384 research outputs found
Statistical mechanics of an ideal Bose gas in a confined geometry
We study the behaviour of an ideal non-relativistic Bose gas in a
three-dimensional space where one of the dimensions is compactified to form a
circle. In this case there is no phase transition like that for the case of an
infinite volume, nevertheless Bose-Einstein condensation signified by a sudden
buildup of particles in the ground state can occur. We use the grand canonical
ensemble to study this problem. In particular, the specific heat is evaluated
numerically, as well as analytically in certain limits. We show analytically
how the familiar result for the specific heat is recovered as we let the size
of the circle become large so that the infinite volume limit is approached. We
also examine in detail the behaviour of the chemical potential and establish
the precise manner in which it approaches zero as the volume becomes large.Comment: 13 pages, 2 eps figures, revtex
Noninteracting Fermions in infinite dimensions
Usually, we study the statistical behaviours of noninteracting Fermions in
finite (mainly two and three) dimensions. For a fixed number of fermions, the
average energy per fermion is calculated in two and in three dimensions and it
becomes equal to 50 and 60 per cent of the fermi energy respectively. However,
in the higher dimensions this percentage increases as the dimensionality
increases and in infinite dimensions it becomes 100 per cent. This is an
intersting result, at least pedagogically. Which implies all fermions are
moving with Fermi momentum. This result is not yet discussed in standard text
books of quantum statistics. In this paper, this fact is discussed and
explained. I hope, this article will be helpful for graduate students to study
the behaviours of free fermions in generalised dimensionality.Comment: To appear in European Journal of Physics (2010
Reply to "Comment on `Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined' ''
In his Comment [see preceding Comment, Phys. Rev. A 82, 037601 (2010)] on the
paper by Roux [Phys. Rev. A 79, 021608(R) (2009)], Rigol argued that the energy
distribution after a quench is not related to standard statistical ensembles
and cannot explain thermalization. The latter is proposed to stem from what he
calls the eigenstate thermalization hypothesis and which boils down to the fact
that simple observables are expected to be smooth functions of the energy. In
this Reply, we show that there is no contradiction or confusion between the
observations and discussions of Roux and the expected thermalization scenario
discussed by Rigol. In addition, we emphasize a few other important aspects, in
particular the definition of temperature and the equivalence of ensemble, which
are much more difficult to show numerically even though we believe they are
essential to the discussion of thermalization. These remarks could be of
interest to people interested in the interpretation of the data obtained on
finite-size systems.Comment: 3 page
Nuclear condensation and the equation of state of nuclear matter
The isothermal compression of a dilute nucleonic gas invoking cluster degrees
of freedom is studied in an equilibrium statistical model; this clusterized
system is found to be more stable than the pure nucleonic system. The equation
of state (EoS) of this matter shows features qualitatively very similar to the
one obtained from pure nucleonic gas. In the isothermal compression process,
there is a sudden enhancement of clusterization at a transition density
rendering features analogous to the gas-liquid phase transition in normal
dilute nucleonic matter. Different observables like the caloric curves, heat
capacity, isospin distillation, etc. are studied in both the models. Possible
changes in the observables due to recently indicated medium modifications in
the symmetry energy are also investigated.Comment: 18 pages and 11 figures. Phys. Rev. C (in press
Viscosity calculated in simulations of strongly-coupled dusty plasmas with gas friction
A two-dimensional strongly-coupled dusty plasma is modeled using Langevin and
frictionless molecular dynamical simulations. The static viscosity and
the wave-number-dependent viscosity are calculated from the
microscopic shear in the random motion of particles. A recently developed
method of calculating the wave-number-dependent viscosity is
validated by comparing the results of from the two simulations. It is
also verified that the Green-Kubo relation can still yield an accurate measure
of the static viscosity in the presence of a modest level of friction as
in dusty plasma experiments.Comment: 6 pages, 3 figures, Physics of Plasmas invited pape
Statistical mechanics of confined quantum particles
We develop statistical mechanics and thermodynamics of Bose and Fermi systems
in relativistic harmonic oscillator (RHO) confining potential, which may be
applicable in quark gluon plasma (QGP), astrophysics, Bose-Einstein
condensation (BEC), condensed matter physics etc. Detailed study of QGP system
is carried out and compared with lattice results. Further, as an application,
our equation of state (EoS) of QGP is used to study compact stars like quark
star.Comment: 9 pages, 2 figures, articl
Cold atoms at unitarity and inverse square interaction
Consider two identical atoms in a spherical harmonic oscillator interacting
with a zero-range interaction which is tuned to produce an s-wave zero-energy
bound state. The quantum spectrum of the system is known to be exactly
solvable. We note that the same partial wave quantum spectrum is obtained by
the one-dimensional scale-invariant inverse square potential. Long known as the
Calogero-Sutherland-Moser (CSM) model, it leads to Fractional Exclusion
Statistics (FES) of Haldane and Wu. The statistical parameter is deduced from
the analytically calculated second virial coefficient. When FES is applied to a
Fermi gas at unitarity, it gives good agreement with experimental data without
the use of any free parameter.Comment: 11 pages, 3 figures, To appear in J. Phys. B. Atomic, Molecular and
Optical Physic
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
Feshbach Resonances and Limiting Thermodynamics of Strongly Correlated Nucleons
A finite temperature model of strongly correlated nucleons with underlying
isospin symmetries is developed. The model can be used to study the role of
bound states and Feshbach resonances on the thermal properties of a spin 1/2,
isospin 1/2 system of protons and neutrons by varying the proton fraction. An
analysis of features associated with a universal thermodynamic limit or unitary
limit is given. In the limit of very large scattering length, the effective
range to quantum thermal wavelength appears as a limiting scale in an
interaction energy and equation of state.Comment: 8 pages, 4 figure
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