443 research outputs found
Thermodynamic properties of confined interacting Bose gases - a renormalization group approach
A renormalization group method is developed with which thermodynamic
properties of a weakly interacting, confined Bose gas can be investigated.
Thereby effects originating from a confining potential are taken into account
by periodic boundary conditions and by treating the resulting discrete energy
levels of the confined degrees of freedom properly. The resulting density of
states modifies the flow equations of the renormalization group in momentum
space. It is shown that as soon as the characteristic length of confinement
becomes comparable to the thermal wave length of a weakly interacting and
trapped Bose gas its thermodynamic properties are changed significantly. This
is exemplified by investigating characteristic bunching properties of the
interacting Bose gas which manifest themselves in the second order coherence
factor
Entropy, time irreversibility and Schroedinger equation in a primarily discrete space-time
In this paper we show that the existence of a primarily discrete space-time
may be a fruitful assumption from which we may develop a new approach of
statistical thermodynamics in pre-relativistic conditions. The discreetness of
space-time structure is determined by a condition that mimics the Heisenberg
uncertainty relations and the motion in this space-time model is chosen as
simple as possible. From these two assumptions we define a path-entropy that
measures the number of closed paths associated with a given energy of the
system preparation. This entropy has a dynamical character and depends on the
time interval on which we count the paths. We show that it exists an
like-equilibrium condition for which the path-entropy corresponds exactly to
the usual thermodynamic entropy and, more generally, the usual statistical
thermodynamics is reobtained. This result derived without using the Gibbs
ensemble method shows that the standard thermodynamics is consistent with a
motion that is time-irreversible at a microscopic level. From this change of
paradigm it becomes easy to derive a . A comparison with the
traditional Boltzmann approach is presented. We also show how our approach can
be implemented in order to describe reversible processes. By considering a
process defined simultaneously by initial and final conditions a well defined
stochastic process is introduced and we are able to derive a Schroedinger
equation, an example of time reversible equation.Comment: latex versio
Path Integral Approach to the Non-Relativistic Electron Charge Transfer
A path integral approach has been generalized for the non-relativistic
electron charge transfer processes. The charge transfer - the capture of an
electron by an ion passing another atom or more generally the problem of
rearrangement collisions is formulated in terms of influence functionals. It
has been shown that the electron charge transfer process can be treated either
as electron transition problem or as elastic scattering of ion and atom in the
some effective potential field. The first-order Born approximation for the
electron charge transfer cross section has been reproduced to prove the
adequacy of the path integral approach for this problem.Comment: 19 pages, 1 figure, to appear in Journal of Physics B: Atomic,
Molecular & Optical, vol.34, 200
Brownian Motion and Polymer Statistics on Certain Curved Manifolds
We have calculated the probability distribution function G(R,L|R',0) of the
end-to-end vector R-R' and the mean-square end-to-end distance (R-R')^2 of a
Gaussian polymer chain embedded on a sphere S^(D-1) in D dimensions and on a
cylinder, a cone and a curved torus in 3-D.
We showed that: surface curvature induces a geometrical localization area; at
short length the polymer is locally "flat" and (R-R')^2 = L l in all cases; at
large scales, (R-R')^2 is constant for the sphere, it is linear in L for the
cylinder and reaches different constant values for the torus. The cone vertex
induces (function of opening angle and R') contraction of the chain for all
lengths. Explicit crossover formulas are derived.Comment: 9 pages, 4 figures, RevTex, uses amssymb.sty and multicol.sty, to
appear in Phys. Rev
Onsager-Machlup theory and work fluctuation theorem for a harmonically driven Brownian particle
We extend Tooru-Cohen analysis for nonequilirium steady state(NSS) of a
Brownian particle to nonequilibrium oscillatory state (NOS) of Brownian
particle by considering time dependent external drive protocol. We consider an
unbounded charged Brownian particle in the presence of an oscillating electric
field and prove work fluctuation theorem, which is valid for any initial
distribution and at all times. For harmonically bounded and constantly dragged
Brownian particle considered by Tooru and Cohen, work fluctuation theorem is
valid for any initial condition(also NSS), but only in large time limit. We use
Onsager-Machlup Lagrangian with a constraint to obtain frequency dependent work
distribution function, and describe entropy production rate and properties of
dissipation functions for the present system using Onsager-Machlup functional.Comment: 6 pages, 1 figur
Why is the DNA Denaturation Transition First Order?
