867 research outputs found
Equilibrium Properties of Quantum Spin Systems with Non-additive Long-Range Interactions
We study equilibrium states of quantum spin systems with non-additive
long-range interactions by adopting an appropriate scaling of the interaction
strength, i.e., the so called Kac prescription. In classical spin systems, it
is known that the equilibrium free energy is obtained by minimizing the free
energy functional over the coarse-grained magnetization. Here we show that it
is also true for quantum spin systems. From this observation, it is found that
when the canonical ensemble and the microcanonical ensemble are not equivalent
in some parameter region, it is not necessarily justified to replace the actual
long-range interaction by the infinite-range interaction (Curie-Weiss type
interaction). On the other hand, in the parameter region where the two
ensembles are equivalent, this replacement is always justified. We examine the
Heisenberg XXZ model as an illustrative example, and discuss the relation to
experiments.Comment: 13 pages, two columns; to appear in Phys. Rev.
Can we model DNA at the mesoscale ? Comment on: Fluctuations in the DNA double helix: A critical review
Comment on "Fluctuations in the DNA double helix: A critical review" by
Frank-Kamenetskii and Prakas
Effect of defects on thermal denaturation of DNA Oligomers
The effect of defects on the melting profile of short heterogeneous DNA
chains are calculated using the Peyrard-Bishop Hamiltonian. The on-site
potential on a defect site is represented by a potential which has only the
short-range repulsion and the flat part without well of the Morse potential.
The stacking energy between the two neigbouring pairs involving a defect site
is also modified. The results are found to be in good agreement with the
experiments.Comment: 11 pages including 5 postscript figure; To be appear in Phys. Rev.
Discreteness effects on soliton dynamics: a simple experiment
We present a simple laboratory experiment to illustrate some aspects of the
soliton theory in discrete lattices with a system that models the dynamics of
dislocations in a crystal or the properties of adsorbed atomic layers. The
apparatus not only shows the role of the Peierls-Nabarro potential but also
illustrates the hierarchy of depinning transitions and the importance of the
collective motion in mass transport.Comment: 9 pages, 4 Figures, to Appear in American Journal of Physic
Violation of ensemble equivalence in the antiferromagnetic mean-field XY model
It is well known that long-range interactions pose serious problems for the
formulation of statistical mechanics. We show in this paper that ensemble
equivalence is violated in a simple mean-field model of N fully coupled
classical rotators with repulsive interaction (antiferromagnetic XY model).
While in the canonical ensemble the rotators are randomly dispersed over all
angles, in the microcanonical ensemble a bi-cluster of rotators separated by
angle , forms in the low energy limit. We attribute this behavior to the
extreme degeneracy of the ground state: only one harmonic mode is present,
together with N-1 zero modes. We obtain empirically an analytical formula for
the probability density function for the angle made by the rotator, which
compares extremely well with numerical data and should become exact in the zero
energy limit. At low energy, in the presence of the bi-cluster, an extensive
amount of energy is located in the single harmonic mode, with the result that
the energy temperature relation is modified. Although still linear, , it has the slope , instead of the canonical value
.Comment: 12 pages, Latex, 7 Figure
Modulational Estimate for Fermi-Pasta-Ulam Chain Lyapunov Exponents
In the framework of the Fermi-Pasta-Ulam (FPU) model, we show a simple method
to give an accurate analytical estimation of the maximal Lyapunov exponent at
high energy density. The method is based on the computation of the mean value
of the modulational instability growth rates associated to unstable modes.
Moreover, we show that the strong stochasticity threshold found in the
-FPU system is closely related to a transition in tangent space: the
Lyapunov eigenvector being more localized in space at high energy.Comment: 4 pages, revtex, 4 ps figures, submitted to PR
Aging phenomena in nonlinear dissipative chains: Application to polymer
We study energy relaxation in a phenomenological model for polymer built from
rheological considerations: a one dimensional nonlinear lattice with
dissipative couplings. These couplings are well known in polymer's community to
be possibly responsible of beta-relaxation (as in Burger's model). After
thermalisation of this system, the extremities of the chain are put in contact
with a zero-temperature reservoir, showing the existence of surprising
quasi-stationary states with non zero energy when the dissipative coupling is
high. This strange behavior, due to long-lived nonlinear localized modes,
induces stretched exponential laws. Furthermore, we observe a strong dependence
on the waiting time tw after the quench of the two-time intermediate
correlation function C(tw+t,tw). This function can be scaled onto a master
curve, similar to the case of spin or Lennard-Jones glasses.Comment: 8 pages, 10 figure
Statistical mechanics and dynamics of solvable models with long-range interactions
The two-body potential of systems with long-range interactions decays at
large distances as , with , where is the
space dimension. Examples are: gravitational systems, two-dimensional
hydrodynamics, two-dimensional elasticity, charged and dipolar systems.
Although such systems can be made extensive, they are intrinsically non
additive. Moreover, the space of accessible macroscopic thermodynamic
parameters might be non convex. The violation of these two basic properties is
at the origin of ensemble inequivalence, which implies that specific heat can
be negative in the microcanonical ensemble and temperature jumps can appear at
microcanonical first order phase transitions. The lack of convexity implies
that ergodicity may be generically broken. We present here a comprehensive
review of the recent advances on the statistical mechanics and
out-of-equilibrium dynamics of systems with long-range interactions. The core
of the review consists in the detailed presentation of the concept of ensemble
inequivalence, as exemplified by the exact solution, in the microcanonical and
canonical ensembles, of mean-field type models. Relaxation towards
thermodynamic equilibrium can be extremely slow and quasi-stationary states may
be present. The understanding of such unusual relaxation process is obtained by
the introduction of an appropriate kinetic theory based on the Vlasov equation.Comment: 118 pages, review paper, added references, slight change of conten
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