132 research outputs found
Time evolution of correlation functions and thermalization
We investigate the time evolution of a classical ensemble of isolated
periodic chains of O(N)-symmetric anharmonic oscillators. Our method is based
on an exact evolution equation for the time dependence of correlation
functions. We discuss its solutions in an approximation which retains all
contributions in next-to-leading order in a 1/N expansion and preserves time
reflection symmetry. We observe effective irreversibility and approximate
thermalization. At large time the system approaches stationary solutions in the
vicinity of, but not identical to, thermal equilibrium. The ensemble therefore
retains some memory of the initial condition beyond the conserved total energy.
Such a behavior with incomplete thermalization is referred to as "mesoscopic
dynamics". It is expected for systems in a small volume. Surprisingly, we find
that the nonthermal asymptotic stationary solutions do not change for large
volume. This raises questions on Boltzmann's conjecture that macroscopic
isolated systems thermalize.Comment: 40 pages, 9 figure
Analysis of path integrals at low temperature : Box formula, occupation time and ergodic approximation
We study the low temperature behaviour of path integrals for a simple
one-dimensional model. Starting from the Feynman-Kac formula, we derive a new
functional representation of the density matrix at finite temperature, in terms
of the occupation times of Brownian motions constrained to stay within boxes
with finite sizes. From that representation, we infer a kind of ergodic
approximation, which only involves double ordinary integrals. As shown by its
applications to different confining potentials, the ergodic approximation turns
out to be quite efficient, especially in the low-temperature regime where other
usual approximations fail
Targeted free energy perturbation
A generalization of the free energy perturbation identity is derived, and a
computational strategy based on this result is presented. A simple example
illustrates the efficiency gains that can be achieved with this method.Comment: 8 pages + 1 color figur
Discrete breathers in polyethylene chain
The existence of discrete breathers (DBs), or intrinsic localized modes
(localized periodic oscillations of transzigzag) is shown. In the localization
region periodic contraction-extension of valence C-C bonds occurs which is
accompanied by decrease-increase of valence angles. It is shown that the
breathers present in thermalized chain and their contribution dependent on
temperature has been revealed.Comment: 5 pages, 6 figure
Condensation of Hard Spheres Under Gravity: Exact Results in One Dimension
We present exact results for the density profile of the one dimensional array
of N hard spheres of diameter D and mass m under gravity g. For a strictly one
dimensional system, the liquid-solid transition occurs at zero temperature,
because the close-pakced density, , is one. However, if we relax this
condition slightly such that , we find a series of critical
temperatures T_c^i=mgD(N+1-i)/\mu_o with \mu_o=const, at which the i-th
particle undergoes the liquid-solid transition. The functional form of the
onset temperature, T_c^1=mgDN/\mu_o, is consistent with the previous result
[Physica A 271, 192 (1999)] obtained by the Enskog equation. We also show that
the increase in the center of mass is linear in T before the transition, but it
becomes quadratic in T after the transition because of the formation of solid
near the bottom
Molecular scale contact line hydrodynamics of immiscible flows
From extensive molecular dynamics simulations on immiscible two-phase flows,
we find the relative slipping between the fluids and the solid wall everywhere
to follow the generalized Navier boundary condition, in which the amount of
slipping is proportional to the sum of tangential viscous stress and the
uncompensated Young stress. The latter arises from the deviation of the
fluid-fluid interface from its static configuration. We give a continuum
formulation of the immiscible flow hydrodynamics, comprising the generalized
Navier boundary condition, the Navier-Stokes equation, and the Cahn-Hilliard
interfacial free energy. Our hydrodynamic model yields interfacial and velocity
profiles matching those from the molecular dynamics simulations at the
molecular-scale vicinity of the contact line. In particular, the behavior at
high capillary numbers, leading to the breakup of the fluid-fluid interface, is
accurately predicted.Comment: 33 pages for text in preprint format, 10 pages for 10 figures with
captions, content changed in this resubmissio
The McKean-Vlasov Equation in Finite Volume
We study the McKean--Vlasov equation on the finite tori of length scale
in --dimensions. We derive the necessary and sufficient conditions for the
existence of a phase transition, which are based on the criteria first
uncovered in \cite{GP} and \cite{KM}. Therein and in subsequent works, one
finds indications pointing to critical transitions at a particular model
dependent value, of the interaction parameter. We show that
the uniform density (which may be interpreted as the liquid phase) is
dynamically stable for and prove, abstractly, that a
{\it critical} transition must occur at . However for
this system we show that under generic conditions -- large, and
isotropic interactions -- the phase transition is in fact discontinuous and
occurs at some \theta\t < \theta^{\sharp}. Finally, for H--stable, bounded
interactions with discontinuous transitions we show that, with suitable
scaling, the \theta\t(L) tend to a definitive non--trivial limit as
Onset of entanglement
We have developed a theory of polymer entanglement using an extended
Cahn-Hilliard functional, with two extra terms. One is a nonlocal attractive
term, operating over mesoscales, which is interpreted as giving rise to
entanglement, and the other a local repulsive term indicative of excluded
volume interactions. We show how such a functional can be derived using notions
from gauge theory. We go beyond the Gaussian approximation, to the one-loop
level, to show that the system exhibits a crossover to a state of entanglement
as the average chain length between points of entanglement decreases. This
crossover is marked by critical slowing down, as the effective diffusion
constant goes to zero. We have also computed the tensile modulus of the system,
and we find a corresponding crossover to a regime of high modulus.Comment: 18 pages, with 4 figure
Majority versus minority dynamics: Phase transition in an interacting two-state spin system
We introduce a simple model of opinion dynamics in which binary-state agents
evolve due to the influence of agents in a local neighborhood. In a single
update step, a fixed-size group is defined and all agents in the group adopt
the state of the local majority with probability p or that of the local
minority with probability 1-p. For group size G=3, there is a phase transition
at p_c=2/3 in all spatial dimensions. For p>p_c, the global majority quickly
predominates, while for p<p_c, the system is driven to a mixed state in which
the densities of agents in each state are equal. For p=p_c, the average
magnetization (the difference in the density of agents in the two states) is
conserved and the system obeys classical voter model dynamics. In one dimension
and within a Kirkwood decoupling scheme, the final magnetization in a
finite-length system has a non-trivial dependence on the initial magnetization
for all p.ne.p_c, in agreement with numerical results. At p_c, the exact 2-spin
correlation functions decay algebraically toward the value 1 and the system
coarsens as in the classical voter model.Comment: 11 pages, 3 figures, revtex4 2-column format; minor revisions for
publication in PR
Superfluidity of a perfect quantum crystal
In recent years, experimental data were published which point to the
possibility of the existence of superfluidity in solid helium. To investigate
this phenomenon theoretically we employ a hierarchy of equations for reduced
density matrices which describes a quantum system that is in thermodynamic
equilibrium below the Bose-Einstein condensation point, the hierarchy being
obtained earlier by the author. It is shown that the hierarchy admits solutions
relevant to a perfect crystal (immobile) in which there is a frictionless flow
of atoms, which testifies to the possibility of superfluidity in ideal solids.
The solutions are studied with the help of the bifurcation method and some
their peculiarities are found out. Various physical aspects of the problem,
among them experimental ones, are discussed as well.Comment: 24 pages with 2 figures, version accepted for publication in
Eur.Phys.J.
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