24 research outputs found
Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Six Loops
We compute the shift of the transition temperature for a homogenous weakly
interacting Bose gas in leading order in the scattering length a for given
particle density n. Using variational perturbation theory through six loops in
a classical three-dimensional scalar field theory, we obtain Delta T_c/T_c =
1.25+/-0.13 a n^(1/3), in agreement with recent Monte-Carlo results.Comment: 4 pages; omega' corrected: final result changes slightly to
1.25+/-0.13; references added; several minor change
S-matrix approach to quantum gases in the unitary limit II: the three-dimensional case
A new analytic treatment of three-dimensional homogeneous Bose and Fermi
gases in the unitary limit of negative infinite scattering length is presented,
based on the S-matrix approach to statistical mechanics we recently developed.
The unitary limit occurs at a fixed point of the renormalization group with
dynamical exponent z=2 where the S-matrix equals -1. For fermions we find T_c
/T_F is approximately 0.1. For bosons we present evidence that the gas does not
collapse, but rather has a critical point that is a strongly interacting form
of Bose-Einstein condensation. This bosonic critical point occurs at n lambda^3
approximately 1.3 where n is the density and lambda the thermal wavelength,
which is lower than the ideal gas value of 2.61.Comment: 26 pages, 16 figure
Large Scale Rapidity Correlations in Heavy Ion Collisions
We discuss particle production mechanisms for heavy ion collisions. We
present an argument demonstrating how the fluctuations of the number of
produced particles in a series of classical emissions can account for KNO
scaling. We predict rapidity correlations in the particle production in the
event by event analysis of heavy ion collisions on the rapidity scales of the
order of one over the strong coupling constant.Comment: REVTeX, 13 pages, 3 figure
From colored glass condensate to gluon plasma: equilibration in high energy heavy ion collisions
The initial distribution of gluons at the very early times after a high
energy heavy ion collision is described by the bulk scale of gluon
saturation in the nuclear wavefunction. The subsequent evolution of the system
towards kinetic equilibrium is described by a non-linear Landau equation for
the single particle distributions \cite{Mueller1,Mueller2}. In this paper, we
solve this equation numerically for the idealized initial conditions proposed
by Mueller, and study the evolution of the system to equilibrium. We discuss
the sensitivity of our results on the dynamical screening of collinear
divergences. In a particular model of dynamical screening, the convergence to
the hydrodynamic limit is seen to be rapid relative to hydrodynamic time
scales. The equilibration time, the initial temperature, and the chemical
potential are shown to have a strong functional dependence on the initial gluon
saturation scale .Comment: 34 pages, 10 figure
Vortex lattice of a Bose-Einstein Condensate in a rotating anisotropic trap
We study the vortex lattices in a Bose-Einstein Condensate in a rotating
anisotropic harmonic trap. We first investigate the single particle
wavefunctions obtained by the exact solution of the problem and give simple
expressions for these wavefunctions in the small anisotropy limit. Depending on
the strength of the interactions, a few or a large number of vortices can be
formed. In the limit of many vortices, we calculate the density profile of the
cloud and show that the vortex lattice stays triangular. We also find that the
vortex lattice planes align themselves with the weak axis of the external
potential. For a small number of vortices, we numerically solve the
Gross-Pitaevskii equation and find vortex configurations that are very
different from the vortex configurations in an axisymmetric rotating trap.Comment: 15 pages,4 figure
What Have We Learned from RHIC?
