2,464 research outputs found
Proof of the cases of the Lieb-Seiringer formulation of the Bessis-Moussa-Villani conjecture
It is shown that the polynomial has
nonnegative coefficients when and A and B are any two complex
positive semidefinite matrices with arbitrary . This proofs a
general nontrivial case of the Lieb-Seiringer formulation of the
Bessis-Moussa-Villani conjecture which is a long standing problem in
theoretical physics.Comment: 5 pages; typos corrected; accepted for publication in Journal of
Statistical Physic
Nonadiabatic coherent evolution of two-level systems under spontaneous decay
In this paper we extend current perspectives in engineering reservoirs by
producing a time-dependent master equation leading to a nonstationary
superposition equilibrium state that can be nonadiabatically controlled by the
system-reservoir parameters. Working with an ion trapped inside a nonindeal
cavity we first engineer effective Hamiltonians that couple the electronic
states of the ion with the cavity mode. Subsequently, two classes of
decoherence-free evolution of the superposition of the ground and decaying
excited levels are achieved: those with time-dependent azimuthal or polar
angle. As an application, we generalise the purpose of an earlier study [Phys.
Rev. Lett. 96, 150403 (2006)], showing how to observe the geometric phases
acquired by the protected nonstationary states even under a nonadiabatic
evolution.Comment: 5 pages, no figure
Hydrodynamic coupling and rotational mobilities near planar elastic membranes
We study theoretically and numerically the coupling and rotational
hydrodynamic interactions between spherical particles near a planar elastic
membrane that exhibits resistance towards shear and bending. Using a
combination of the multipole expansion and Faxen's theorems, we express the
frequency-dependent hydrodynamic mobility functions as a power series of the
ratio of the particle radius to the distance from the membrane for the self
mobilities, and as a power series of the ratio of the radius to the
interparticle distance for the pair mobilities. In the quasi-steady limit of
zero frequency, we find that the shear- and bending-related contributions to
the particle mobilities may have additive or suppressive effects depending on
the membrane properties in addition to the geometric configuration of the
interacting particles relative to the confining membrane. To elucidate the
effect and role of the change of sign observed in the particle self and pair
mobilities, we consider an example involving a torque-free doublet of
counterrotating particles near an elastic membrane. We find that the induced
rotation rate of the doublet around its center of mass may differ in magnitude
and direction depending on the membrane shear and bending properties. Near a
membrane of only energetic resistance toward shear deformation, such as that of
a certain type of elastic capsules, the doublet undergoes rotation of the same
sense as observed near a no-slip wall. Near a membrane of only energetic
resistance toward bending, such as that of a fluid vesicle, we find a reversed
sense of rotation. Our analytical predictions are supplemented and compared
with fully resolved boundary integral simulations where a very good agreement
is obtained over the whole range of applied frequencies.Comment: 14 pages, 7 figures. Revised manuscript resubmitted to J. Chem. Phy
Quantitative Relativistic Effects in the Three-Nucleon Problem
The quantitative impact of the requirement of relativistic invariance in the
three-nucleon problem is examined within the framework of Poincar\'e invariant
quantum mechanics. In the case of the bound state, and for a wide variety of
model implementations and reasonable interactions, most of the quantitative
effects come from kinematic factors that can easily be incorporated within a
non-relativistic momentum-space three-body code.Comment: 15 pages, 15 figure
Engineering cavity-field states by projection synthesis
We propose a reliable scheme for engineering a general cavity-field state.
This is different from recently presented strategies,where the cavity is
supposed to be initially empty and the field is built up photon by photon
through resonant atom-field interactions. Here, a coherent state is previously
injected into the cavity. So, the Wigner distribution function of the desired
state is constructed from that of the initially coherent state. Such an
engineering process is achieved through an adaptation of the recently proposed
technique of projection synthesis to cavity QED phenomena.Comment: 5 ps pages plus 3 included figure
Continuous pumping and control of mesoscopic superposition state in a lossy QED cavity
Here we consider the continuous pumping of a dissipative QED cavity and
derive the time-dependent density operator of the cavity field prepared
initially as a superposition of mesoscopic coherent states. The control of the
coherence of this superposition is analyzed considering the injection of a beam
of two-level Rydberg atoms through the cavity. Our treatment is compared to
other approaches.Comment: 15 pages, 6 PostScript figures, To appear in Phys. Rev.
Basis States for Relativistic, Dynamically-Entangled Particles
In several recent papers on entanglement in relativistic quantum systems and
relativistic Bell's inequalities, relativistic Bell-type two-particle states
have been constructed in analogy to non-relativistic states. These
constructions do not have the form suggested by relativistic invariance of the
dynamics. Two relativistic formulations of Bell-type states are shown for
massive particles, one using the standard Wigner spin basis and one using the
helicity basis. The construction hinges on the use of Clebsch-Gordan
coefficients of the Poincar\'e group to reduce the direct product of two
unitary irreducible representations (UIRs) into a direct sum of UIRs.Comment: 19 pages, three tables, revte
First Order Relativistic Three-Body Scattering
Relativistic Faddeev equations for three-body scattering at arbitrary
energies are formulated in momentum space and in first order in the two-body
transition-operator directly solved in terms of momentum vectors without
employing a partial wave decomposition. Relativistic invariance is incorporated
within the framework of Poincare invariant quantum mechanics, and presented in
some detail.
Based on a Malfliet-Tjon type interaction, observables for elastic and
break-up scattering are calculated up to projectile energies of 1 GeV. The
influence of kinematic and dynamic relativistic effects on those observables is
systematically studied. Approximations to the two-body interaction embedded in
the three-particle space are compared to the exact treatment.Comment: 26 pages, 13 figure
Representations of the Canonical group, (the semi-direct product of the Unitary and Weyl-Heisenberg groups), acting as a dynamical group on noncommuting extended phase space
The unitary irreducible representations of the covering group of the Poincare
group P define the framework for much of particle physics on the physical
Minkowski space P/L, where L is the Lorentz group. While extraordinarily
successful, it does not provide a large enough group of symmetries to encompass
observed particles with a SU(3) classification. Born proposed the reciprocity
principle that states physics must be invariant under the reciprocity transform
that is heuristically {t,e,q,p}->{t,e,p,-q} where {t,e,q,p} are the time,
energy, position, and momentum degrees of freedom. This implies that there is
reciprocally conjugate relativity principle such that the rates of change of
momentum must be bounded by b, where b is a universal constant. The appropriate
group of dynamical symmetries that embodies this is the Canonical group C(1,3)
= U(1,3) *s H(1,3) and in this theory the non-commuting space Q= C(1,3)/
SU(1,3) is the physical quantum space endowed with a metric that is the second
Casimir invariant of the Canonical group, T^2 + E^2 - Q^2/c^2-P^2/b^2 +(2h
I/bc)(Y/bc -2) where {T,E,Q,P,I,Y} are the generators of the algebra of
Os(1,3). The idea is to study the representations of the Canonical dynamical
group using Mackey's theory to determine whether the representations can
encompass the spectrum of particle states. The unitary irreducible
representations of the Canonical group contain a direct product term that is a
representation of U(1,3) that Kalman has studied as a dynamical group for
hadrons. The U(1,3) representations contain discrete series that may be
decomposed into infinite ladders where the rungs are representations of U(3)
(finite dimensional) or C(2) (with degenerate U(1)* SU(2) finite dimensional
representations) corresponding to the rest or null frames.Comment: 25 pages; V2.3, PDF (Mathematica 4.1 source removed due to technical
problems); Submitted to J.Phys.
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