464 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
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
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
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
Comment on Phys. Rev. B 83, 054515 (2011) by V. G. Kogan and J. Schmalian and comment on their reply Phys. Rev. B 86, 016502 (2012)
The recent paper by V. G. Kogan and J. Schmalian Phys. Rev. B 83, 054515
(2011) argues that the widely used two-component Ginzburg-Landau (GL) models
are not correct, and further concludes that in the regime which is described by
a GL theory there could be no disparity in the coherence lengths of two
superconducting components. This would in particular imply that (in contrast to
superconductors), there could be no "type-1.5"
superconducting regime in U(1) multiband systems for any finite interband
coupling strength. We point out that these claims are incorrect and based on an
erroneous scheme of reduction of a two-component GL theory. We also attach a
separate rejoinder on reply by Kogan and Schmalian. In their reply Phys. Rev. B
86, 016502 (2012) to our comment Phys. Rev. B 86, 016501 (2012) Kogan and
Schmalian did not refute or, indeed, discuss the main points of criticism in
the comment. Unfortunately they instead advance new incorrect claims regarding
two-band and type-1.5 superconductivity. The main purpose of the attached
rejoinder is to discuss these new incorrect claims.Comment: v3: a comment on reply by Kogan and Schmalian is include
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
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
Ultracold heteronuclear molecules and ferroelectric superfluids
We analyze the possibility of a ferroelectric transition in heteronuclear
molecules consisting of Bose-Bose, Bose-Fermi or Fermi-Fermi atom pairs. This
transition is characterized by the appearance of a spontaneous electric
polarization below a critical temperature. We discuss the existence of a
ferroelectric Fermi liquid phase for Fermi molecules and the existence of a
ferroelectric superfluid phase for Bose molecules characterized by the
coexistence of ferroelectric and superfluid orders. Lastly, we propose an
experiment to detect ferroelectric correlations through the observation of
coherent dipole radiation pulses during time of flight.Comment: 4 pages and 3 figure
Ideal Gas in a strong Gravitational field: Area dependence of Entropy
We study the thermodynamic parameters like entropy, energy etc. of a box of
gas made up of indistinguishable particles when the box is kept in various
static background spacetimes having a horizon. We compute the thermodynamic
variables using both statistical mechanics as well as by solving the
hydrodynamical equations for the system. When the box is far away from the
horizon, the entropy of the gas depends on the volume of the box except for
small corrections due to background geometry. As the box is moved closer to the
horizon with one (leading) edge of the box at about Planck length (L_p) away
from the horizon, the entropy shows an area dependence rather than a volume
dependence. More precisely, it depends on a small volume A*L_p/2 of the box,
upto an order O(L_p/K)^2 where A is the transverse area of the box and K is the
(proper) longitudinal size of the box related to the distance between leading
and trailing edge in the vertical direction (i.e in the direction of the
gravitational field). Thus the contribution to the entropy comes from only a
fraction O(L_p/K) of the matter degrees of freedom and the rest are suppressed
when the box approaches the horizon. Near the horizon all the thermodynamical
quantities behave as though the box of gas has a volume A*L_p/2 and is kept in
a Minkowski spacetime. These effects are: (i) purely kinematic in their origin
and are independent of the spacetime curvature (in the sense that Rindler
approximation of the metric near the horizon can reproduce the results) and
(ii) observer dependent. When the equilibrium temperature of the gas is taken
to be equal to the the horizon temperature, we get the familiar A/L_p^2
dependence in the expression for entropy. All these results hold in a D+1
dimensional spherically symmetric spacetime.Comment: 19 pages, added some discussion, matches published versio
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