We study a model for the denaturation transition of DNA in which the
molecules are considered as composed of a sequence of alternating bound
segments and denaturated loops. We take into account the excluded-volume
interactions between denaturated loops and the rest of the chain by exploiting
recent results on scaling properties of polymer networks of arbitrary topology.
The phase transition is found to be first order in d=2 dimensions and above, in
agreement with experiments and at variance with previous theoretical results,
in which only excluded-volume interactions within denaturated loops were taken
into account. Our results agree with recent numerical simulations.Comment: Revised version. To appear in Phys. Rev. Let
Quench Induced Vortices in the Symmetry Broken Phase of Liquid He
Motivated by the study of cosmological phase transitions, our understanding
of the formation of topological defects during spontaneous symmetry-breaking
and the associated non-equilibrium field theory has recently changed.
Experiments have been performed in superfluid He to test the new ideas
involved. In particular, it has been observed that a vortex density is seen
immediately after pressure quenches from just below the transition.
We discuss possible interpretations of these vortices, conclude they are
consistent with our ideas of vortex formation and propose a modification of the
original experiments.Comment: 29 pages, RevTeX with one EPS figur
Path-integral analysis of fluctuation theorems for general Langevin processes
We examine classical, transient fluctuation theorems within the unifying
framework of Langevin dynamics. We explicitly distinguish between the effects
of non-conservative forces that violate detailed balance, and non-autonomous
dynamics arising from the variation of an external parameter. When both these
sources of nonequilibrium behavior are present, there naturally arise two
distinct fluctuation theorems.Comment: 24 pages, one figur
Statistical Mechanics of Membrane Protein Conformation: A Homopolymer Model
The conformation and the phase diagram of a membrane protein are investigated
via grand canonical ensemble approach using a homopolymer model. We discuss the
nature and pathway of -helix integration into the membrane that results
depending upon membrane permeability and polymer adsorptivity. For a membrane
with the permeability larger than a critical value, the integration becomes the
second order transition that occurs at the same temperature as that of the
adsorption transition. For a nonadsorbing membrane, the integration is of the
first order due to the aggregation of -helices.Comment: RevTeX with 5 postscript figure
Kinetics of a Network of Vortex Loops in He II and a Theory of Superfluid Turbulence
A theory is developed to describe the superfluid turbulence on the base of
kinetics of the merging and splitting vortex loops. Because of very frequent
reconnections the vortex loops (as a whole) do not live long enough to perform
any essential evolution due to the deterministic motion. On the contrary, they
rapidly merge and split, and these random recombination processes prevail over
other slower dynamic processes. To develop quantitative description we take the
vortex loops to have a Brownian structure with the only degree of freedom,
which is the length of the loop. We perform investigation on the base of
the Boltzmann type kinetic equation for the distribution function of
number of loops with length . By use of the special ansatz in the collision
integral we have found the exact power-like solution to kinetic equation in the
stationary case. This solution is not (thermodynamically) equilibrium, but on
the contrary, it describes the state with two mutual fluxes of the length (or
energy) in space of sizes of the vortex loops. The term flux means just
redistribution of length (or energy) among the loops of different sizes due to
reconnections. Analyzing this solution we drew several results on the structure
and dynamics of the vortex tangle in the turbulent superfluid helium. In
particular, we evaluated the mean radius of the curvature and the full rate of
the reconnection events. We also studied the evolution of the full length of
vortex loops per unit volume-the so-called vortex line density. It is shown
this evolution to obey the famous Vinen equation. The properties of the Vinen
equation from the point of view of the developed approach had been discussed.Comment: 34 pages, 9 Postscript figures, [aps,preprint,12pt]{revtex4
- …