704 research outputs found

### Diverging equilibration times in long-range quantum spin models

The approach to equilibrium is studied for long-range quantum Ising models
where the interaction strength decays like r^{-\alpha} at large distances r
with an exponent $\alpha$ not exceeding the lattice dimension. For a large
class of observables and initial states, the time evolution of expectation
values can be calculated. We prove analytically that, at a given instant of
time t and for sufficiently large system size N, the expectation value of some
observable (t) will practically be unchanged from its initial value (0).
This finding implies that, for large enough N, equilibration effectively occurs
on a time scale beyond the experimentally accessible one and will not be
observed in practice.Comment: 4+ pages, 1 figur

### Limits of the equivalence of time and ensemble averages in shear flows

In equilibrium systems, time and ensemble averages of physical quantities are
equivalent due to ergodic exploration of phase space. In driven systems, it is
unknown if a similar equivalence of time and ensemble averages exists. We
explore effective limits of such convergence in a sheared bubble raft using
averages of the bubble velocities. In independent experiments, averaging over
time leads to well converged velocity profiles. However, the time-averages from
independent experiments result in distinct velocity averages. Ensemble averages
are approximated by randomly selecting bubble velocities from independent
experiments. Increasingly better approximations of ensemble averages converge
toward a unique velocity profile. Therefore, the experiments establish that in
practical realizations of non-equilibrium systems, temporal averaging and
ensemble averaging can yield convergent (stationary) but distinct
distributions.Comment: accepted to PRL - final figure revision

### Scaled Particle Theory for Hard Sphere Pairs. I. Mathematical Structure

We develop an extension of the original Reiss-Frisch-Lebowitz scaled particle
theory that can serve as a predictive method for the hard sphere pair
correlation function g(r). The reversible cavity creation work is analyzed both
for a single spherical cavity of arbitrary size, as well as for a pair of
identical such spherical cavities with variable center-to-center separation.
These quantities lead directly to prediction of g(r). Smooth connection
conditions have been identified between the small-cavity situation where the
work can be exactly and completely expressed in terms of g(r), and the
large-cavity regime where macroscopic properties become relevant. Closure
conditions emerge which produce a nonlinear integral equation that must be
satisfied by the pair correlation function. This integral equation has a
structure which straightforwardly generates a solution that is a power series
in density. The results of this series replicate the exact second and third
virial coefficients for the hard sphere system via the contact value of the
pair correlation function. The predicted fourth virial coefficient is
approximately 0.6 percent lower than the known exact value. Detailed numerical
analysis of the nonlinear integral equation has been deferred to the sequel
(following paper

### Verschraenkung versus Stosszahlansatz: Disappearance of the Thermodynamic Arrow in a High-Correlation Environment

The crucial role of ambient correlations in determining thermodynamic
behavior is established. A class of entangled states of two macroscopic systems
is constructed such that each component is in a state of thermal equilibrium at
a given temperature, and when the two are allowed to interact heat can flow
from the colder to the hotter system. A dilute gas model exhibiting this
behavior is presented. This reversal of the thermodynamic arrow is a
consequence of the entanglement between the two systems, a condition that is
opposite to molecular chaos and shown to be unlikely in a low-entropy
environment. By contrast, the second law is established by proving Clausius'
inequality in a low-entropy environment. These general results strongly support
the expectation, first expressed by Boltzmann and subsequently elaborated by
others, that the second law is an emergent phenomenon that requires a
low-entropy cosmological environment, one that can effectively function as an
ideal information sink.Comment: 4 pages, REVTeX

### Loschmidt echo in one-dimensional interacting Bose gases

We explore Loschmidt echo in two regimes of one-dimensional (1D) interacting
Bose gases: the strongly interacting Tonks-Girardeau (TG) regime, and the
weakly-interacting mean-field regime. We find that the Loschmidt echo of a TG
gas decays as a Gaussian when small perturbations are added to the Hamiltonian
(the exponent is proportional to the number of particles and the magnitude of a
small perturbation squared). In the mean-field regime the Loschmidt echo decays
faster for larger interparticle interactions (nonlinearity), and it shows
richer behavior than the TG Loschmidt echo dynamics, with oscillations
superimposed on the overall decay.Comment: Comparison between Tonks-Girardeau and mean-field fidelities
corrected; see new Figure 4 and the "Note added". New references are include

