407 research outputs found
Quantum kinetic theory of shift current electron pumping in semiconductors
We develop a theory of laser beam generation of shift currents in
non-centrosymmetric semiconductors. The currents originate when the excited
electrons transfer between different bands or scatter inside these bands, and
asymmetrically shift their centers of mass in elementary cells. Quantum kinetic
equations for hot-carrier distributions and expressions for the induced
currents are derived by nonequilibrium Green functions. In applications, we
simplify the approach to the Boltzmann limit and use it to model laser-excited
GaAs in the presence of LO phonon scattering. The shift currents are calculated
in a steady-state regime.Comment: 23 pages, 5 figures (Latex
A new bound for the 2/3 conjecture
We show that any n-vertex complete graph with edges colored with three colors
contains a set of at most four vertices such that the number of the neighbors
of these vertices in one of the colors is at least 2n/3. The previous best
value, proved by Erdos, Faudree, Gould, Gy\'arf\'as, Rousseau and Schelp in
1989, is 22. It is conjectured that three vertices suffice
Generalized gradient expansions in quantum transport equations
Gradient expansions in quantum transport equations of a Kadanoff-Baym form
have been reexamined. We have realized that in a consistent approach the
expansion should be performed also inside of the self-energy in the scattering
integrals of these equations. In the first perturbation order this internal
expansion gives new correction terms to the generalized Boltzman equation.
These correction terms are found here for several typical systems. Possible
corrections to the theory of a linear response to weak electric fields are also
discussed.Comment: 20 pages, latex, to appear in Journal of Statistical Physics, March
(1997
Testing Linear-Invariant Non-Linear Properties
We consider the task of testing properties of Boolean functions that are
invariant under linear transformations of the Boolean cube. Previous work in
property testing, including the linearity test and the test for Reed-Muller
codes, has mostly focused on such tasks for linear properties. The one
exception is a test due to Green for "triangle freeness": a function
f:\cube^{n}\to\cube satisfies this property if do not all
equal 1, for any pair x,y\in\cube^{n}.
Here we extend this test to a more systematic study of testing for
linear-invariant non-linear properties. We consider properties that are
described by a single forbidden pattern (and its linear transformations), i.e.,
a property is given by points v_{1},...,v_{k}\in\cube^{k} and
f:\cube^{n}\to\cube satisfies the property that if for all linear maps
L:\cube^{k}\to\cube^{n} it is the case that do
not all equal 1. We show that this property is testable if the underlying
matroid specified by is a graphic matroid. This extends
Green's result to an infinite class of new properties.
Our techniques extend those of Green and in particular we establish a link
between the notion of "1-complexity linear systems" of Green and Tao, and
graphic matroids, to derive the results.Comment: This is the full version; conference version appeared in the
proceedings of STACS 200
Electric Polarization of Heteropolar Nanotubes as a Geometric Phase
The three-fold symmetry of planar boron nitride, the III-V analog to
graphene, prohibits an electric polarization in its ground state, but this
symmetry is broken when the sheet is wrapped to form a BN nanotube. We show
that this leads to an electric polarization along the nanotube axis which is
controlled by the quantum mechanical boundary conditions on its electronic
states around the tube circumference. Thus the macroscopic dipole moment has an
{\it intrinsically nonlocal quantum} mechanical origin from the wrapped
dimension. We formulate this novel phenomenon using the Berry's phase approach
and discuss its experimental consequences.Comment: 4 pages with 3 eps figures, updated with correction to Eqn (9
Optical excitations in hexagonal nanonetwork materials
Optical excitations in hexagonal nanonetwork materials, for example,
Boron-Nitride (BN) sheets and nanotubes, are investigated theoretically. The
bonding of BN systems is positively polarized at the B site, and is negatively
polarized at the N site. There is a permanent electric dipole moment along the
BN bond, whose direction is from the B site to the N site. When the exciton
hopping integral is restricted to the nearest neighbors, the flat band of the
exciton appears at the lowest energy. The higher optical excitations have
excitation bands similar to the electronic bands of graphene planes and carbon
nanotubes. The symmetry of the flat exciton band is optically forbidden,
