659 research outputs found
Design of Matched Zero-Index Metamaterials Using Non-Magnetic Inclusions in Epsilon-Near-Zero (ENZ) Media
In this work, we study the electrodynamics of metamaterials that consist of
resonant non-magnetic inclusions embedded in an epsilon-near-zero (ENZ) host
medium. It is shown that the inclusions can be designed in such a way that both
the effective permittivity and permeability of the composite structure are
simultaneously zero. Two different metamaterial configurations are studied and
analyzed in detail. For a particular class of problems, it is analytically
proven that such matched zero-index metamaterials may help improving the
transmission through a waveguide bend, and that the scattering parameters may
be completely independent of the specific arrangement of the inclusions and of
the granularity of the crystal. The proposed concepts are numerically
demonstrated at microwaves with a metamaterial realization based on an
artificial plasma.Comment: 38 pages, 10 Figures, under revie
Quantum walks on quotient graphs
A discrete-time quantum walk on a graph is the repeated application of a
unitary evolution operator to a Hilbert space corresponding to the graph. If
this unitary evolution operator has an associated group of symmetries, then for
certain initial states the walk will be confined to a subspace of the original
Hilbert space. Symmetries of the original graph, given by its automorphism
group, can be inherited by the evolution operator. We show that a quantum walk
confined to the subspace corresponding to this symmetry group can be seen as a
different quantum walk on a smaller quotient graph. We give an explicit
construction of the quotient graph for any subgroup of the automorphism group
and illustrate it with examples. The automorphisms of the quotient graph which
are inherited from the original graph are the original automorphism group
modulo the subgroup used to construct it. We then analyze the behavior of
hitting times on quotient graphs. Hitting time is the average time it takes a
walk to reach a given final vertex from a given initial vertex. It has been
shown in earlier work [Phys. Rev. A {\bf 74}, 042334 (2006)] that the hitting
time can be infinite. We give a condition which determines whether the quotient
graph has infinite hitting times given that they exist in the original graph.
We apply this condition for the examples discussed and determine which quotient
graphs have infinite hitting times. All known examples of quantum walks with
fast hitting times correspond to systems with quotient graphs much smaller than
the original graph; we conjecture that the existence of a small quotient graph
with finite hitting times is necessary for a walk to exhibit a quantum
speed-up.Comment: 18 pages, 7 figures in EPS forma
Displacement energy of unit disk cotangent bundles
We give an upper bound of a Hamiltonian displacement energy of a unit disk
cotangent bundle in a cotangent bundle , when the base manifold
is an open Riemannian manifold. Our main result is that the displacement
energy is not greater than , where is the inner radius of ,
and is a dimensional constant. As an immediate application, we study
symplectic embedding problems of unit disk cotangent bundles. Moreover,
combined with results in symplectic geometry, our main result shows the
existence of short periodic billiard trajectories and short geodesic loops.Comment: Title slightly changed. Close to the version published online in Math
Zei
State Sum Models and Simplicial Cohomology
We study a class of subdivision invariant lattice models based on the gauge
group , with particular emphasis on the four dimensional example. This
model is based upon the assignment of field variables to both the - and
-dimensional simplices of the simplicial complex. The property of
subdivision invariance is achieved when the coupling parameter is quantized and
the field configurations are restricted to satisfy a type of mod- flatness
condition. By explicit computation of the partition function for the manifold
, we establish that the theory has a quantum Hilbert space
which differs from the classical one.Comment: 28 pages, Latex, ITFA-94-13, (Expanded version with two new sections
Quantum Fourier transform, Heisenberg groups and quasiprobability distributions
This paper aims to explore the inherent connection among Heisenberg groups,
quantum Fourier transform and (quasiprobability) distribution functions.
Distribution functions for continuous and finite quantum systems are examined
first as a semiclassical approach to quantum probability distribution. This
leads to studying certain functionals of a pair of "conjugate" observables,
connected via the quantum Fourier transform. The Heisenberg groups emerge
naturally from this study and we take a rapid look at their representations.
The quantum Fourier transform appears as the intertwining operator of two
equivalent representation arising out of an automorphism of the group.
Distribution functions correspond to certain distinguished sets in the group
algebra. The marginal properties of a particular class of distribution
functions (Wigner distributions) arise from a class of automorphisms of the
group algebra of the Heisenberg group. We then study the reconstruction of
Wigner function from the marginal distributions via inverse Radon transform
giving explicit formulas. We consider applications of our approach to quantum
information processing and quantum process tomography.Comment: 39 page
Asymptotic Behavior of Ext functors for modules of finite complete intersection dimension
Let be a local ring, and let and be finitely generated
-modules such that has finite complete intersection dimension. In this
paper we define and study, under certain conditions, a pairing using the
modules \Ext_R^i(M,N) which generalizes Buchweitz's notion of the Herbrand
diference. We exploit this pairing to examine the number of consecutive
vanishing of \Ext_R^i(M,N) needed to ensure that \Ext_R^i(M,N)=0 for all
. Our results recover and improve on most of the known bounds in the
literature, especially when has dimension at most two
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