### On the relation between virial coefficients and the close-packing of hard disks and hard spheres

The question of whether the known virial coefficients are enough to determine
the packing fraction $\eta_\infty$ at which the fluid equation of state of a
hard-sphere fluid diverges is addressed. It is found that the information
derived from the direct Pad\'e approximants to the compressibility factor
constructed with the virial coefficients is inconclusive. An alternative
approach is proposed which makes use of the same virial coefficients and of the
equation of state in a form where the packing fraction is explicitly given as a
function of the pressure. The results of this approach both for hard-disk and
hard-sphere fluids, which can straightforwardly accommodate higher virial
coefficients when available, lends support to the conjecture that $\eta_\infty$
is equal to the maximum packing fraction corresponding to an ordered
crystalline structure.Comment: 10 pages, 6 figures; v2: discussion about hard-square and
hard-hexagon systems on a lattice added; five new reference

### Some Late-time Asymptotics of General Scalar-Tensor Cosmologies

We study the asymptotic behaviour of isotropic and homogeneous universes in
general scalar-tensor gravity theories containing a p=-rho vacuum fluid stress
and other sub-dominant matter stresses. It is shown that in order for there to
be approach to a de Sitter spacetime at large 4-volumes the coupling function,
omega(phi), which defines the scalar-tensor theory, must diverge faster than
|phi_infty-phi|^(-1+epsilon) for all epsilon>0 as phi rightarrow phi_infty 0
for large values of the time. Thus, for a given theory, specified by
omega(phi), there must exist some phi_infty in (0,infty) such that omega ->
infty and omega' / omega^(2+epsilon) -> 0 as phi -> 0 phi_infty in order for
cosmological solutions of the theory to approach de Sitter expansion at late
times. We also classify the possible asymptotic time variations of the
gravitation `constant' G(t) at late times in scalar-tensor theories. We show
that (unlike in general relativity) the problem of a profusion of ``Boltzmann
brains'' at late cosmological times can be avoided in scalar-tensor theories,
including Brans-Dicke theory, in which phi -> infty and omega ~ o(\phi^(1/2))
at asymptotically late times.Comment: 14 page

### A branch-point approximant for the equation of state of hard spheres

Using the first seven known virial coefficients and forcing it to possess two
branch-point singularities, a new equation of state for the hard-sphere fluid
is proposed. This equation of state predicts accurate values of the higher
virial coefficients, a radius of convergence smaller than the close-packing
value, and it is as accurate as the rescaled virial expansion and better than
the Pad\'e [3/3] equations of state. Consequences regarding the convergence
properties of the virial series and the use of similar equations of state for
hard-core fluids in $d$ dimensions are also pointed out.Comment: 6 pages, 4 tables, 3 figures; v2: enlarged version, extension to
other dimensionalities; v3: typos in references correcte

### Time and irreversibility in an accelerating universe

It is a remarkable fact that all processes occurring in the observable
Universe are irreversible, whereas the equations through which the fundamental
laws of physics are formulated are invariant under time reversal. The emergence
of irreversibility from the fundamental laws has been a topic of consideration
by physicists, astronomers and philosophers since Boltzmann's formulation of
his famous "H" theorem. In this paper we shall discuss some aspects of this
problem and its connection with the dynamics of space-time, within the
framework of modern cosmology. We conclude that the existence of cosmological
horizons allows a coupling of the global state of the Universe with the local
events determined through electromagnetic processes.Comment: 8 pages, revised version accepted for publication in IJMP D. This
paper received an Honorable Mention in the Gravity Research Foundation
competition 201

### Individual and collective behavior of dust particles in a protoplanetary nebula

We study the interaction between gas and dust particles in a protoplanetary
disk, comparing analytical and numerical results. We first calculate
analytically the trajectories of individual particles undergoing gas drag in
the disk, in the asymptotic cases of very small particles (Epstein regime) and
very large particles (Stokes regime). Using a Boltzmann averaging method, we
then infer their collective behavior. We compare the results of this analytical
formulation against numerical computations of a large number of particles.
Using successive moments of the Boltzmann equation, we derive the equivalent
fluid equations for the average motion of the particles; these are
intrinsically different in the Epstein and Stokes regimes. We are also able to
study analytically the temporal evolution of a collection of particles with a
given initial size-distribution provided collisions are ignored.Comment: 15 pages, 9 figures, submitted to Ap

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