177 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
Nearsightedness of Electronic Matter in One Dimension
The concept of nearsightedeness of electronic matter (NEM) was introduced by
W. Kohn in 1996 as the physical principal underlining Yang's electronic
structure alghoritm of divide and conquer. It describes the fact that, for
fixed chemical potential, local electronic properties at a point , like the
density , depend significantly on the external potential only at
nearby points. Changes of that potential, {\it no matter how large},
beyond a distance , have {\it limited} effects on local electronic
properties, which tend to zero as function of . This remains true
even if the changes in the external potential completely surrounds the point
. NEM can be quantitatively characterized by the nearsightedness range,
, defined as the smallest distance from ,
beyond which {\it any} change of the external potential produces a density
change, at , smaller than a given . The present paper gives a
detailed analysis of NEM for periodic metals and insulators in 1D and includes
sharp, explicit estimates of the nearsightedness range. Since NEM involves
arbitrary changes of the external potential, strong, even qualitative changes
can occur in the system, such as the discretization of energy bands or the
complete filling of the insulating gap of an insulator with continuum spectrum.
In spite of such drastic changes, we show that has only a limited
effect on the density, which can be quantified in terms of simple parameters of
the unperturbed system.Comment: 10 pages, 9 figure
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
Dimensional crossover of a boson gas in multilayers
We obtain the thermodynamic properties for a non-interacting Bose gas
constrained on multilayers modeled by a periodic Kronig-Penney delta potential
in one direction and allowed to be free in the other two directions. We report
Bose-Einstein condensation (BEC) critical temperatures, chemical potential,
internal energy, specific heat, and entropy for different values of a
dimensionless impenetrability between layers. The BEC critical
temperature coincides with the ideal gas BEC critical temperature
when and rapidly goes to zero as increases to infinity for
any finite interlayer separation. The specific heat \textit{vs} for
finite and plane separation exhibits one minimum and one or two maxima
in addition to the BEC, for temperatures larger than which highlights
the effects due to particle confinement. Then we discuss a distinctive
dimensional crossover of the system through the specific heat behavior driven
by the magnitude of . For the crossover is revealed by the change
in the slope of and when , it is evidenced by a broad
minimum in .Comment: Ten pages, nine figure
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
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
Phonon Hall effect in ionic crystals in the presence of static magnetic field
We study phonon Hall effect (PHE) for ionic crystals in the presence of
static magnetic field. Using Green-Kubo formula, we present an exact
calculation of thermal conductivity tensor by considering both positive and
negative frequency phonons. Numerical results are shown for some lattices such
as hexagonal lattices, triangular lattices, and square lattices. We find that
the PHE occurs on the nonmagnetic ionic crystal NaCl, although the magnitude is
very small which is due to the tiny charge-to-mass ratio of the ions. The
off-diagonal thermal conductivity is finite for nonzero magnetic field and
changes sign for high value of magnetic field at high temperature. We also
found that the off-diagonal thermal conductivity diverges as at low
temperature
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
Friedel oscillations in a gas of interacting one-dimensional fermionic atoms confined in a harmonic trap
Using an asymptotic phase representation of the particle density operator
in the one-dimensional harmonic trap, the part which describes the Friedel oscillations is extracted. The
expectation value with respect to the interacting
ground state requires the calculation of the mean square average of a properly
defined phase operator. This calculation is performed analytically for the
Tomonaga-Luttinger model with harmonic confinement. It is found that the
envelope of the Friedel oscillations at zero temperature decays with the
boundary exponent away from the classical boundaries. This
value differs from that known for open boundary conditions or strong pinning
impurities. The soft boundary in the present case thus modifies the decay of
Friedel oscillations. The case of two components is also discussed.Comment: Revised version to appear in Journal of Physics B: Atomic, Molecular
and Optical Physic
Low-frequency plasma conductivity in the average-atom approximation
Low-frequency properties of a plasma are examined within the average-atom
approximation, which presumes that scattering of a conducting electron on each
atom takes place independently of other atoms. The relaxation time tau
distinguishes a high-frequency region omega tau > 1, where the single-atom
approximation is applicable explicitly, from extreme low frequencies omega tau
< 1, where, naively, the single-atom approximation is invalid. A proposed
generalization of the formalism, which takes into account many-atom collisions,
is found to be accurate in all frequency regions, from omega =0 to omega tau
>1, reproducing the Ziman formula in the static limit, results based on the
Kubo-Greenwood formula for high frequencies, and satisfying the conductivity
sum-rule precisely. The correspondence between physical processes leading to
the conventional Ohm's law and the infrared properties of QED is discussed. The
suggested average-atom approach to frequency-dependent conductivity is
illustrated by numerical calculations for the an aluminum plasma in the
temperature range 2--10 eV.Comment: 9 pages 3 figure
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