346 research outputs found
Pressure in an exactly solvable model of active fluid
We consider the pressure in the steady-state regime of three stochastic
models characterized by self-propulsion and persistent motion and widely
employed to describe the behavior of active particles, namely the Active
Brownian particle (ABP) model, the Gaussian colored noise (GCN) model and the
unified colored noise model (UCNA). Whereas in the limit of short but finite
persistence time the pressure in the UCNA model can be obtained by different
methods which have an analog in equilibrium systems, in the remaining two
models only the virial route is, in general, possible.
According to this method, notwithstanding each model obeys its own specific
microscopic law of evolution, the pressure displays a certain universal
behavior. For generic interparticle and confining potentials, we derive a
formula which establishes a correspondence between the GCN and the UCNA
pressures. In order to provide explicit formulas and examples, we specialize
the discussion to the case of an assembly of elastic dumbbells confined to a
parabolic well. By employing the UCNA we find that, for this model, the
pressure determined by the thermodynamic method coincides with the pressures
obtained by the virial and mechanical methods. The three methods when applied
to the GCN give a pressure identical to that obtained via the UCNA. Finally, we
find that the ABP virial pressure exactly agrees with the UCNA and GCN result.Comment: 12 pages, 1 figure Submitted for publication 23rd of January 2017 The
introduction has been modifie
Higher Order Corrections to Density and Temperature of Fermions from Quantum Fluctuations
A novel method to determine the density and temperature of a system based on
quantum Fermionic fluctuations is generalized to the limit where the reached
temperature T is large compared to the Fermi energy {\epsilon}f . Quadrupole
and particle multiplicity fluctuations relations are derived in terms of T .
The relevant Fermi integrals are numerically solved for any values of T and
compared to the analytical approximations. The classical limit is obtained, as
expected, in the limit of large temperatures and small densities. We propose
simple analytical formulas which reproduce the numerical results, valid for all
values of T . The entropy can also be easily derived from quantum fluctuations
and give important insight for the behavior of the system near a phase
transition. A comparison of the quantum entropy to the entropy derived from the
ratio of the number of deuterons to neutrons gives a very good agreement
especially when the density of the system is very low
Microstructure and velocity of field-driven solid-on-solid interfaces moving under stochastic dynamics with local energy barriers
We study the microscopic structure and the stationary propagation velocity of
(1+1)-dimensional solid-on-solid interfaces in an Ising lattice-gas model,
which are driven far from equilibrium by an applied force, such as a magnetic
field or a difference in (electro)chemical potential. We use an analytic
nonlinear-response approximation [P.A. Rikvold and M. Kolesik, J. Stat. Phys.
100, 377 (2000)] together with kinetic Monte Carlo simulations. Here we
consider interfaces that move under Arrhenius dynamics, which include a
microscopic energy barrier between the allowed Ising/lattice-gas states. Two
different dynamics are studied: the standard one-step dynamic (OSD) [H.C. Kang
and W. Weinberg, J. Chem. Phys. 90, 2824 (1992)] and the two-step
transition-dynamics approximation (TDA) [T. Ala-Nissila, J. Kjoll, and S.C.
Ying, Phys. Rev. B 46, 846 (1992)]. In the OSD the effects of the applied force
and the interaction energies in the model factorize in the transition rates (a
soft dynamic), while in the TDA such factorization is not possible (a hard
dynamic). In full agreement with previous general theoretical results we find
that the local interface width under the TDA increases dramatically with the
applied force. In contrast, the interface structure with the OSD is only weakly
influenced by the force, in qualitative agreement with the theoretical
expectations. Results are also obtained for the force-dependence and anisotropy
of the interface velocity, which also show differences in good agreement with
the theoretical expectations for the differences between soft and hard
dynamics. Our results confirm that different stochastic interface dynamics that
all obey detailed balance and the same conservation laws nevertheless can lead
to radically different interface responses to an applied force.Comment: 18 pages RevTex. Minor revisions. Phys. Rev. B, in pres
The virial expansion of a classical interacting system
We consider N particles interacting pair-wise by an inverse square potential
in one dimension (Calogero-Sutherland-Moser model). When trapped harmonically,
its classical canonical partition function for the repulsive regime is known in
the literature. We start by presenting a concise re-derivation of this result.
