295 research outputs found
Emulating Non-Abelian Topological Matter in Cold Atom Optical Lattices
Certain proposed extended Bose-Hubbard models may exhibit topologically
ordered ground states with excitations obeying non-Abelian braid statistics. A
sufficient tuning of Hubbard parameters could yield excitation braiding rules
allowing implementation of a universal set of topologically protected quantum
gates. We discuss potential difficulties in realizing a model with a proposed
non-Abelian topologically ordered ground state using optical lattices
containing bosonic dipoles. Our direct implementation scheme does not realize
the necessary anisotropic hopping, anisotropic interactions, and low
temperatures
Dispersive estimates for Schr\"odinger operators with point interactions in
The study of dispersive properties of Schr\"odinger operators with point
interactions is a fundamental tool for understanding the behavior of many body
quantum systems interacting with very short range potential, whose dynamics can
be approximated by non linear Schr\"odinger equations with singular
interactions. In this work we proved that, in the case of one point interaction
in , the perturbed Laplacian satisfies the same
estimates of the free Laplacian in the smaller regime . These
estimates are implied by a recent result concerning the boundedness of
the wave operators for the perturbed Laplacian. Our approach, however, is more
direct and relatively simple, and could potentially be useful to prove optimal
weighted estimates also in the regime .Comment: To appear on: "Advances in Quantum Mechanics: Contemporary Trends and
Open Problems", G. Dell'Antonio and A. Michelangeli eds., Springer-INdAM
series 201
Q^2 Evolution of Generalized Baldin Sum Rule for the Proton
The generalized Baldin sum rule for virtual photon scattering, the
unpolarized analogy of the generalized Gerasimov-Drell-Hearn integral, provides
an important way to investigate the transition between perturbative QCD and
hadronic descriptions of nucleon structure. This sum rule requires integration
of the nucleon structure function F_1, which until recently had not been
measured at low Q^2 and large x, i.e. in the nucleon resonance region. This
work uses new data from inclusive electron-proton scattering in the resonance
region obtained at Jefferson Lab, in combination with SLAC deep inelastic
scattering data, to present first precision measurements of the generalized
Baldin integral for the proton in the Q^2 range of 0.3 to 4.0 GeV^2.Comment: 4 pages, 3 figures, one table; text added, one figure replace
Proper incorporation of self-adjoint extension method to Green's function formalism : one-dimensional -function potential case
One-dimensional -function potential is discussed in the framework
of Green's function formalism without invoking perturbation expansion. It is
shown that the energy-dependent Green's function for this case is crucially
dependent on the boundary conditions which are provided by self-adjoint
extension method. The most general Green's function which contains four real
self-adjoint extension parameters is constructed. Also the relation between the
bare coupling constant and self-adjoint extension parameter is derived.Comment: LATEX, 13 page
Spin dependent point potentials in one and three dimensions
We consider a system realized with one spinless quantum particle and an array
of spins 1/2 in dimension one and three. We characterize all the
Hamiltonians obtained as point perturbations of an assigned free dynamics in
terms of some ``generalized boundary conditions''. For every boundary condition
we give the explicit formula for the resolvent of the corresponding
Hamiltonian. We discuss the problem of locality and give two examples of spin
dependent point potentials that could be of interest as multi-component
solvable models.Comment: 15 pages, some misprints corrected, one example added, some
references modified or adde
Enhanced suppresion of localization in a continuous Random-Dimer Model
We consider a one-dimensional continuous (Kronig-Penney) extension of the
(tight-binding) Random Dimer model of Dunlap et al. [Phys. Rev. Lett. 65, 88
(1990)]. We predict that the continuous model has infinitely many resonances
(zeroes of the reflection coefficient) giving rise to extended states instead
of the one resonance arising in the discrete version. We present exact,
transfer-matrix numerical calculations supporting, both realizationwise and on
the average, the conclusion that the model has a very large number of extended
states.Comment: 10 pages, 3 Figures available on request, REVTeX 3.0, MA/UC3M/1/9
Can Light Signals Travel Faster than c in Nontrivial Vacuua in Flat space-time? Relativistic Causality II
In this paper we show that the Scharnhorst effect (Vacuum with boundaries or
a Casimir type vacuum) cannot be used to generate signals showing measurable
faster-than-c speeds. Furthermore, we aim to show that the Scharnhorst effect
would violate special relativity, by allowing for a variable speed of light in
vacuum, unless one can specify a small invariant length scale. This invariant
length scale would be agreed upon by all inertial observers. We hypothesize the
approximate scale of the invariant length.Comment: 12 pages no figure
Compromise of Localized Graviton with a Small Cosmological Constant in Randall-Sundrum Scenario
A new mechanism which leads to a linearized massless graviton localized on
the brane is found in the /CFT setting, {\it i.e.} in a single copy of
spacetime with a singular brane on the boundary, within the
Randall-Sundrum brane-world scenario. With an help of a recent development in
path-integral techniques, a one-parameter family of propagators for linearized
gravity is obtained analytically, in which a parameter reflects various
kinds of boundary conditions that arise as a result of the half-line
constraint. In the case of a Dirichlet boundary condition () the
graviton localized on the brane can be massless {\it via} coupling constant
renormalization. Our result supports a conjecture that the usual
Randall-Sundrum scenario is a regularized version of a certain underlying
theory.Comment: 6 pages, no figure, V2 12 pages, one more author added, will appear
in PL
On the Green function of linear evolution equations for a region with a boundary
We derive a closed-form expression for the Green function of linear evolution
equations with the Dirichlet boundary condition for an arbitrary region, based
on the singular perturbation approach to boundary problems.Comment: 9 page
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