4,740 research outputs found
Detection techniques for tenuous planetary atmospheres Fifth six-month report, 1 Jul. - 30 Dec. 1965
Physical methods description for detection and analysis of tenuous planetary atmospheric component gases, especially water vapo
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
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 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
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
On Duffin-Kemmer-Petiau particles with a mixed minimal-nonminimal vector coupling and the nondegenerate bound states for the one-dimensional inversely linear background
The problem of spin-0 and spin-1 bosons in the background of a general mixing
of minimal and nonminimal vector inversely linear potentials is explored in a
unified way in the context of the Duffin-Kemmer-Petiau theory. It is shown that
spin-0 and spin-1 bosons behave effectively in the same way. An orthogonality
criterion is set up and it is used to determine uniquely the set of solutions
as well as to show that even-parity solutions do not exist.Comment: 10 page
Theory of resonance energy transfer involving nanocrystals: the role of high multipoles
A theory for the fluorescence resonance energy transfer (FRET) between a pair
of semiconducting nanocrystal quantum dots is developed. Two types of
donor-acceptor couplings for the FRET rate are described: dipole-dipole (d-d)
and the dipole-quadrupole (d-q) coupling. The theory builds on a simple
effective mass model which is used to relate the FRET rate to measureable
quantities such as the nanocrystal size, fundamental gap, effective mass,
exciton radius and dielectric constant. We discuss the relative contribution to
the FRET rate of the different multipole terms, the role of strong to weak
confinement limits, and the effects of nanocrystal siz-es.Comment: 12 pages, 7 figure
PT-Invariant Periodic Potentials with a Finite Number of Band Gaps
We obtain the band edge eigenstates and the mid-band states for the complex,
PT-invariant generalized associated Lam\'e potentials V^{PT}(x)=-a(a+1)m
\sn^2(y,m)-b(b+1)m {\sn^2 (y+K(m),m)} -f(f+1)m {\sn^2
(y+K(m)+iK'(m),m)}-g(g+1)m {\sn^2 (y+iK'(m),m)}, where ,
and there are four parameters . This work is a substantial
generalization of previous work with the associated Lam\'e potentials
V(x)=a(a+1)m\sn^2(x,m)+b(b+1)m{\sn^2 (x+K(m),m)} and their corresponding
PT-invariant counterparts , both of which involving
just two parameters . We show that for many integer values of ,
the PT-invariant potentials are periodic problems with a finite
number of band gaps. Further, usingsupersymmetry, we construct several
additional, new, complex, PT-invariant, periodic potentials with a finite
number of band gaps. We also point out the intimate connection between the
above generalized associated Lam\'e potential problem and Heun's differential
equation.Comment: 30 pages, 0 figure
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
Representation of the three-body Coulomb Green's function in parabolic coordinates: paths of integration
The possibility is discussed of using straight-line paths of integration in
computing the integral representation of the three-body Coulomb Green's
function. In our numerical examples two different integration contours are
considered. It is demonstrated that only one of these straight-line paths
provides that the integral representation is valid
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