1,591 research outputs found

### Long-range correlations and ensemble inequivalence in a generalized ABC model

A generalization of the ABC model, a one-dimensional model of a driven system
of three particle species with local dynamics, is introduced, in which the
model evolves under either (i) density-conserving or (ii) nonconserving
dynamics. For equal average densities of the three species, both dynamical
models are demonstrated to exhibit detailed balance with respect to a
Hamiltonian with long-range interactions. The model is found to exhibit two
distinct phase diagrams, corresponding to the canonical (density-conserving)
and grand canonical (density nonconserving) ensembles, as expected in
long-range interacting systems. The implication of this result to
nonequilibrium steady states, such as those of the ABC model with unequal
average densities, are briefly discussed.Comment: 4 pages, 2 figures. v2: minor changes with an added reference,
published versio

### Supercoil formation in DNA denaturation

We generalize the Poland-Scheraga (PS) model to the case of a circular DNA,
taking into account the twisting of the two strains around each other. Guided
by recent single-molecule experiments on DNA strands, we assume that the
torsional stress induced by denaturation enforces formation of supercoils whose
writhe absorbs the linking number expelled by the loops. Our model predicts
that, when the entropy parameter of a loop satisfies $c \le 2$, denaturation
transition does not take place. On the other hand for $c>2$ a first-order
denaturation transition is consistent with our model and may take place in the
actual system, as in the case with no supercoils. These results are in contrast
with other treatments of circular DNA melting where denaturation is assumed to
be accompanied by an increase in twist rather than writhe on the bound
segments.Comment: 4 pages, 3 figures, accepted for publication in PRE Rapid Com

### Cascading and Local-Field Effects in Non-Linear Optics Revisited; A Quantum-Field Picture Based on Exchange of Photons

The semi-classical theory of radiation-matter coupling misses local-field
effects that may alter the pulse time-ordering and cascading that leads to the
generation of new signals. These are then introduced macroscopically by solving
Maxwell's equations. This procedure is convenient and intuitive but ad hoc. We
show that both effects emerge naturally by including coupling to quantum modes
of the radiation field in the vacuum state to second order. This approach is
systematic and suggests a more general class of corrections that only arise in
a QED framework. In the semi-classical theory, which only includes classical
field modes, the susceptibility of a collection of $N$ non-interacting
molecules is additive and scales as $N$. Second-order coupling to a vacuum mode
generates an effective retarded interaction that leads to cascading and local
field effects both of which scale as $N^2$

### Slow Coarsening in a Class of Driven Systems

The coarsening process in a class of driven systems is studied. These systems
have previously been shown to exhibit phase separation and slow coarsening in
one dimension. We consider generalizations of this class of models to higher
dimensions. In particular we study a system of three types of particles that
diffuse under local conserving dynamics in two dimensions. Arguments and
numerical studies are presented indicating that the coarsening process in any
number of dimensions is logarithmically slow in time. A key feature of this
behavior is that the interfaces separating the various growing domains are
smooth (well approximated by a Fermi function). This implies that the
coarsening mechanism in one dimension is readily extendible to higher
dimensions.Comment: submitted to EPJB, 13 page

### Many-body Green's function approach to attosecond nonlinear X-ray spectroscopy

Closed expressions are derived for resonant multidimensional X-ray
spectroscopy using the quasiparticle nonlinear exciton representation of
optical response. This formalism is applied to predict coherent four wave
mixing signals which probe single and two core-hole states. Nonlinear X-ray
signals are compactly expressed in terms of one- and two- particle Green's
functions which can be obtained from the solution of Hedin-like equations at
the $GW$ level.Comment: 10 pages and 3 figures (To appear in Physical Review B

### The grand canonical ABC model: a reflection asymmetric mean field Potts model

We investigate the phase diagram of a three-component system of particles on
a one-dimensional filled lattice, or equivalently of a one-dimensional
three-state Potts model, with reflection asymmetric mean field interactions.
The three types of particles are designated as $A$, $B$, and $C$. The system is
described by a grand canonical ensemble with temperature $T$ and chemical
potentials $T\lambda_A$, $T\lambda_B$, and $T\lambda_C$. We find that for
$\lambda_A=\lambda_B=\lambda_C$ the system undergoes a phase transition from a
uniform density to a continuum of phases at a critical temperature $\hat
T_c=(2\pi/\sqrt3)^{-1}$. For other values of the chemical potentials the system
has a unique equilibrium state. As is the case for the canonical ensemble for
this $ABC$ model, the grand canonical ensemble is the stationary measure
satisfying detailed balance for a natural dynamics. We note that $\hat
T_c=3T_c$, where $T_c$ is the critical temperature for a similar transition in
the canonical ensemble at fixed equal densities $r_A=r_B=r_C=1/3$.Comment: 24 pages, 3 figure

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