276 research outputs found
Molecular regimes in ultracold Fermi gases
The use of Feshbach resonances for tuning the interparticle interaction in
ultracold Fermi gases has led to remarkable developments, in particular to the
creation and Bose-Einstein condensation of weakly bound diatomic molecules of
fermionic atoms. These are the largest diatomic molecules obtained so far, with
a size of the order of thousands of angstroms. They represent novel composite
bosons, which exhibit features of Fermi statistics at short intermolecular
distances. Being highly excited, these molecules are remarkably stable with
respect to collisional relaxation, which is a consequence of the Pauli
exclusion principle for identical fermionic atoms. The purpose of this review
is to introduce theoretical approaches and describe the physics of molecular
regimes in two-component Fermi gases and Fermi-Fermi mixtures, focusing
attention on quantum statistical effects.Comment: Chapter of the book: "Cold Molecules: Theory, Experiment,
Applications" edited by R. V. Krems, B. Friedrich and W. C. Stwalley
(publication expected in March 2009
Diffusion in Stationary Flow from Mesoscopic Non-equilibrium Thermodynamics
We analyze the diffusion of a Brownian particle in a fluid under stationary
flow. By using the scheme of non-equilibrium thermodynamics in phase space, we
obtain the Fokker-Planck equation which is compared with others derived from
kinetic theory and projector operator techniques. That equation exhibits
violation of the fluctuation dissipation-theorem. By implementing the
hydrodynamic regime described by the first moments of the non-equilibrium
distribution, we find relaxation equations for the diffusion current and
pressure tensor, allowing us to arrive at a complete description of the system
in the inertial and diffusion regimes. The simplicity and generality of the
method we propose, makes it applicable to more complex situations, often
encountered in problems of soft condensed matter, in which not only one but
more degrees of freedom are coupled to a non-equilibrium bath.Comment: 10 pages, accepted in Phys. Rev.
Diffusion in Stationary Flow from Mesoscopic Non-equilibrium Thermodynamics
We analyze the diffusion of a Brownian particle in a fluid under stationary
flow. By using the scheme of non-equilibrium thermodynamics in phase space, we
obtain the Fokker-Planck equation which is compared with others derived from
kinetic theory and projector operator techniques. That equation exhibits
violation of the fluctuation dissipation-theorem. By implementing the
hydrodynamic regime described by the first moments of the non-equilibrium
distribution, we find relaxation equations for the diffusion current and
pressure tensor, allowing us to arrive at a complete description of the system
in the inertial and diffusion regimes. The simplicity and generality of the
method we propose, makes it applicable to more complex situations, often
encountered in problems of soft condensed matter, in which not only one but
more degrees of freedom are coupled to a non-equilibrium bath.Comment: 10 pages, accepted in Phys. Rev.
Anisotropic scale invariant cosmology
We study a possibility of anisotropic scale invariant cosmology. It is shown
that within the conventional Einstein gravity, the violation of the null energy
condition is necessary. We construct an example based on a ghost condensation
model that violates the null energy condition. The cosmological solution
necessarily contains at least one contracting spatial direction as in the
Kasner solution. Our cosmology is conjectured to be dual to, if any, a
non-unitary anisotropic scale invariant Euclidean field theory. We investigate
simple correlation functions of the dual theory by using the holographic
computation. After compactification of the contracting direction, our setup may
yield a dual field theory description of the winding tachyon condensation that
might solve the singularity of big bang/crunch of the universe.Comment: 12 pages, v2: reference adde
First order Born-Infeld Hydrodynamics via Gauge/Gravity Duality
By performing a derivative expansion on a class of boosted Born-Infeld-AdS_5
black branes, we study the hydrodynamics of the dual field theory - in the
spirit of AdS/CFT correspondence. We determine the fluid dynamical
stress-energy tensor to first order, and find that the ratio of the shear
viscosity to entropy density conforms to the universal value of to all
orders of the inverse of the Born-Infeld parameter.Comment: 14 pages, JHEP3, minor revision
Renormalization group study of interacting electrons