indicating that the excitons related to this band will show quite long lifetime
which will cause strong luminescence properties.Comment: 4 pages; 3 figures; proceedings of "XVIth International Winterschool
on Electronic Properties of Novel Materials (IWEPNM2002)
Electron-Phonon Interacation in Quantum Dots: A Solvable Model
The relaxation of electrons in quantum dots via phonon emission is hindered
by the discrete nature of the dot levels (phonon bottleneck). In order to
clarify the issue theoretically we consider a system of discrete fermionic
states (dot levels) coupled to an unlimited number of bosonic modes with the
same energy (dispersionless phonons). In analogy to the Gram-Schmidt
orthogonalization procedure, we perform a unitary transformation into new
bosonic modes. Since only of them couple to the fermions, a
numerically exact treatment is possible. The formalism is applied to a GaAs
quantum dot with only two electronic levels. If close to resonance with the
phonon energy, the electronic transition shows a splitting due to quantum
mechanical level repulsion. This is driven mainly by one bosonic mode, whereas
the other two provide further polaronic renormalizations. The numerically exact
results for the electron spectral function compare favourably with an analytic
solution based on degenerate perturbation theory in the basis of shifted
oscillator states. In contrast, the widely used selfconsistent first-order Born
approximation proves insufficient in describing the rich spectral features.Comment: 8 pages, 4 figure
Complexity of Coloring Graphs without Paths and Cycles
Let and denote a path on vertices and a cycle on
vertices, respectively. In this paper we study the -coloring problem for
-free graphs. Maffray and Morel, and Bruce, Hoang and Sawada,
have proved that 3-colorability of -free graphs has a finite forbidden
induced subgraphs characterization, while Hoang, Moore, Recoskie, Sawada, and
Vatshelle have shown that -colorability of -free graphs for
does not. These authors have also shown, aided by a computer search, that
4-colorability of -free graphs does have a finite forbidden induced
subgraph characterization. We prove that for any , the -colorability of
-free graphs has a finite forbidden induced subgraph
characterization. We provide the full lists of forbidden induced subgraphs for
and . As an application, we obtain certifying polynomial time
algorithms for 3-coloring and 4-coloring -free graphs. (Polynomial
time algorithms have been previously obtained by Golovach, Paulusma, and Song,
but those algorithms are not certifying); To complement these results we show
that in most other cases the -coloring problem for -free
graphs is NP-complete. Specifically, for we show that -coloring is
NP-complete for -free graphs when and ; for we show that -coloring is NP-complete for -free graphs
when , ; and additionally, for , we show that
-coloring is also NP-complete for -free graphs if and
. This is the first systematic study of the complexity of the
-coloring problem for -free graphs. We almost completely
classify the complexity for the cases when , and
identify the last three open cases
Counting flags in triangle-free digraphs
Motivated by the Caccetta-Haggkvist Conjecture, we prove that every digraph
on n vertices with minimum outdegree 0.3465n contains an oriented triangle.
This improves the bound of 0.3532n of Hamburger, Haxell and Kostochka. The main
new tool we use in our proof is the theory of flag algebras developed recently
by Razborov.Comment: 19 pages, 7 figures; this is the final version to appear in
Combinatoric
Exhaustive generation of -critical -free graphs
We describe an algorithm for generating all -critical -free
graphs, based on a method of Ho\`{a}ng et al. Using this algorithm, we prove
that there are only finitely many -critical -free graphs, for
both and . We also show that there are only finitely many
-critical graphs -free graphs. For each case of these cases we
also give the complete lists of critical graphs and vertex-critical graphs.
These results generalize previous work by Hell and Huang, and yield certifying
algorithms for the -colorability problem in the respective classes.
Moreover, we prove that for every , the class of 4-critical planar
-free graphs is finite. We also determine all 27 4-critical planar
-free graphs.
We also prove that every -free graph of girth at least five is
3-colorable, and determine the smallest 4-chromatic -free graph of
girth five. Moreover, we show that every -free graph of girth at least
six and every -free graph of girth at least seven is 3-colorable. This
strengthens results of Golovach et al.Comment: 17 pages, improved girth results. arXiv admin note: text overlap with
arXiv:1504.0697
- âŚ