433 research outputs found
Positive solutions of Schr\"odinger equations and fine regularity of boundary points
Given a Lipschitz domain in and a nonnegative
potential in such that is bounded
in we study the fine regularity of boundary points with respect to
the Schr\"odinger operator in . Using potential
theoretic methods, several conditions equivalent to the fine regularity of are established. The main result is a simple (explicit if
is smooth) necessary and sufficient condition involving the size of
for to be finely regular. An essential intermediate result consists in
a majorization of for
positive harmonic in and . Conditions for
almost everywhere regularity in a subset of are also
given as well as an extension of the main results to a notion of fine
-regularity, if , being two potentials, with and a second order elliptic operator.Comment: version 1. 23 pages version 3. 28 pages. Mainly a typo in Theorem 1.1
is correcte
Mutual Orientation Effects on Electron-Transfer Reactions between Porphyrins
Mutual orientation effects on the rate of nonadiabatic electron transfer between several diporphyrin pairs of experimental interest are examined. The electronic matrix element for electron transfer is calculated within a one-electron spheroidal model for a variety of states and orientations which are relevant to both biological and synthetic electron-transfer systems. Both the mutual orientation of the pairs and the nodal structure of the donor and acceptor orbitals can have large effects on calculated rates
Weak-Localization in Chaotic Versus Non-Chaotic Cavities: A Striking Difference in the Line Shape
We report experimental evidence that chaotic and non-chaotic scattering
through ballistic cavities display distinct signatures in quantum transport. In
the case of non-chaotic cavities, we observe a linear decrease in the average
resistance with magnetic field which contrasts markedly with a Lorentzian
behavior for a chaotic cavity. This difference in line-shape of the
weak-localization peak is related to the differing distribution of areas
enclosed by electron trajectories. In addition, periodic oscillations are
observed which are probably associated with the Aharonov-Bohm effect through a
periodic orbit within the cavities.Comment: 4 pages revtex + 4 figures on request; amc.hub.94.
Coin Tossing as a Billiard Problem
We demonstrate that the free motion of any two-dimensional rigid body
colliding elastically with two parallel, flat walls is equivalent to a billiard
system. Using this equivalence, we analyze the integrable and chaotic
properties of this new class of billiards. This provides a demonstration that
coin tossing, the prototypical example of an independent random process, is a
completely chaotic (Bernoulli) problem. The related question of which billiard
geometries can be represented as rigid body systems is examined.Comment: 16 pages, LaTe
Orbital effect of in-plane magnetic field on quantum transport in chaotic lateral dots
We show how the in-plane magnetic field, which breaks time-reversal and
rotational symmetries of the orbital motion of electrons in a heterostructure
due to the momentum-dependent inter-subband mixing, affects weak localisation
correction to conductance of a large-area chaotic lateral quantum dot and
parameteric dependences of universal conductance fluctuations in it.Comment: 4 pages with a figur
Heisenberg's Uncertainty Relation and Bell Inequalities in High Energy Physics
An effective formalism is developed to handle decaying two-state systems.
Herewith, observables of such systems can be described by a single operator in
the Heisenberg picture. This allows for using the usual framework in quantum
information theory and, hence, to enlighten the quantum feature of such systems
compared to non-decaying systems. We apply it to systems in high energy
physics, i.e. to oscillating meson-antimeson systems. In particular, we discuss
the entropic Heisenberg uncertainty relation for observables measured at
different times at accelerator facilities including the effect of CP violation,
i.e. the imbalance of matter and antimatter. An operator-form of Bell
inequalities for systems in high energy physics is presented, i.e. a
Bell-witness operator, which allows for simple analysis of unstable systems.Comment: 17 page
Quantum master equation for a system influencing its environment
A perturbative quantum master equation is derived for a system interacting
with its environment, which is more general than the ones derived before. Our
master equation takes into account the effect of the energy exchanges between
the system and the environment and the conservation of energy in a finite total
system. This master quantum describes relaxation mechanisms in isolated
nanoscopic quantum systems. In its most general form, this equation is
non-Markovian and a Markovian version of it rules the long-time relaxation. We
show that our equation reduces to the Redfield equation in the limit where the
energy of the system does not affect the density of state of its environment.
This master equation and the Redfield one are applied to a spin-environment
model defined in terms of random matrices and compared with the solutions of
the exact von Neumann equation. The comparison proves the necessity to allow
energy exchange between the subsystem and the environment in order to correctly
describe the relaxation in isolated nanoscopic total system.Comment: 39 pages, 10 figure
Revealing Bell's Nonlocality for Unstable Systems in High Energy Physics
Entanglement and its consequences - in particular the violation of Bell
inequalities, which defies our concepts of realism and locality - have been
proven to play key roles in Nature by many experiments for various quantum
systems. Entanglement can also be found in systems not consisting of ordinary
matter and light, i.e. in massive meson--antimeson systems. Bell inequalities
have been discussed for these systems, but up to date no direct experimental
test to conclusively exclude local realism was found. This mainly stems from
the fact that one only has access to a restricted class of observables and that
these systems are also decaying. In this Letter we put forward a Bell
inequality for unstable systems which can be tested at accelerator facilities
with current technology. Herewith, the long awaited proof that such systems at
different energy scales can reveal the sophisticated "dynamical" nonlocal
feature of Nature in a direct experiment gets feasible. Moreover, the role of
entanglement and CP violation, an asymmetry between matter and antimatter, is
explored, a special feature offered only by these meson-antimeson systems.Comment: 6 pages, 3 figure
Superconformal Multi-Black Hole Moduli Spaces in Four Dimensions
Quantum mechanics on the moduli space of N supersymmetric Reissner-Nordstrom
black holes is shown to admit 4 supersymmetries using an unconventional
supermultiplet which contains 3N bosons and 4N fermions. A near-horizon limit
is found in which the quantum mechanics of widely separated black holes
decouples from that of strongly-interacting, near-coincident black holes. This
near-horizon theory is shown to have an enhanced D(2,1;0) superconformal
symmetry. The bosonic symmetries are SL(2,R) conformal symmetry and SU(2)xSU(2)
R-symmetry arising from spatial rotations and the R-symmetry of N=2
supergravity.Comment: 23 pages, harvmac. v2: many typos fixe
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