The renormalization-group (RG) approach proposed earlier by Shankar for
interacting spinless fermions at is extended to the case of non-zero
temperature and spin. We study a model with -invariant short-range
effective interaction and rotationally invariant Fermi surface in two and three
dimensions. We show that the Landau interaction function of the Fermi liquid,
constructed from the bare parameters of the low-energy effective action, is RG
invariant. On the other hand, the physical forward scattering vertex is found
as a stable fixed point of the RG flow. We demonstrate that in and 3, the
RG approach to this model is equivalent to Landau's mean-field treatment of the
Fermi liquid. We discuss subtleties associated with the symmetry properties of
the scattering amplitude, the Landau function and the low-energy effective
action. Applying the RG to response functions, we find the compressibility and
the spin susceptibility as fixed points.Comment: 11 pages, RevTeX 3.0, 2 PostScript figure
Solving the Hamilton-Jacobi Equation for General Relativity
We demonstrate a systematic method for solving the Hamilton-Jacobi equation
for general relativity with the inclusion of matter fields. The generating
functional is expanded in a series of spatial gradients. Each term is
manifestly invariant under reparameterizations of the spatial coordinates
(``gauge-invariant''). At each order we solve the Hamiltonian constraint using
a conformal transformation of the 3-metric as well as a line integral in
superspace. This gives a recursion relation for the generating functional which
then may be solved to arbitrary order simply by functionally differentiating
previous orders. At fourth order in spatial gradients, we demonstrate solutions
for irrotational dust as well as for a scalar field. We explicitly evolve the
3-metric to the same order. This method can be used to derive the Zel'dovich
approximation for general relativity.Comment: 13 pages, RevTeX, DAMTP-R93/2
Computational aspects of the gravitational instability problem for a multicomponent cosmological medium
The paper presents results for deriving closed-form analytic solutions of the
non-relativistic linear perturbation equations, which govern the evolution of
inhomogeneities in a homogeneous spatially flat multicomponent cosmological
model. Mathematical methods to derive computable forms of the perturbations are
outlined.Comment: 20 pages in LaTeX, McGill University preprin
Quantum magneto-oscillations in a two-dimensional Fermi liquid
Quantum magneto-oscillations provide a powerfull tool for quantifying
Fermi-liquid parameters of metals. In particular, the quasiparticle effective
mass and spin susceptibility are extracted from the experiment using the
Lifshitz-Kosevich formula, derived under the assumption that the properties of
the system in a non-zero magnetic field are determined uniquely by the
zero-field Fermi-liquid state. This assumption is valid in 3D but, generally
speaking, erroneous in 2D where the Lifshitz-Kosevich formula may be applied
only if the oscillations are strongly damped by thermal smearing and disorder.
In this work, the effects of interactions and disorder on the amplitude of
magneto-oscillations in 2D are studied. It is found that the effective mass
diverges logarithmically with decreasing temperature signaling a deviation from
the Fermi-liquid behavior. It is also shown that the quasiparticle lifetime due
to inelastic interactions does not enter the oscillation amplitude, although
these interactions do renormalize the effective mass. This result provides a
generalization of the Fowler-Prange theorem formulated originally for the
electron-phonon interaction.Comment: 4 pages, 1 figur
Large negative velocity gradients in Burgers turbulence
We consider 1D Burgers equation driven by large-scale white-in-time random
force. The tails of the velocity gradients probability distribution function
(PDF) are analyzed by saddle-point approximation in the path integral
describing the velocity statistics. The structure of the saddle-point
(instanton), that is velocity field configuration realizing the maximum of
probability, is studied numerically in details. The numerical results allow us
to find analytical solution for the long-time part of the instanton. Its
careful analysis confirms the result of [Phys. Rev. Lett. 78 (8) 1452 (1997)
[chao-dyn/9609005]] based on short-time estimations that the left tail of PDF
has the form ln P(u_x) \propto -|u_x|^(3/2).Comment: 10 pages, RevTeX, 10 figure
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