5,790 research outputs found
Scale invariant thermodynamics of a toroidally trapped Bose gas
We consider a system of bosonic atoms in an axially symmetric harmonic trap
augmented with a two dimensional repulsive Gaussian optical potential. We find
an expression for the grand free energy of the system for configurations
ranging from the harmonic trap to the toroidal regime. For large tori we
identify an accessible regime where the ideal gas thermodynamics of the system
are found to be independent of toroidal radius. This property is a consequence
of an invariant extensive volume of the system that we identify analytically in
the regime where the toroidal potential is radially harmonic. In considering
corrections to the scale invariant transition temperature, we find that the
first order interaction shift is the dominant effect in the thermodynamic
limit, and is also scale invariant. We also consider adiabatic loading from the
harmonic to toroidal trap configuration, which we show to have only a small
effect on the condensate fraction of the ideal gas, indicating that loading
into the scale invariant regime may be experimentally practical.Comment: 10 pages, 3 figures, to appear in Phys. Rev. A, typos corrected,
references added, rewritten to emphasize generalized volume. Results
unchange
RKKY Interaction in Graphene from Lattice Green's Function
We study the exchange interaction between two magnetic impurities in
graphene (the RKKY interaction) by directly computing the lattice Green's
function for the tight-binding band structure for the honeycomb lattice. The
method allows us to compute numerically for much larger distances than can
be handled by finite-lattice calculations as well as for small distances. %
avoids the use of a cutoff function often invoked in the literature to curtail
the diverging contributions from the linear bands and yields results that are
valid for all distances. In addition, we rederive the analytical long-distance
behavior of for linearly dispersive bands and find corrections to the
oscillatory factor that were previously missed in the literature. The main
features of the RKKY interaction in graphene are that unlike the behavior of an ordinary 2D metal in the
long-distance limit, in graphene falls off as , shows the -type oscillations with additional phase factors depending on the
direction, and exhibits a ferromagnetic interaction for moments on the same
sublattice and an antiferromagnetic interaction for moments on the opposite
sublattices as required by particle-hole symmetry. The computed with the
full band structure agrees with our analytical results in the long-distance
limit including the oscillatory factors with the additional phases.Comment: 8 pages, 11 figure
Cooling in the single-photon strong-coupling regime of cavity optomechanics
In this paper we discuss how red-sideband cooling is modified in the
single-photon strong-coupling regime of cavity optomechanics where the
radiation pressure of a single photon displaces the mechanical oscillator by
more than its zero-point uncertainty. Using Fermi's Golden rule we calculate
the transition rates induced by the optical drive without linearizing the
optomechanical interaction. In the resolved-sideband limit we find
multiple-phonon cooling resonances for strong single-photon coupling that lead
to non-thermal steady states including the possibility of phonon anti-bunching.
Our study generalizes the standard linear cooling theory.Comment: 4 pages, 3 figure
The effect of hydrogen sulphide on ammonium bisulphite when used as an oxygen scavenger in aqueous solutions
Peer reviewedPostprin
Approximate solutions of the Dirac equation for the Rosen-Morse potential including the spin-orbit centrifugal term
We give the approximate analytic solutions of the Dirac equations for the
Rosen-Morse potential including the spin-orbit centrifugal term. In the
framework of the spin and pseudospin symmetry concept, we obtain the analytic
bound state energy spectra and corresponding two-component upper- and
lower-spinors of the two Dirac particles, in closed form, by means of the
Nikiforov-Uvarov method. The special cases of the s-wave kappa=1,-1 (l=l bar=0)
Rosen-Morse potential, the Eckart-type potential, the PT-symmetric Rosen-Morse
potential and non-relativistic limits are briefly studied.Comment: 23 page
Dissipation control in cavity QED with oscillating mode structures
We demonstrate how a time-dependent dissipative environment may be used as a tool for controlling the quantum state of a two-level atom. In our model system the frequency and coupling strength associated with microscopic reservoir modes are modulated, while the principal features of the reservoir structure remain fixed in time. Physically, this may be achieved by containing a static atom-cavity system inside an oscillating external bath. We show that it is possible to dynamically decouple the atom from its environment, despite the fact that the two remain resonant at all times. This can lead to Markovian dynamics, even for a strong atom-bath coupling, as the atomic decay becomes inhibited into all but a few channels; the reservoir occupation spectrum consequently acquires a sideband structure, with peaks separated by the frequency of the environmental modulation. The reduction in the rate of spontaneous emission using this approach can be significantly greater than could be achieved with an oscillatory atom-bath detuning using the same parameters
Strong-coupling asymptotic expansion for Schr\"odinger operators with a singular interaction supported by a curve in
We investigate a class of generalized Schr\"{o}dinger operators in
with a singular interaction supported by a smooth curve
. We find a strong-coupling asymptotic expansion of the discrete
spectrum in case when is a loop or an infinite bent curve which is
asymptotically straight. It is given in terms of an auxiliary one-dimensional
Schr\"{o}dinger operator with a potential determined by the curvature of
. In the same way we obtain an asymptotics of spectral bands for a
periodic curve. In particular, the spectrum is shown to have open gaps in this
case if is not a straight line and the singular interaction is strong
enough.Comment: LaTeX 2e, 30 pages; minor improvements, to appear in Rev. Math. Phy
The subdiffusive target problem: Survival probability
The asymptotic survival probability of a spherical target in the presence of
a single subdiffusive trap or surrounded by a sea of subdiffusive traps in a
continuous Euclidean medium is calculated. In one and two dimensions the
survival probability of the target in the presence of a single trap decays to
zero as a power law and as a power law with logarithmic correction,
respectively. The target is thus reached with certainty, but it takes the trap
an infinite time on average to do so. In three dimensions a single trap may
never reach the target and so the survival probability is finite and, in fact,
does not depend on whether the traps move diffusively or subdiffusively. When
the target is surrounded by a sea of traps, on the other hand, its survival
probability decays as a stretched exponential in all dimensions (with a
logarithmic correction in the exponent for ). A trap will therefore reach
the target with certainty, and will do so in a finite time. These results may
be directly related to enzyme binding kinetics on DNA in the crowded cellular
environment.Comment: 6 pages. References added, improved account of previous results and
typos correcte
Birefringent Gravitational Waves and the Consistency Check of Inflation
In this work we show that the gravitational Chern-Simons term, aside from
being a key ingredient in inflationary baryogenesis, modifies super-horizon
gravitational waves produced during inflation. We compute the super-Hubble
gravitational power spectrum in the slow-roll approximation and show that its
overall amplitude is modified while its spectral index remains unchanged (at
leading order in the slow-roll parameters). Then, we calculate the correction
to the tensor to scalar ratio, T/S. We find a correction of T/S which is
dependent on (more precisely quadratic in ), the parameter
characterizing the amplitude of the Chern-Simons terms. In a stringy embedding
of the leptogenesis mechanism, is the ratio between the Planck scale
and the fundamental string scale. Thus, in principle, we provide a direct probe
of leptogenesis due to stringy dynamics in the Cosmic Microwave Background
(CMB). However, we demonstrate that the corresponding correction of T/S is in
fact very small and not observable in the regime where our calculations are
valid. To obtain a sizable effect, we argue that a non-linear calculation is
necessary.Comment: 9 pages, 1 figure, RevTe
Unified Treatment of Mixed Vector-Scalar Screened Coulomb Potentials for Fermions
The problem of a fermion subject to a general mixing of vector and scalar
screened Coulomb potentials in a two-dimensional world is analyzed and
quantization conditions are found.Comment: 7 page
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