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 $n(r)$, depend significantly on the effective external potential only at nearby points. Changes of that potential, {\it no matter how large}, beyond a distance $\textsf{R}$ have {\it limited} effects on local electronic properties, which rapidly tend to zero as function of $\textsf{R}$. 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 $r$, like the density $n(r)$, depend significantly on the external potential $v$ only at nearby points. Changes $\Delta v$ of that potential, {\it no matter how large}, beyond a distance $\textsf{R}$, have {\it limited} effects on local electronic properties, which tend to zero as function of $\textsf{R}$. This remains true even if the changes in the external potential completely surrounds the point $r$. NEM can be quantitatively characterized by the nearsightedness range, $\textsf{\textsf{R}}(r,\Delta n)$, defined as the smallest distance from $r$, beyond which {\it any} change of the external potential produces a density change, at $r$, smaller than a given $\Delta n$. 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 $\Delta v$ 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 δ′\delta^{'}-function potential case

One-dimensional $\delta^{'}$-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 $P\geqslant 0$ between layers. The BEC critical temperature $T_{c}$ coincides with the ideal gas BEC critical temperature $T_{0}$ when $P=0$ and rapidly goes to zero as $P$ increases to infinity for any finite interlayer separation. The specific heat $C_{V}$ \textit{vs} $T$ for finite $P$ and plane separation $a$ exhibits one minimum and one or two maxima in addition to the BEC, for temperatures larger than $T_{c}$ 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 $P$. For $T<T_{c}$ the crossover is revealed by the change in the slope of $\log C_{V}(T)$ and when $T>T_{c}$, it is evidenced by a broad minimum in $C_{V}(T)$.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 $AdS$/CFT setting, {\it i.e.} in a single copy of $AdS_5$ 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 $\xi$ reflects various kinds of boundary conditions that arise as a result of the half-line constraint. In the case of a Dirichlet boundary condition ($\xi = 0$) 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 $\pm{1/T}$ 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