22,246 research outputs found
Castaing's instability in a trapped ultra-cold gas
We consider a trapped ultra-cold gas of (non-condensed) bosons with two
internal states (described by a pseudo spin) and study the stability of a
longitudinal pseudo spin polarization gradient. For this purpose, we
numerically solve a kinetic equation corresponding to a situation close to an
experiment at JILA. It shows the presence of Castaing's instability of
transverse spin polarization fluctuations at long wavelengths. This phenomenon
could be used to create spontaneous transverse spin waves.Comment: 5 pages, 3 figures; equation (8) corrected; submitted to EPJ
Large amplitude spin waves in ultra-cold gases
We discuss the theory of spin waves in non-degenerate ultra-cold gases, and
compare various methods which can be used to obtain appropriate kinetic
equations. We then study non-hydrodynamic situations, where the amplitude of
spin waves is sufficiently large to bring the system far from local
equilibrium. In the first part of the article, we compare two general methods
which can be used to derive a kinetic equation for a dilute gas of atoms
(bosons or fermions) with two internal states (treated as a pseudo-spin 1/2).
The collisional methods are in the spirit of Boltzmann's original derivation of
his kinetic equation where, at each point of space, the effects of all sorts of
possible binary collisions are added. We discuss two different versions of
collisional methods, the Yvon-Snider approach and the S matrix approach. The
second method uses the notion of mean field, which modifies the drift term of
the kinetic equation, in the line of the Landau theory of transport in quantum
liquids. For a dilute cold gas, it turns out that all these derivations lead to
the same drift terms in the transport equation, but differ in the precise
expression of the collision integral and in higher order gradient terms. In the
second part of the article, the kinetic equation is applied to spin waves in
trapped ultra-cold gases. Numerical simulations are used to illustrate the
strongly non-hydrodynamic character of the spin waves recently observed with
trapped Rb87 atoms. The decay of the phenomenon, which takes place when the
system relaxes back towards equilibrium, is also discussed, with a short
comment on decoherence.Comment: To appear in Eur. Phys. J.
Vector magnetic field microscopy using nitrogen vacancy centers in diamond
The localized spin triplet ground state of a nitrogen vacancy (NV) center in
diamond can be used in atomic-scale detection of local magnetic fields. Here we
present a technique using these defects in diamond to image fields around
magnetic structures. We extract the local magnetic field vector by probing
resonant transitions of the four fixed tetrahedral NV orientations. In
combination with confocal microscopy techniques, we construct a 2-dimensional
image of the local magnetic field vectors. Measurements are done in external
fields less than 50 G and under ambient conditions.Comment: 9 pages, 3 figure
On Verifiable Sufficient Conditions for Sparse Signal Recovery via Minimization
We propose novel necessary and sufficient conditions for a sensing matrix to
be "-good" - to allow for exact -recovery of sparse signals with
nonzero entries when no measurement noise is present. Then we express the error
bounds for imperfect -recovery (nonzero measurement noise, nearly
-sparse signal, near-optimal solution of the optimization problem yielding
the -recovery) in terms of the characteristics underlying these
conditions. Further, we demonstrate (and this is the principal result of the
paper) that these characteristics, although difficult to evaluate, lead to
verifiable sufficient conditions for exact sparse -recovery and to
efficiently computable upper bounds on those for which a given sensing
matrix is -good. We establish also instructive links between our approach
and the basic concepts of the Compressed Sensing theory, like Restricted
Isometry or Restricted Eigenvalue properties
Criteria for Continuous-Variable Quantum Teleportation
We derive an experimentally testable criterion for the teleportation of
quantum states of continuous variables. This criterion is especially relevant
to the recent experiment of Furusawa et al. [Science 282, 706-709 (1998)] where
an input-output fidelity of was achieved for optical coherent
states. Our derivation demonstrates that fidelities greater than 1/2 could not
have been achieved through the use of a classical channel alone; quantum
entanglement was a crucial ingredient in the experiment.Comment: 12 pages, to appear in Journal of Modern Optic
Nonequilibrium fluctuation dissipation relations of interacting Brownian particles driven by shear
We present a detailed analysis of the fluctuation dissipation theorem (FDT)
close to the glass transition in colloidal suspensions under steady shear using
mode coupling approximations. Starting point is the many-particle Smoluchowski
equation. Under shear, detailed balance is broken and the response functions in
the stationary state are smaller at long times than estimated from the
equilibrium FDT. An asymptotically constant relation connects response and
fluctuations during the shear driven decay, restoring the form of the FDT with,
however, a ratio different from the equilibrium one. At short times, the
equilibrium FDT holds. We follow two independent approaches whose results are
in qualitative agreement. To discuss the derived fluctuation dissipation
ratios, we show an exact reformulation of the susceptibility which contains not
the full Smoluchowski operator as in equilibrium, but only its well defined
Hermitian part. This Hermitian part can be interpreted as governing the
dynamics in the frame comoving with the probability current. We present a
simple toy model which illustrates the FDT violation in the sheared colloidal
system.Comment: 21 pages, 13 figures, submitted to Phys. Rev.
Flow curves of colloidal dispersions close to the glass transition: Asymptotic scaling laws in a schematic model of mode coupling theory
The flow curves, viz. the curves of stationary stress under steady shearing,
are obtained close to the glass transition in dense colloidal dispersions using
asymptotic expansions in a schematic model of mode coupling theory. The shear
thinning of the viscosity in fluid states and the yielding of glassy states is
discussed. At the transition between fluid and shear-molten glass, simple and
generalized Herschel-Bulkley laws are derived with power law exponents that can
be computed for different particle interactions from the equilibrium structure
factor.Comment: 14 pages, 14 figures, 4 tables, Eur. Phys. J. E (submitted
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