254 research outputs found
Nearsightedness of Electronic Matter
In an earlier paper, W. Kohn had qualitatively introduced the concept of
"nearsightedness" of electrons in many-atom systems. It can be viewed as
underlying such important ideas as Pauling's "chemical bond," "transferability"
and Yang's computational principle of "divide and conquer." It describes the
fact that, for fixed chemical potential, local electronic properties, like the
density , depend significantly on the effective 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 rapidly tend to zero as function of . In the
present paper, the concept is first sharpened for representative models of
uncharged fermions moving in external potentials, followed by a discussion of
the effects of electron-electron interactions and of perturbing external
charges.Comment: final for
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
Electronic states and transport properties in the Kronig-Penney model with correlated compositional and structural disorder
We study the structure of the electronic states and the transport properties
of a Kronig-Penney model with weak compositional and structural disorder. Using
a perturbative approach we obtain an analytical expression for the localisation
length which is valid for disorder with arbitrary correlations. We show how to
generate disorder with self- and cross-correlations and we analyse both the
known delocalisation effects of the long-range self-correlations and new
effects produced by cross-correlations. We finally discuss how both kinds of
correlations alter the transport properties in Kronig-Penney models of finite
size.Comment: 23 pages, 5 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
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
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
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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