14,808 research outputs found
Anisotropic Spin Diffusion in Trapped Boltzmann Gases
Recent experiments in a mixture of two hyperfine states of trapped Bose gases
show behavior analogous to a spin-1/2 system, including transverse spin waves
and other familiar Leggett-Rice-type effects. We have derived the kinetic
equations applicable to these systems, including the spin dependence of
interparticle interactions in the collision integral, and have solved for
spin-wave frequencies and longitudinal and transverse diffusion constants in
the Boltzmann limit. We find that, while the transverse and longitudinal
collision times for trapped Fermi gases are identical, the Bose gas shows
diffusion anisotropy. Moreover, the lack of spin isotropy in the interactions
leads to the non-conservation of transverse spin, which in turn has novel
effects on the hydrodynamic modes.Comment: 10 pages, 4 figures; submitted to PR
A quantitative test of the mode-coupling theory of the ideal glass transition for a binary Lennard-Jones system
Using a molecular dynamics computer simulation we determine the temperature
dependence of the partial structure factors for a binary Lennard-Jones system.
These structure factors are used as input data to solve numerically the
wave-vector dependent mode-coupling equations in the long time limit. Using the
so determined solutions, we compare the predictions of mode-coupling theory
(MCT) with the results of a previously done molecular dynamics computer
simulation [Phys. Rev. E 51, 4626 (1995), ibid. 52, 4134 (1995)]. From this
comparison we conclude that MCT gives a fair estimate of the critical coupling
constant, a good estimate of the exponent parameter, predicts the wave-vector
dependence of the various nonergodicity parameters very well, except for very
large wave-vectors, and gives also a very good description of the space
dependence of the various critical amplitudes. In an attempt to correct for
some of the remaining discrepancies between the theory and the results of the
simulation, we investigate two small (ad hoc) modifications of the theory. We
find that one modification gives a worse agreement between theory and
simulation, whereas the second one leads to an improved agreement.Comment: Figures available from W. Ko
Lectures on conformal field theory and Kac-Moody algebras
This is an introduction to the basic ideas and to a few further selected
topics in conformal quantum field theory and in the theory of Kac-Moody
algebras.Comment: 59 pages, LaTeX2e, extended version of lectures given at the Graduate
Course on Conformal Field Theory and Integrable Models (Budapest, August
1996), to appear in Springer Lecture Notes in Physic
The mean-squared displacement of a molecule moving in a glassy system
The mean-squared displacement (MSD) of a hard sphere and of a dumbbell
molecule consisting of two fused hard spheres immersed in a dense hard-sphere
system is calculated within the mode-coupling theory for ideal liquid-glass
transitions. It is proven that the velocity correlator, which is the second
time derivative of the MSD, is the negative of a completely monotone function
for times within the structural-relaxation regime. The MSD is found to exhibit
a large time interval for structural relaxation prior to the onset of the
-process which cannot be described by the asymptotic formulas for the
mode-coupling-theory-bifurcation dynamics. The -process for molecules
with a large elongation is shown to exhibit an anomalously wide cross-over
interval between the end of the von-Schweidler decay and the beginning of
normal diffusion. The diffusivity of the molecule is predicted to vary
non-monotonically as function of its elongation.Comment: 18 pages, 12 figures, Phys. Rev. E, in prin
Integration through transients for Brownian particles under steady shear
Starting from the microscopic Smoluchowski equation for interacting Brownian
particles under stationary shearing, exact expressions for shear-dependent
steady-state averages, correlation and structure functions, and
susceptibilities are obtained, which take the form of generalized Green-Kubo
relations. They require integration of transient dynamics. Equations of motion
with memory effects for transient density fluctuation functions are derived
from the same microscopic starting point. We argue that the derived formal
expressions provide useful starting points for approximations in order to
describe the stationary non-equilibrium state of steadily sheared dense
colloidal dispersions.Comment: 17 pages, Submitted to J. Phys.: Condens. Matter; revised version
with minor correction
Comparative simulation study of colloidal gels and glasses
Using computer simulations, we identify the mechanisms causing aggregation
and structural arrest of colloidal suspensions interacting with a short-ranged
attraction at moderate and high densities. Two different non-ergodicity
transitions are observed. As the density is increased, a glass transition takes
place, driven by excluded volume effects. In contrast, at moderate densities,
gelation is approached as the strength of the attraction increases. At high
density and interaction strength, both transitions merge, and a logarithmic
decay in the correlation function is observed. All of these features are
correctly predicted by mode coupling theory
Information Tradeoff Relations for Finite-Strength Quantum Measurements
In this paper we give a new way to quantify the folklore notion that quantum
measurements bring a disturbance to the system being measured. We consider two
observers who initially assign identical mixed-state density operators to a
two-state quantum system. The question we address is to what extent one
observer can, by measurement, increase the purity of his density operator
without affecting the purity of the other observer's. If there were no
restrictions on the first observer's measurements, then he could carry this out
trivially by measuring the initial density operator's eigenbasis. If, however,
the allowed measurements are those of finite strength---i.e., those
measurements strictly within the interior of the convex set of all
measurements---then the issue becomes significantly more complex. We find that
for a large class of such measurements the first observer's purity increases
the most precisely when there is some loss of purity for the second observer.
More generally the tradeoff between the two purities, when it exists, forms a
monotonic relation. This tradeoff has potential application to quantum state
control and feedback.Comment: 15 pages, revtex3, 3 eps figure
The Lie Algebraic Significance of Symmetric Informationally Complete Measurements
Examples of symmetric informationally complete positive operator valued
measures (SIC-POVMs) have been constructed in every dimension less than or
equal to 67. However, it remains an open question whether they exist in all
finite dimensions. A SIC-POVM is usually thought of as a highly symmetric
structure in quantum state space. However, its elements can equally well be
regarded as a basis for the Lie algebra gl(d,C). In this paper we examine the
resulting structure constants, which are calculated from the traces of the
triple products of the SIC-POVM elements and which, it turns out, characterize
the SIC-POVM up to unitary equivalence. We show that the structure constants
have numerous remarkable properties. In particular we show that the existence
of a SIC-POVM in dimension d is equivalent to the existence of a certain
structure in the adjoint representation of gl(d,C). We hope that transforming
the problem in this way, from a question about quantum state space to a
question about Lie algebras, may help to make the existence problem tractable.Comment: 56 page
Geometric scaling in high-energy QCD at nonzero momentum transfer
We show how one can obtain geometric scaling properties from the
Balitsky-Kovchegov (BK) equation. We start by explaining how, this property
arises for the b-independent BK equation. We show that it is possible to extend
this model to the full BK equation including momentum transfer. The saturation
scale behaves like max(q,Q_T) where q is the momentum transfer and Q_T a
typical scale of the target.Comment: 4 pages, 2 figures. Talk given by G. Soyez at the "Rencontres de
Moriond", 12-19 March 2005, La Thuile, Ital
- …