1,095 research outputs found
Generalized Wannier Functions
We consider single particle Schrodinger operators with a gap in the en ergy
spectrum. We construct a complete, orthonormal basis function set for the inv
ariant space corresponding to the spectrum below the spectral gap, which are
exponentially localized a round a set of closed surfaces of monotonically
increasing sizes. Estimates on the exponential dec ay rate and a discussion of
the geometry of these surfaces is included
Analytic structure of Bloch functions for linear molecular chains
This paper deals with Hamiltonians of the form H=-{\bf \nabla}^2+v(\rr),
with v(\rr) periodic along the direction, . The
wavefunctions of are the well known Bloch functions
\psi_{n,\lambda}(\rr), with the fundamental property
and
. We give the generic analytic structure
(i.e. the Riemann surface) of \psi_{n,\lambda}(\rr) and their corresponding
energy, , as functions of . We show that
and are different branches of two multi-valued
analytic functions, and , with an essential
singularity at and additional branch points, which are generically
of order 1 and 3, respectively. We show where these branch points come from,
how they move when we change the potential and how to estimate their location.
Based on these results, we give two applications: a compact expression of the
Green's function and a discussion of the asymptotic behavior of the density
matrix for insulating molecular chains.Comment: 13 pages, 11 figure
Symmetry breaking in the self-consistent Kohn-Sham equations
The Kohn-Sham (KS) equations determine, in a self-consistent way, the
particle density of an interacting fermion system at thermal equilibrium. We
consider a situation when the KS equations are known to have a unique solution
at high temperatures and this solution is a uniform particle density. We show
that, at zero temperature, there are stable solutions that are not uniform. We
provide the general principles behind this phenomenon, namely the conditions
when it can be observed and how to construct these non-uniform solutions. Two
concrete examples are provided, including fermions on the sphere which are
shown to crystallize in a structure that resembles the C molecule.Comment: a few typos eliminate
An edge index for the Quantum Spin-Hall effect
Quantum Spin-Hall systems are topological insulators displaying
dissipationless spin currents flowing at the edges of the samples. In
contradistinction to the Quantum Hall systems where the charge conductance of
the edge modes is quantized, the spin conductance is not and it remained an
open problem to find the observable whose edge current is quantized. In this
paper, we define a particular observable and the edge current corresponding to
this observable. We show that this current is quantized and that the
quantization is given by the index of a certain Fredholm operator. This
provides a new topological invariant that is shown to take same values as the
Spin-Chern number previously introduced in the literature. The result gives an
effective tool for the investigation of the edge channels' structure in Quantum
Spin-Hall systems. Based on a reasonable assumption, we also show that the edge
conducting channels are not destroyed by a random edge.Comment: 4 pages, 3 figure
Correcting the polarization effect in low frequency Dielectric Spectroscopy
We demonstrate a simple and robust methodology for measuring and analyzing
the polarization impedance appearing at interface between electrodes and ionic
solutions, in the frequency range from 1 to Hz. The method assumes no
particular behavior of the electrode polarization impedance and it only makes
use of the fact that the polarization effect dies out with frequency. The
method allows a direct and un-biased measurement of the polarization impedance,
whose behavior with the applied voltages and ionic concentration is
methodically investigated. Furthermore, based on the previous findings, we
propose a protocol for correcting the polarization effect in low frequency
Dielectric Spectroscopy measurements of colloids. This could potentially lead
to the quantitative resolution of the -dispersion regime of live cells
in suspension
The Laplace-Beltrami operator on surfaces with axial symmetry
A practical solution for the mathematical problem of functional calculus with
Laplace-Beltrami operator on surfaces with axial symmetry is found. A
quantitative analysis of the spectrum is presented.Comment: 13 pages, 11 figure
Unique Solutions to Hartree-Fock Equations for Closed Shell Atoms
In this paper we study the problem of uniqueness of solutions to the Hartree
and Hartree-Fock equations of atoms. We show, for example, that the
Hartree-Fock ground state of a closed shell atom is unique provided the atomic
number is sufficiently large compared to the number of electrons. More
specifically, a two-electron atom with atomic number has a unique
Hartree-Fock ground state given by two orbitals with opposite spins and
identical spatial wave functions. This statement is wrong for some , which
exhibits a phase segregation.Comment: 18 page
Gutzwiller density functional theory for correlated electron systems
We develop a new density functional theory (DFT) and formalism for correlated
electron systems by taking as reference an interacting electron system that has
a ground state wavefunction which obeys exactly the Gutzwiller approximation
for all one particle operators. The solution of the many electron problem is
mapped onto the self-consistent solution of a set of single particle
Schroedinger equations analogous to standard DFT-LDA calculations.Comment: 4 page
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