1,479 research outputs found
The plasmonic eigenvalue problem
A plasmon of a bounded domain is a non-trivial
bounded harmonic function on which is
continuous at and whose exterior and interior normal
derivatives at have a constant ratio. We call this ratio a
plasmonic eigenvalue of . Plasmons arise in the description of
electromagnetic waves hitting a metallic particle . We investigate
these eigenvalues and prove that they form a sequence of numbers converging to
one. Also, we prove regularity of plasmons, derive a variational
characterization, and prove a second order perturbation formula. The problem
can be reformulated in terms of Dirichlet-Neumann operators, and as a side
result we derive a formula for the shape derivative of these operators.Comment: 22 pages; replacement 8-March-14: minor corrections; to appear in
Review in Mathematical Physic
Sequential measurements of conjugate observables
We present a unified treatment of sequential measurements of two conjugate
observables. Our approach is to derive a mathematical structure theorem for all
the relevant covariant instruments. As a consequence of this result, we show
that every Weyl-Heisenberg covariant observable can be implemented as a
sequential measurement of two conjugate observables. This method is applicable
both in finite and infinite dimensional Hilbert spaces, therefore covering
sequential spin component measurements as well as position-momentum sequential
measurements.Comment: 25 page
Extreme Covariant Quantum Observables in the Case of an Abelian Symmetry Group and a Transitive Value Space
We represent quantum observables as POVMs (normalized positive operator
valued measures) and consider convex sets of observables which are covariant
with respect to a unitary representation of a locally compact Abelian symmetry
group . The value space of such observables is a transitive -space. We
characterize the extreme points of covariant observables and also determine the
covariant extreme points of the larger set of all quantum observables. The
results are applied to position, position difference and time observables.Comment: 23 page
On a certain class of semigroups of operators
We define an interesting class of semigroups of operators in Banach spaces,
namely, the randomly generated semigroups. This class contains as a remarkable
subclass a special type of quantum dynamical semigroups introduced by
Kossakowski in the early 1970s. Each randomly generated semigroup is
associated, in a natural way, with a pair formed by a representation or an
antirepresentation of a locally compact group in a Banach space and by a
convolution semigroup of probability measures on this group. Examples of
randomly generated semigroups having important applications in physics are
briefly illustrated.Comment: 11 page
Haar expectations of ratios of random characteristic polynomials
We compute Haar ensemble averages of ratios of random characteristic
polynomials for the classical Lie groups K = O(N), SO(N), and USp(N). To that
end, we start from the Clifford-Weyl algebera in its canonical realization on
the complex of holomorphic differential forms for a C-vector space V. From it
we construct the Fock representation of an orthosymplectic Lie superalgebra osp
associated to V. Particular attention is paid to defining Howe's oscillator
semigroup and the representation that partially exponentiates the Lie algebra
representation of sp in osp. In the process, by pushing the semigroup
representation to its boundary and arguing by continuity, we provide a
construction of the Shale-Weil-Segal representation of the metaplectic group.
To deal with a product of n ratios of characteristic polynomials, we let V =
C^n \otimes C^N where C^N is equipped with its standard K-representation, and
focus on the subspace of K-equivariant forms. By Howe duality, this is a
highest-weight irreducible representation of the centralizer g of Lie(K) in
osp. We identify the K-Haar expectation of n ratios with the character of this
g-representation, which we show to be uniquely determined by analyticity, Weyl
group invariance, certain weight constraints and a system of differential
equations coming from the Laplace-Casimir invariants of g. We find an explicit
solution to the problem posed by all these conditions. In this way we prove
that the said Haar expectations are expressed by a Weyl-type character formula
for all integers N \ge 1. This completes earlier work by Conrey, Farmer, and
Zirnbauer for the case of U(N).Comment: LaTeX, 70 pages, Complex Analysis and its Synergies (2016) 2:
Seismic modeling using the frozen Gaussian approximation
We adopt the frozen Gaussian approximation (FGA) for modeling seismic waves.
The method belongs to the category of ray-based beam methods. It decomposes
seismic wavefield into a set of Gaussian functions and propagates these
Gaussian functions along appropriate ray paths. As opposed to the classic
Gaussian-beam method, FGA keeps the Gaussians frozen (at a fixed width) during
the propagation process and adjusts their amplitudes to produce an accurate
approximation after summation. We perform the initial decomposition of seismic
data using a fast version of the Fourier-Bros-Iagolnitzer (FBI) transform and
propagate the frozen Gaussian beams numerically using ray tracing. A test using
a smoothed Marmousi model confirms the validity of FGA for accurate modeling of
seismic wavefields.Comment: 5 pages, 8 figure
The orientation-preserving diffeomorphism group of S^2 deforms to SO(3) smoothly
Smale proved that the orientation-preserving diffeomorphism group of S^2 has
a continuous strong deformation retraction to SO(3). In this paper, we
construct such a strong deformation retraction which is diffeologically smooth.Comment: 16 page
Hospital Mergers with Regulated Prices
We study the effects of a hospital merger in a spatial competition framework where semi-altruistic hospitals choose quality and cost-containment effort. Whereas a merger always leads to higher average cost efficiency, the effect on quality provision depends on the strategic nature of quality competition, which in turn depends on the degree of altruism and the effectiveness of cost-containment effort. If qualities are strategic complements, then a merger leads to lower quality for all hospitals. If qualities are strategic substitutes, then a merger leads to higher quality for at least one hospital, and might also yield higher average quality provision and increased patient utility
Quantum Homodyne Tomography as an Informationally Complete Positive Operator Valued Measure
We define a positive operator valued measure on
describing the measurement of randomly sampled quadratures in quantum homodyne
tomography, and we study its probabilistic properties. Moreover, we give a
mathematical analysis of the relation between the description of a state in
terms of and the description provided by its Wigner transform.Comment: 9 page
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