154 research outputs found
Quasi-equilibria in one-dimensional self-gravitating many body systems
The microscopic dynamics of one-dimensional self-gravitating many-body
systems is studied. We examine two courses of the evolution which has the
isothermal and stationary water-bag distribution as initial conditions. We
investigate the evolution of the systems toward thermal equilibrium. It is
found that when the number of degrees of freedom of the system is increased,
the water-bag distribution becomes a quasi-equilibrium, and also the
stochasticity of the system reduces. This results suggest that the phase space
of the system is effectively not ergodic and the system with large degreees of
freedom approaches to the near-integrable one.Comment: 21pages + 7 figures (available upon request), revtex, submitted to
Physical Review
Relaxation processes in one-dimensional self-gravitating many-body systems
Though one dimensional self-gravitating -body systems have been studied
for three decade, the nature of relaxation was still unclear. There were
inconsistent results about relaxation time; some initial state relaxed in the
time scale , but another state did not relax even after , where is the crossing time. The water-bag distribution was
believed not to relax after . In our previous paper, however,
we found there are two different relaxation times in the water-bag
distribution;in the faster relaxation ( microscopic relaxation ) the
equipartition of energy distribution is attains but the macroscopic
distribution turns into the isothermal distribution in the later relaxation
(macroscopic relaxation). In this paper, we investigated the properties of the
two relaxation. We found that the microscopic relaxation time is , and the macroscopic relaxation time is proportional to , thus
the water-bag does relax. We can see the inconsistency about the relaxation
times is resolved as that we see the two different aspect of relaxations.
Further, the physical mechanisms of the relaxations are presented.Comment: 11 pages, uuencoded, compressed Postscript, no figure, figures
available at ftp://ferio.mtk.nao.ac.jp/pub/tsuchiya/Tsuchiya95.tar.g
Shifts and widths of collective excitations in trapped Bose gases by the dielectric formalism
We present predictions for the temperature dependent shifts and damping
rates. They are obtained by applying the dielectric formalism to a simple model
of a trapped Bose gas. Within the framework of the model we use lowest order
perturbation theory to determine the first order correction to the results of
Hartree-Fock-Bogoliubov-Popov theory for the complex collective excitation
frequencies, and present numerical results for the temperature dependence of
the damping rates and the frequency shifts. Good agreement with the
experimental values measured at JILA are found for the m=2 mode, while we find
disagreements in the shifts for m=0. The latter point to the necessity of a
non-perturbative treatment for an explanation of the temperature-dependence of
the m=0 shifts.Comment: 10 pages revtex, 3 figures in postscrip
Energies and damping rates of elementary excitations in spin-1 Bose-Einstein condensed gases
Finite temperature Green's function technique is used to calculate the
energies and damping rates of elementary excitations of the homogeneous,
dilute, spin-1 Bose gases below the Bose-Einstein condensation temperature both
in the density and spin channels. For this purpose the self-consistent
dynamical Hartree-Fock model is formulated, which takes into account the direct
and exchange processes on equal footing by summing up certain classes of
Feynman diagrams. The model is shown to fulfil the Goldstone theorem and to
exhibit the hybridization of one-particle and collective excitations correctly.
The results are applied to the gases of ^{23}Na and ^{87}Rb atoms.Comment: 26 pages, 21 figures. Added 2 new figures, detailed discussio
Cyclobutanone Inhibitors of Diaminopimelate Desuccinylase (DapE) as Potential New Antibiotics
Based on our previous success in using cyclobutanone derivatives as enzyme inhibitors, we have designed and prepared a 37-member library of α-aminocyclobutanone amides and sulfonamides, screened for inhibition of the bacterial enzyme diaminopimelate desuccinylase (DapE), which is a promising antibiotic target, and identified several inhibitors with micromolar inhibitory potency. Molecular docking suggests binding of the deprotonated hydrate of the strained cyclobutanone, and thermal shift analysis with the most potent inhibitor (3y, IC50 = 23.1 µM) enabled determination of a Ki value of 10.2 +/− 0.26 µM and observed two separate Tm values for H. influenzae DapE (HiDapE)
Effect of angular momentum on equilibrium properties of a self-gravitating system
The microcanonical properties of a two dimensional system of N classical
particles interacting via a smoothed Newtonian potential as a function of the
total energy E and the total angular momentum L are discussed. In order to
estimate suitable observables a numerical method based on an importance
sampling algorithm is presented. The entropy surface shows a negative specific
heat region at fixed L for all L. Observables probing the average mass
distribution are used to understand the link between thermostatistical
properties and the spatial distribution of particles. In order to define a
phase in non-extensive system we introduce a more general observable than the
one proposed by Gross and Votyakov [Eur. Phys. J. B:15, 115 (2000)]: the sign
of the largest eigenvalue of the entropy surface curvature. At large E the
gravitational system is in a homogeneous gas phase. At low E there are several
collapse phases; at L=0 there is a single cluster phase and for L>0 there are
several phases with 2 clusters. All these pure phases are separated by first
order phase transition regions. The signal of critical behaviour emerges at
different points of the parameter space (E,L). We also discuss the ensemble
introduced in a recent pre-print by Klinko & Miller; this ensemble is the
canonical analogue of the one at constant energy and constant angular momentum.