In this talk, I present what I believe we have learned from the recent RHIC
heavy ion experiments. The goal of these experiments is to make and study
matter at very high energy densities, greater than an order of magnitude larger
than that of nuclear matter. Have we made such matter? What have we learned
about the properties of this matter? What do we hope and expect to learn in the
future?Comment: 34 figure
Blow-up profile of rotating 2D focusing Bose gases
We consider the Gross-Pitaevskii equation describing an attractive Bose gas
trapped to a quasi 2D layer by means of a purely harmonic potential, and which
rotates at a fixed speed of rotation . First we study the behavior of
the ground state when the coupling constant approaches , the critical
strength of the cubic nonlinearity for the focusing nonlinear Schr{\"o}dinger
equation. We prove that blow-up always happens at the center of the trap, with
the blow-up profile given by the Gagliardo-Nirenberg solution. In particular,
the blow-up scenario is independent of , to leading order. This
generalizes results obtained by Guo and Seiringer (Lett. Math. Phys., 2014,
vol. 104, p. 141--156) in the non-rotating case. In a second part we consider
the many-particle Hamiltonian for bosons, interacting with a potential
rescaled in the mean-field manner w\int\_{\mathbb{R}^2} w(x) dx = 1\beta < 1/2a\_N \to a\_*N \to \infty$
Vortices in multicomponent Bose-Einstein condensates
We review the topic of quantized vortices in multicomponent Bose-Einstein
condensates of dilute atomic gases, with an emphasis on that in two-component
condensates. First, we review the fundamental structure, stability and dynamics
of a single vortex state in a slowly rotating two-component condensates. To
understand recent experimental results, we use the coupled Gross-Pitaevskii
equations and the generalized nonlinear sigma model. An axisymmetric vortex
state, which was observed by the JILA group, can be regarded as a topologically
trivial skyrmion in the pseudospin representation. The internal, coherent
coupling between the two components breaks the axisymmetry of the vortex state,
resulting in a stable vortex molecule (a meron pair). We also mention
unconventional vortex states and monopole excitations in a spin-1 Bose-Einstein
condensate. Next, we discuss a rich variety of vortex states realized in
rapidly rotating two-component Bose-Einstein condensates. We introduce a phase
diagram with axes of rotation frequency and the intercomponent coupling
strength. This phase diagram reveals unconventional vortex states such as a
square lattice, a double-core lattice, vortex stripes and vortex sheets, all of
which are in an experimentally accessible parameter regime. The coherent
coupling leads to an effective attractive interaction between two components,
providing not only a promising candidate to tune the intercomponent interaction
to study the rich vortex phases but also a new regime to explore vortex states
consisting of vortex molecules characterized by anisotropic vorticity. A recent
experiment by the JILA group vindicated the formation of a square vortex
lattice in this system.Comment: 69 pages, 25 figures, Invited review article for International
Journal of Modern Physics
Transport Properties of the Quark-Gluon Plasma -- A Lattice QCD Perspective
Transport properties of a thermal medium determine how its conserved charge
densities (for instance the electric charge, energy or momentum) evolve as a
function of time and eventually relax back to their equilibrium values. Here
the transport properties of the quark-gluon plasma are reviewed from a
theoretical perspective. The latter play a key role in the description of
heavy-ion collisions, and are an important ingredient in constraining particle
production processes in the early universe. We place particular emphasis on
lattice QCD calculations of conserved current correlators. These Euclidean
correlators are related by an integral transform to spectral functions, whose
small-frequency form determines the transport properties via Kubo formulae. The
universal hydrodynamic predictions for the small-frequency pole structure of
spectral functions are summarized. The viability of a quasiparticle description
implies the presence of additional characteristic features in the spectral
functions. These features are in stark contrast with the functional form that
is found in strongly coupled plasmas via the gauge/gravity duality. A central
goal is therefore to determine which of these dynamical regimes the quark-gluon
plasma is qualitatively closer to as a function of temperature. We review the
analysis of lattice correlators in relation to transport properties, and
tentatively estimate what computational effort is required to make decisive
progress in this field.Comment: 54 pages, 37 figures, review written for EPJA and APPN; one parag.
added end of section 3.4, and one at the end of section 3.2.2; some Refs.
added, and some other minor change
Matter in Strong Magnetic Fields
The properties of matter are significantly modified by strong magnetic
fields, Gauss (), as are typically
found on the surfaces of neutron stars. In such strong magnetic fields, the
Coulomb force on an electron acts as a small perturbation compared to the
magnetic force. The strong field condition can also be mimicked in laboratory
semiconductors. Because of the strong magnetic confinement of electrons
perpendicular to the field, atoms attain a much greater binding energy compared
to the zero-field case, and various other bound states become possible,
including molecular chains and three-dimensional condensed matter. This article
reviews the electronic structure of atoms, molecules and bulk matter, as well
as the thermodynamic properties of dense plasma, in strong magnetic fields,
. The focus is on the basic physical pictures and
approximate scaling relations, although various theoretical approaches and
numerical results are also discussed. For the neutron star surface composed of
light elements such as hydrogen or helium, the outermost layer constitutes a
nondegenerate, partially ionized Coulomb plasma if , and may be in
the form of a condensed liquid if the magnetic field is stronger (and
temperature K). For the iron surface, the outermost layer of the
neutron star can be in a gaseous or a condensed phase depending on the cohesive
property of the iron condensate.Comment: 45 pages with 9 figures. Many small additions/changes. Accepted for
publication in Rev. Mod. Phy