477 research outputs found

### Relativistic harmonic oscillator model for quark stars

The relativistic harmonic oscillator (RHO) model of hadrons is used to study
quark stars. The mass-radius relationship is obtained and compared with bag
model of quark star, using Tolman-Oppenheimer-Volkoff equation. In this model,
the outward degenerate pressure due to discrete Landau levels and Landau
degeneracy balances the inward gravitational pressure. Where as in bag model
the degenerate pressure is due to the standard continuum levels which balances
the combined inward pressure due to gravitation and bag pressure. So in RHO
model, the confinement effect is included in the degenerate pressure. We found
a qualitative similarity, but quantitative differences in mass-radius
relationship of quark stars in these two models. Masses and radii are
relatively larger and the central energy densities, required for stable quark
stars, are lower in RHO model than that of bag model.Comment: 7 pages, 1 figure, articl

### 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

### Dynamical instability of a spin spiral in an interacting Fermi gas as a probe of the Stoner transition

We propose an experiment to probe ferromagnetic phenomena in an ultracold
Fermi gas, while alleviating the sensitivity to three-body loss and competing
many-body instabilities. The system is initialized in a small pitch spin
spiral, which becomes unstable in the presence of repulsive interactions. To
linear order the exponentially growing collective modes exhibit critical
slowing down close to the Stoner transition point. Also, to this order, the
dynamics are identical on the paramagnetic and ferromagnetic sides of the
transition. However, we show that scattering off the exponentially growing
modes qualitatively alters the collective mode structure. The critical slowing
down is eliminated and in its place a new unstable branch develops at large
wave vectors. Furthermore, long-wavelength instabilities are quenched on the
paramagnetic side of the transition. We study the experimental observation of
the instabilities, specifically addressing the trapping geometry and how
phase-contrast imaging will reveal the emerging domain structure. These probes
of the dynamical phenomena could allow experiments to detect the transition
point and distinguish between the paramagnetic and ferromagnetic regimes

### 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

### Dirac particle in a spherical scalar potential well

In this paper we investigate a solution of the Dirac equation for a
spin-$\frac{1}2$ particle in a scalar potential well with full spherical
symmetry. The energy eigenvalues for the quark particle in $s_{1/2}$ states
(with $\kappa=-1$) and $p_{1/2}$ states (with $\kappa=1$) are calculated. We
also study the continuous Dirac wave function for a quark in such a potential,
which is not necessarily infinite. Our results, at infinite limit, are in good
agreement with the MIT bag model. We make some remarks about the sharpness
value of the wave function on the wall. This model, for finite values of
potential, also could serve as an effective model for the nucleus where $U(r)$
is the effective single particle potential.Comment: 9 pages, 8 figures, revtex4, version to appear in PR

### 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

### Theory of cooling by flow through narrow pores

We consider the possibility of adding a stage to a dilution refrigerator to
provide additional cooling by ``filtering out'' hot atoms. Three methods are
considered: 1) Effusion, where holes having diameters larger than a mean-free
path allow atoms to pass through easily; 2) Particle waveguide-like motion
using very narrow channels that greatly restrict the quantum states of the
atoms in a channel. 3) Wall-limited diffusion through channels, in which the
wall scattering is disordered so that local density equilibrium is established
in a channel. We assume that channel dimension are smaller than the mean-free
path for atom-atom interactions. The particle waveguide and the wall-limited
diffusion methods using channels on order of the de Broglie wavelength give
cooling. Recent advances in nano-filters give this method some hope of being
practical.Comment: 10 pages, 3 figures. Corrected typos and made some minor wording
change

### 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 $\eta$ and
the wave-number-dependent viscosity $\eta(k)$ are calculated from the
microscopic shear in the random motion of particles. A recently developed
method of calculating the wave-number-dependent viscosity $\eta(k)$ is
validated by comparing the results of $\eta(k)$ from the two simulations. It is
also verified that the Green-Kubo relation can still yield an accurate measure
of the static viscosity $\eta$ 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

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