5,107 research outputs found
Dynamics of ultracold molecules in confined geometry and electric field
We present a time-independent quantum formalism to describe the dynamics of
molecules with permanent electric dipole moments in a two-dimensional confined
geometry such as a one-dimensional optical lattice, in the presence of an
electric field. Bose/Fermi statistics and selection rules play a crucial role
in the dynamics. As examples, we compare the dynamics of confined fermionic and
bosonic polar KRb molecules under different confinements and electric fields.
We show how chemical reactions can be suppressed, either by a "statistical
suppression" which applies for fermions at small electric fields and
confinements, or by a "potential energy suppression", which applies for both
fermions and bosons at high electric fields and confinements. We also explore
collisions that transfer molecules from one state of the confining potential to
another. Although these collisions can be significant, we show that they do not
play a role in the loss of the total number of molecules in the gas.Comment: 13 pages, 6 figure
Pair creation in boost-invariantly expanding electric fields and two-particle correlations
Pair creation of scalar particles in a boost-invariant electric field which
is confined in the forward light cone is studied. We present the proper-time
evolution of momentum distributions of created particles, which preserve the
boost invariance of the background field. The two-particle correlation of the
created particles is also calculated. We find that long-range rapidity
correlations may arise from the Schwinger mechanism in the boost-invariant
electric field.Comment: 21 pages, 10 figures; v2: minor changes, to appear in Phys. Rev.
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
Reflection above the barrier as tunneling in momentum space
Quantum mechanics predicts an exponentially small probability that a particle
with energy greater than the height of a potential barrier will nevertheless
reflect from the barrier in violation of classical expectations. This process
can be regarded as tunneling in momentum space, leading to a simple derivation
of the reflection probability.Comment: 7 pages, 3 figures, submitted to American Journal of Physics. Version
2: MIT preprint number added, typographical error in caption to Figure 2
correcte
Bound state equivalent potentials with the Lagrange mesh method
The Lagrange mesh method is a very simple procedure to accurately solve
eigenvalue problems starting from a given nonrelativistic or semirelativistic
two-body Hamiltonian with local or nonlocal potential. We show in this work
that it can be applied to solve the inverse problem, namely, to find the
equivalent local potential starting from a particular bound state wave function
and the corresponding energy. In order to check the method, we apply it to
several cases which are analytically solvable: the nonrelativistic harmonic
oscillator and Coulomb potential, the nonlocal Yamaguchi potential and the
semirelativistic harmonic oscillator. The potential is accurately computed in
each case. In particular, our procedure deals efficiently with both
nonrelativistic and semirelativistic kinematics.Comment: 6 figure
Dangerous Angular KK/Glueball Relics in String Theory Cosmology
The presence of Kaluza-Klein particles in the universe is a potential
manifestation of string theory cosmology. In general, they can be present in
the high temperature bath of the early universe. In particular examples, string
theory inflation often ends with brane-antibrane annihilation followed by the
energy cascading through massive closed string loops to KK modes which then
decay into lighter standard model particles. However, massive KK modes in the
early universe may become dangerous cosmological relics if the inner manifold
contains warped throat(s) with approximate isometries. In the complimentary
picture, in the AdS/CFT dual gauge theory with extra symmetries, massive
glueballs of various spins become the dangerous cosmological relics. The decay
of these angular KK modes/glueballs, located around the tip of the throat, is
caused by isometry breaking which results from gluing the throat to the compact
CY manifold. We address the problem of these angular KK particles/glueballs,
studying their interactions and decay channels, from the theory side, and the
resulting cosmological constraints on the warped compactification parameters,
from the phenomenology side. The abundance and decay time of the long-lived
non-relativistic angular KK modes depend strongly on the parameters of the
warped geometry, so that observational constraints rule out a significant
fraction of the parameter space. In particular, the coupling of the angular KK
particles can be weaker than gravitational.Comment: 58 pages, 11 figures, published versio
Ground-state properties of trapped Bose-Einstein condensates: Extension of the Thomas-Fermi approximation
We derive general approximate formulas that provide with remarkable accuracy
the ground-state properties of any mean-field scalar Bose-Einstein condensate
with short-range repulsive interatomic interactions, confined in arbitrary
cylindrically symmetric harmonic traps. Our formulation is even applicable for
condensates containing a multiply quantized axisymmetric vortex. We have
checked the validity of our formulas by numerically solving the 3D
Gross-Pitaevskii equation.Comment: 9 pages, 6 figures. Final version published in Phys. Rev. A. New
formulas for the local sound velocity of cigar-shaped and disk-shaped
condensates have been obtained. This paper generalizes our previous work
cond-mat/070169
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
Effective Hamiltonians for atoms in very strong magnetic fields
We propose three effective Hamiltonians which approximate atoms in very
strong homogeneous magnetic fields modelled by the Pauli Hamiltonian, with
fixed total angular momentum with respect to magnetic field axis. All three
Hamiltonians describe electrons and a fixed nucleus where the Coulomb
interaction has been replaced by -dependent one-dimensional effective
(vector valued) potentials but without magnetic field. Two of them are solvable
in at least the one electron case. We briefly sketch how these Hamiltonians can
be used to analyse the bottom of the spectrum of such atoms.Comment: 43 page
Reflection and Transmission at the Apparent Horizon during Gravitational Collapse
We examine the wave-functionals describing the collapse of a self-gravitating
dust ball in an exact quantization of the gravity-dust system. We show that
ingoing (collapsing) dust shell modes outside the apparent horizon must
necessarily be accompanied by outgoing modes inside the apparent horizon, whose
amplitude is suppressed by the square root of the Boltzmann factor at the
Hawking temperature. Likewise, ingoing modes in the interior must be
accompanied by outgoing modes in the exterior, again with an amplitude
suppressed by the same factor. A suitable superposition of the two solutions is
necessary to conserve the dust probability flux across the apparent horizon,
thus each region contains both ingoing and outgoing dust modes. If one
restricts oneself to considering only the modes outside the apparent horizon
then one should think of the apparent horizon as a partial reflector, the
probability for a shell to reflect being given by the Boltzmann factor at the
Hawking temperature determined by the mass contained within it. However, if one
considers the entire wave function, the outgoing wave in the exterior is seen
to be the transmission through the horizon of the interior outgoing wave that
accompanies the collapsing shells. This transmission could allow information
from the interior to be transferred to the exterior.Comment: 19 pages, no figures. To appear in Phys. Rev.
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