807 research outputs found
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
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
Dielectric Behavior of Nonspherical Cell Suspensions
Recent experiments revealed that the dielectric dispersion spectrum of
fission yeast cells in a suspension was mainly composed of two sub-dispersions.
The low-frequency sub-dispersion depended on the cell length, whereas the
high-frequency one was independent of it. The cell shape effect was
qualitatively simulated by an ellipsoidal cell model. However, the comparison
between theory and experiment was far from being satisfactory. In an attempt to
close up the gap between theory and experiment, we considered the more
realistic cells of spherocylinders, i.e., circular cylinders with two
hemispherical caps at both ends. We have formulated a Green function formalism
for calculating the spectral representation of cells of finite length. The
Green function can be reduced because of the azimuthal symmetry of the cell.
This simplification enables us to calculate the dispersion spectrum and hence
access the effect of cell structure on the dielectric behavior of cell
suspensions.Comment: Preliminary results have been reported in the 2001 March Meeting of
the American Physical Society. Accepted for publications in J. Phys.:
Condens. Matte
Disorder-Induced Multiple Transition involving Z2 Topological Insulator
Effects of disorder on two-dimensional Z2 topological insulator are studied
numerically by the transfer matrix method. Based on the scaling analysis, the
phase diagram is derived for a model of HgTe quantum well as a function of
disorder strength and magnitude of the energy gap. In the presence of sz
non-conserving spin-orbit coupling, a finite metallic region is found that
partitions the two topologically distinct insulating phases. As disorder
increases, a narrow-gap topologically trivial insulator undergoes a series of
transitions; first to metal, second to topological insulator, third to metal,
and finally back to trivial insulator. We show that this multiple transition is
a consequence of two disorder effects; renormalization of the band gap, and
Anderson localization. The metallic region found in the scaling analysis
corresponds roughly to the region of finite density of states at the Fermi
level evaluated in the self-consistent Born approximation.Comment: 5 pages, 5 figure
Coherently Controlled Nanoscale Molecular Deposition
Quantum interference effects are shown to provide a means of controlling and
enhancing the focusing a collimated neutral molecular beam onto a surface. The
nature of the aperiodic pattern formed can be altered by varying laser field
characteristics and the system geometry.Comment: 13 pages (inculding 4 figures), LaTeX (Phys. Rev. Lett., 2000, in
Press
Concave Plasmonic Particles: Broad-Band Geometrical Tunability in the Near Infra-Red
Optical resonances spanning the Near and Short Infra-Red spectral regime were
exhibited experimentally by arrays of plasmonic nano-particles with concave
cross-section. The concavity of the particle was shown to be the key ingredient
for enabling the broad band tunability of the resonance frequency, even for
particles with dimensional aspect ratios of order unity. The atypical
flexibility of setting the resonance wavelength is shown to stem from a unique
interplay of local geometry with surface charge distributions
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