188 research outputs found
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
Conserving and Gapless Approximations for an Inhomogeneous Bose Gas at Finite Temperatures
We derive and discuss the equations of motion for the condensate and its
fluctuations for a dilute, weakly interacting Bose gas in an external potential
within the self--consistent Hartree--Fock--Bogoliubov (HFB) approximation.
Account is taken of the depletion of the condensate and the anomalous Bose
correlations, which are important at finite temperatures. We give a critical
analysis of the self-consistent HFB approximation in terms of the
Hohenberg--Martin classification of approximations (conserving vs gapless) and
point out that the Popov approximation to the full HFB gives a gapless
single-particle spectrum at all temperatures. The Beliaev second-order
approximation is discussed as the spectrum generated by functional
differentiation of the HFB single--particle Green's function. We emphasize that
the problem of determining the excitation spectrum of a Bose-condensed gas
(homogeneous or inhomogeneous) is difficult because of the need to satisfy
several different constraints.Comment: plain tex, 19 page
Landau-Khalatnikov two-fluid hydrodynamics of a trapped Bose gas
Starting from the quantum kinetic equation for the non-condensate atoms and
the generalized Gross-Pitaevskii equation for the condensate, we derive the
two-fluid hydrodynamic equations of a trapped Bose gas at finite temperatures.
We follow the standard Chapman-Enskog procedure, starting from a solution of
the kinetic equation corresponding to the complete local equilibrium between
the condensate and the non-condensate components. Our hydrodynamic equations
are shown to reduce to a form identical to the well-known Landau-Khalatnikov
two-fluid equations, with hydrodynamic damping due to the deviation from local
equilibrium. The deviation from local equilibrium within the thermal cloud
gives rise to dissipation associated with shear viscosity and thermal
conduction. In addition, we show that effects due to the deviation from the
diffusive local equilibrium between the condensate and the non-condensate
(recently considered by Zaremba, Nikuni and Griffin) can be described by four
frequency-dependent second viscosity transport coefficients. We also derive
explicit formulas for all the transport coefficients. These results are used to
introduce two new characteristic relaxation times associated with hydrodynamic
damping. These relaxation times give the rate at which local equilibrium is
reached and hence determine whether one is in the two-fluid hydrodynamic
region.Comment: 26 pages, 3 postscript figures, submitted to PR
Finite temperature theory of the trapped two dimensional Bose gas
We present a Hartree-Fock-Bogoliubov (HFB) theoretical treatment of the
two-dimensional trapped Bose gas and indicate how semiclassical approximations
to this and other formalisms have lead to confusion. We numerically obtain
results for the fully quantum mechanical HFB theory within the Popov
approximation and show that the presence of the trap stabilizes the condensate
against long wavelength fluctuations. These results are used to show where
phase fluctuations lead to the formation of a quasicondensate.Comment: 4 pages, 3 figure
A particle-number-conserving Bogoliubov method which demonstrates the validity of the time-dependent Gross-Pitaevskii equation for a highly condensed Bose gas
The Bogoliubov method for the excitation spectrum of a Bose-condensed gas is
generalized to apply to a gas with an exact large number of particles.
This generalization yields a description of the Schr\"odinger picture field
operators as the product of an annihilation operator for the total number
of particles and the sum of a ``condensate wavefunction'' and a phonon
field operator in the form when the field operator acts on the N particle subspace. It
is then possible to expand the Hamiltonian in decreasing powers of ,
an thus obtain solutions for eigenvalues and eigenstates as an asymptotic
expansion of the same kind. It is also possible to compute all matrix elements
of field operators between states of different N.Comment: RevTeX, 11 page
On the Origin of the Outgoing Black Hole Modes
The question of how to account for the outgoing black hole modes without
drawing upon a transplanckian reservoir at the horizon is addressed. It is
argued that the outgoing modes must arise via conversion from ingoing modes. It
is further argued that the back-reaction must be included to avoid the
conclusion that particle creation cannot occur in a strictly stationary
background. The process of ``mode conversion" is known in plasma physics by
this name and in condensed matter physics as ``Andreev reflection" or ``branch
conversion". It is illustrated here in a linear Lorentz non-invariant model
introduced by Unruh. The role of interactions and a physical short distance
cutoff is then examined in the sonic black hole formed with Helium-II.Comment: 12 pages, plain latex, 2 figures included using psfig; Analogy to
``Andreev reflection" in superfluid systems noted, references and
acknowledgment added, format changed to shorten tex
Generalized coherent state representation of Bose-Einstein condensates
We show that the quantum many-body state of Bose-Einstein condensates (BEC)
consistent with the time-dependent Hartree-Fock-Bogoliubov (TDHFB) equations is
a generalized coherent state (GCS). At zero temerature, the non-condensate
density and the anomalous non-condensate correlation are not independent,
allowing us to elimiate one of the three variables in the TDHFB.Comment: Submitted to Phys. Rev. A. No figures. Revised version fixes several
minor typos, and adds to some discussions; no change to the conclusio
Mechanical response functions of finite temperature Bose-Einstein Condensates
Using the Liouville space framework developed in nonlinear optics we
calculate the linear response functions and susceptibilities of Bose-Einstein
condensates (BEC) subject to an arbitrary mechanical force. Distinct signatures
of the dynamics of finite temperature BEC are obtained by solving the
Hartree-Fock-Bogoliubov theory. Numerical simulations of the position dependent
linear response functions of one dimensional trapped BEC in the time and the
frequency domains are presented.Comment: 9 figures. Submitted to Phys. Rev.
Expression analysis of the TAB2 protein in adult mouse tissues
Background: The Interleukin-1 (IL-1) signaling component TAK1 binding protein 2 (TAB2) plays a role in activating the NFκB and JNK signaling pathways. Additionally, TAB2 functions in the nucleus as a repressor of NFκB-mediated gene regulation. Objective: To obtain insight into the function of TAB2 in the adult mouse, we analyzed the in vivo TAB2 expression pattern. Materials and methods: Cell lines and adult mouse tissues were analyzed for TAB2 protein expression and localization. Results: Immunohistochemical staining for TAB2 protein revealed expression in the vascular endothelium of most tissues, hematopoietic cells and brain cells. While TAB2 is localized in both the nucleus and the cytoplasm in cell lines, cytoplasmic localization predominates in hematopoietic tissues in vivo. Conclusions: The TAB2 expression pattern shows striking similarities with previously reported IL-1 receptor expression and NFκB activation patterns, suggesting that TAB2 in vivo is playing a role in these signaling pathways
Four simple recommendations to encourage best practices in research software [version 1; referees: awaiting peer review]
Scientific research relies on computer software, yet software is not always developed following practices that ensure its quality and sustainability. This manuscript does not aim to propose new software development best practices, but rather to provide simple recommendations that encourage the adoption of existing best practices. Software development best practices promote better quality software, and better quality software improves the reproducibility and reusability of research. These recommendations are designed around Open Source values, and provide practical suggestions that contribute to making research software and its source code more discoverable, reusable and transparent. This manuscript is aimed at developers, but also at organisations, projects, journals and funders that can increase the quality and sustainability of research software by encouraging the adoption of these recommendations.
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