We show that a huge loss of informations appears if we treat the system as a
function of intensive parameters: besides the known non-equivalence at first
order phase transitions, there exit in the microcanonical ensemble some values
of the temperature and the angular velocity for which the corresponding
canonical ensemble does not exist, i.e. the partition sum diverges.Comment: 17 pages, 11 figures, submitted to Phys. Rev.
Landau damping in trapped Bose-condensed gases
We study Landau damping in dilute Bose-Einstein condensed gases in both
spherical and prolate ellipsoidal harmonic traps. We solve the Bogoliubov
equations for the mode spectrum in both of these cases, and calculate the
damping by summing over transitions between excited quasiparticle states. The
results for the spherical case are compared to those obtained in the
Hartree-Fock approximation, where the excitations take on a single-particle
character, and excellent agreement between the two approaches is found. We have
also taken the semiclassical limit of the Hartree-Fock approximation and obtain
a novel expression for the Landau damping rate involving the time dependent
self-diffusion function of the thermal cloud. As a final approach, we study the
decay of a condensate mode by making use of dynamical simulations in which both
the condensate and thermal cloud are evolved explicitly as a function of time.
A detailed comparison of all these methods over a wide range of sample sizes
and trap geometries is presented.Comment: 18 pages, 13 figures, submitted to the New Journal of Physics focus
issue on Quantum Gase
Equilibrium and dynamical properties of two dimensional self-gravitating systems
A system of N classical particles in a 2D periodic cell interacting via
long-range attractive potential is studied. For low energy density a
collapsed phase is identified, while in the high energy limit the particles are
homogeneously distributed. A phase transition from the collapsed to the
homogeneous state occurs at critical energy U_c. A theoretical analysis within
the canonical ensemble identifies such a transition as first order. But
microcanonical simulations reveal a negative specific heat regime near .
The dynamical behaviour of the system is affected by this transition : below
U_c anomalous diffusion is observed, while for U > U_c the motion of the
particles is almost ballistic. In the collapsed phase, finite -effects act
like a noise source of variance O(1/N), that restores normal diffusion on a
time scale diverging with N. As a consequence, the asymptotic diffusion
coefficient will also diverge algebraically with N and superdiffusion will be
observable at any time in the limit N \to \infty. A Lyapunov analysis reveals
that for U > U_c the maximal exponent \lambda decreases proportionally to
N^{-1/3} and vanishes in the mean-field limit. For sufficiently small energy,
in spite of a clear non ergodicity of the system, a common scaling law \lambda
\propto U^{1/2} is observed for any initial conditions.Comment: 17 pages, Revtex - 15 PS Figs - Subimitted to Physical Review E - Two
column version with included figures : less paper waste
Bose condensates in a harmonic trap near the critical temperature
The mean-field properties of finite-temperature Bose-Einstein gases confined
in spherically symmetric harmonic traps are surveyed numerically. The solutions
of the Gross-Pitaevskii (GP) and Hartree-Fock-Bogoliubov (HFB) equations for
the condensate and low-lying quasiparticle excitations are calculated
self-consistently using the discrete variable representation, while the most
high-lying states are obtained with a local density approximation. Consistency
of the theory for temperatures through the Bose condensation point requires
that the thermodynamic chemical potential differ from the eigenvalue of the GP
equation; the appropriate modifications lead to results that are continuous as
a function of the particle interactions. The HFB equations are made gapless
either by invoking the Popov approximation or by renormalizing the particle
interactions. The latter approach effectively reduces the strength of the
effective scattering length, increases the number of condensate atoms at each
temperature, and raises the value of the transition temperature relative to the
Popov approximation. The renormalization effect increases approximately with
the log of the atom number, and is most pronounced at temperatures near the
transition. Comparisons with the results of quantum Monte Carlo calculations
and various local density approximations are presented, and experimental
consequences are discussed.Comment: 15 pages, 11 embedded figures, revte
Finite temperature excitations of a trapped Bose-Fermi mixture
We present a detailed study of the low-lying collective excitations of a
spherically trapped Bose-Fermi mixture at finite temperature in the
collisionless regime. The excitation frequencies of the condensate are
calculated self-consistently using the static Hartree-Fock-Bogoliubov theory
within the Popov approximation. The frequency shifts and damping rates due to
the coupled dynamics of the condensate, noncondensate, and degenerate Fermi gas
are also taken into account by means of the random phase approximation and
linear response theory. In our treatment, the dipole excitation remains close
to the bare trapping frequency for all temperatures considered, and thus is
consistent with the generalized Kohn theorem. We discuss in some detail the
behavior of monopole and quadrupole excitations as a function of the Bose-Fermi
coupling. At nonzero temperatures we find that, as the mixture moves towards
spatial separation with increasing Bose-Fermi coupling, the damping rate of the
monopole (quadrupole) excitation increases (decreases). This provides us a
useful signature to identify the phase transition of spatial separation.Comment: 10 pages, 8 figures embedded; to be published in Phys. Rev.
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