43,488 research outputs found
Landau damping in the multiscale Vlasov theory
Vlasov kinetic theory is extended by adopting an extra one particle
distribution function as an additional state variable characterizing the
micro-turbulence internal structure. The extended Vlasov equation keeps the
reversibility, the Hamiltonian structure, and the entropy conservation of the
original Vlasov equation. In the setting of the extended Vlasov theory we then
argue that the Fokker-Planck type damping in the velocity dependence of the
extra distribution function induces the Landau damping. The same type of
extension is made also in the setting of fluid mechanics
Stochastic Inflation Revisited: Non-Slow Roll Statistics and DBI Inflation
Stochastic inflation describes the global structure of the inflationary
universe by modeling the super-Hubble dynamics as a system of matter fields
coupled to gravity where the sub-Hubble field fluctuations induce a stochastic
force into the equations of motion. The super-Hubble dynamics are ultralocal,
allowing us to neglect spatial derivatives and treat each Hubble patch as a
separate universe. This provides a natural framework in which to discuss
probabilities on the space of solutions and initial conditions. In this article
we derive an evolution equation for this probability for an arbitrary class of
matter systems, including DBI and k-inflationary models, and discover
equilibrium solutions that satisfy detailed balance. Our results are more
general than those derived assuming slow roll or a quasi-de Sitter geometry,
and so are directly applicable to models that do not satisfy the usual slow
roll conditions. We discuss in general terms the conditions for eternal
inflation to set in, and we give explicit numerical solutions of highly
stochastic, quasi-stationary trajectories in the relativistic DBI regime.
Finally, we show that the probability for stochastic/thermal tunneling can be
significantly enhanced relative to the Hawking-Moss instanton result due to
relativistic DBI effects.Comment: 38 pages, 2 figures. v3: minor revisions; version accepted into JCA
Coupled Hartree-Fock-Bogoliubov kinetic equations for a trapped Bose gas
Using the Kadanoff-Baym non-equilibrium Green's function formalism, we derive
the self-consistent Hartree-Fock-Bogoliubov (HFB) collisionless kinetic
equations and the associated equation of motion for the condensate wavefunction
for a trapped Bose-condensed gas. Our work generalizes earlier work by Kane and
Kadanoff (KK) for a uniform Bose gas. We include the off-diagonal (anomalous)
pair correlations, and thus we have to introduce an off-diagonal distribution
function in addition to the normal (diagonal) distribution function. This
results in two coupled kinetic equations. If the off-diagonal distribution
function can be neglected as a higher-order contribution, we obtain the
semi-classical kinetic equation recently used by Zaremba, Griffin and Nikuni
(based on the simpler Popov approximation). We discuss the static local
equilibrium solution of our coupled HFB kinetic equations within the
semi-classical approximation. We also verify that a solution is the rigid
in-phase oscillation of the equilibrium condensate and non-condensate density
profiles, oscillating with the trap frequency.Comment: 25 page
Matter Wave Turbulence: Beyond Kinetic Scaling
Turbulent scaling phenomena are studied in an ultracold Bose gas away from
thermal equilibrium. Fixed points of the dynamical evolution are characterized
in terms of universal scaling exponents of correlation functions. The scaling
behavior is determined analytically in the framework of quantum field theory,
using a nonperturbative approximation of the two-particle irreducible effective
action. While perturbative Kolmogorov scaling is recovered at higher energies,
scaling solutions with anomalously large exponents arise in the infrared regime
of the turbulence spectrum. The extraordinary enhancement in the momentum
dependence of long-range correlations could be experimentally accessible in
dilute ultracold atomic gases. Such experiments have the potential to provide
insight into dynamical phenomena directly relevant also in other present-day
focus areas like heavy-ion collisions and early-universe cosmology.Comment: 18 pages, 2 figure
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