The equation of state is then calculated both for the trapped and the
homogeneous gas. Finally, the classical limit of Wu's distribution function for
fractional exclusion statistics is obtained and we re-derive the classical
virial expansion of the homogeneous gas using this distribution function.Comment: 9 pages; added references to some earlier work on this problem; this
has led to a significant shortening of the paper and a changed titl
Schrodinger equation for the one particle density matrix of thermal systems: An alternative formulation of Bose-Einstein condensation
We formulate a linear Schrodinger equation with the temperature-dependent
potential for the one-particle density matrix and obtain the condensation
temperature of the Bose-Einstein condensate from a bound-state condition for
the Schrodinger equation both with and without the confining trap. The results
are in very good agreement with those of the full statistical physics
treatment. This is an alternative to the Bose-Einstein condensation in the
standard ideal Bose gas treatment.Comment: 4 pages, 2 figure
Thermodynamics of quantum gases for the entire range of temperature
We have analytically explored thermodynamics of free Bose and Fermi gases for
the entire range of temperature, and have extended the same for harmonically
trapped cases. We have obtained approximate chemical potentials of the quantum
gases in closed forms of temperature so that the thermodynamic properties of
the quantum gases become plausible specially in the intermediate regime between
the classical and quantum limits.Comment: 5 pages, 3 figures. Teaching Articl
Thermal fluctuation field for current-induced domain wall motion
Current-induced domain wall motion in magnetic nanowires is affected by
thermal fluctuation. In order to account for this effect, the
Landau-Lifshitz-Gilbert equation includes a thermal fluctuation field and
literature often utilizes the fluctuation-dissipation theorem to characterize
statistical properties of the thermal fluctuation field. However, the theorem
is not applicable to the system under finite current since it is not in
equilibrium. To examine the effect of finite current on the thermal
fluctuation, we adopt the influence functional formalism developed by Feynman
and Vernon, which is known to be a useful tool to analyze effects of
dissipation and thermal fluctuation. For this purpose, we construct a quantum
mechanical effective Hamiltonian describing current-induced domain wall motion
by generalizing the Caldeira-Leggett description of quantum dissipation. We
find that even for the current-induced domain wall motion, the statistical
properties of the thermal noise is still described by the
fluctuation-dissipation theorem if the current density is sufficiently lower
than the intrinsic critical current density and thus the domain wall tilting
angle is sufficiently lower than pi/4. The relation between our result and a
recent result, which also addresses the thermal fluctuation, is discussed. We
also find interesting physical meanings of the Gilbert damping alpha and the
nonadiabaticy parameter beta; while alpha characterizes the coupling strength
between the magnetization dynamics (the domain wall motion in this paper) and
the thermal reservoir (or environment), beta characterizes the coupling
strength between the spin current and the thermal reservoir.Comment: 16 page, no figur
Equation of state of an interacting Bose gas at finite temperature: a Path Integral Monte Carlo study
By using exact Path Integral Monte Carlo methods we calculate the equation of
state of an interacting Bose gas as a function of temperature both below and
above the superfluid transition. The universal character of the equation of
state for dilute systems and low temperatures is investigated by modeling the
interatomic interactions using different repulsive potentials corresponding to
the same s-wave scattering length. The results obtained for the energy and the
pressure are compared to the virial expansion for temperatures larger than the
critical temperature. At very low temperatures we find agreement with the
ground-state energy calculated using the diffusion Monte Carlo method.Comment: 7 pages, 6 figure
Classical Nucleation Theory of the One-Component Plasma
We investigate the crystallization rate of a one-component plasma (OCP) in
the context of classical nucleation theory. From our derivation of the free
energy of an arbitrary distribution of solid clusters embedded in a liquid
phase, we derive the steady-state nucleation rate of an OCP as a function of
the Coulomb coupling parameter. Our result for the rate is in accord with
recent molecular dynamics simulations, but it is greater than that of previous
analytical estimates by many orders of magnitude. Further molecular dynamics
simulations of the nucleation rate of a supercooled liquid OCP for several
values of the coupling parameter would clarify the physics of this process.Comment: 6 pages, 1 figure, accepted by PR
Continuous distribution of frequencies and deformed dispersion relations
The possibilities that, in the realm of the detection of the so--called
deformed dispersion relation, a light source with a continuous distribution of
frequencies offers is discussed. It will be proved that the presence of finite
coherence length entails the emergence of a new term in the interference
pattern. This is a novel trait, which renders a new possibility in the quest
for bounds associated with these deformed dispersion relations.Comment: Accepted in Classical and Quantum Gravit
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