432 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
Coarse-Grained Picture for Controlling Complex Quantum Systems
We propose a coarse-grained picture to control ``complex'' quantum dynamics,
i.e., multi-level-multi-level transition with a random interaction. Assuming
that optimally controlled dynamics can be described as a Rabi-like oscillation
between an initial and final state, we derive an analytic optimal field as a
solution to optimal control theory. For random matrix systems, we numerically
confirm that the analytic optimal field steers an initial state to a target
state which both contains many eigenstates.Comment: jpsj2.cls, 2 pages, 3 figure files; appear in J. Phys. Soc. Jpn.
Vol.73, No.11 (Nov. 15, 2004
Coherent Control of Photocurrents in Graphene and Carbon Nanotubes
Coherent one photon () and two photon () electronic
excitations are studied for graphene sheets and for carbon nanotubes using a
long wavelength theory for the low energy electronic states. For graphene
sheets we find that coherent superposition of these excitations produces a
polar asymmetry in the momentum space distribution of the excited carriers with
an angular dependence which depends on the relative polarization and phases of
the incident fields. For semiconducting nanotubes we find a similar effect
which depends on the square of the semiconducting gap, and we calculate its
frequency dependence.
We find that the third order nonlinearity which controls the direction of the
photocurrent is robust for semiconducting t ubes and vanishes in the continuum
theory for conducting tubes. We calculate corrections to these results arising
from higher order crystal field effects on the band structure and briefly
discuss some applications of the theory.Comment: 12 pages in RevTex, 6 epsf figure
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
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
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
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
Quasirandom permutations are characterized by 4-point densities
For permutations π and τ of lengths |π|≤|τ| , let t(π,τ) be the probability that the restriction of τ to a random |π| -point set is (order) isomorphic to π . We show that every sequence {τj} of permutations such that |τj|→∞ and t(π,τj)→1/4! for every 4-point permutation π is quasirandom (that is, t(π,τj)→1/|π|! for every π ). This answers a question posed by Graham
Laser optical separation of chiral molecules
The optical trapping of molecules with an off-resonant laser beam involves a forward-Rayleigh scattering mechanism. It is shown that discriminatory effects arise on irradiating chiral molecules with circularly polarized light; the complete representation requires ensemble-weighted averaging to account for the influence of the trapping beam on the distribution of molecular orientations. Results of general application enable comparisons to be drawn between the results for two limits of the input laser intensity. It emerges that, in a racemic mixture, there is a differential driving force whose effect, at high laser intensities, is to produce differing local concentrations of the two enantiomers
Engineering squeezed states in high-Q cavities
While it has been possible to build fields in high-Q cavities with a high
degree of squeezing for some years, the engineering of arbitrary squeezed
states in these cavities has only recently been addressed [Phys. Rev. A 68,
061801(R) (2003)]. The present work examines the question of how to squeeze any
given cavity-field state and, particularly, how to generate the squeezed
displaced number state and the squeezed macroscopic quantum superposition in a
high-Q cavity
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