with
nearest neighbour interaction and periodic boundary condition is considered.
The quadratic algebra used for this representation is generated by 2m operators
which fulfil m^2 quadratic relations and is endowed with a trace. It is shown
that {\em not} every eigenstate with energy and momentum zero can be written as
matrix product state. An explicit counter-example is given. This is in contrast
to the case of open boundary conditions where every zero energy eigenstate can
be written as a matrix product state using a Fock-like representation of the
same quadratic algebra.Comment: 7 pages, late
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