4,210 research outputs found
Potential one-forms for hyperk\"ahler structures with torsion
It is shown that an HKT-space with closed parallel potential 1-form has
-symmetry. Every locally conformally hyperk\"ahler manifold
generates this type of geometry. The HKT-spaces with closed parallel potential
1-form arising in this way are characterized by their symmetries and an
inhomogeneous cubic condition on their torsion.Comment: 16 pages, Latex, no figure
Planar immersion lens with metasurfaces
The solid immersion lens is a powerful optical tool that allows light
entering material from air or vacuum to focus to a spot much smaller than the
free-space wavelength. Conventionally, however, they rely on semispherical
topographies and are non-planar and bulky, which limits their integration in
many applications. Recently, there has been considerable interest in using
planar structures, referred to as metasurfaces, to construct flat optical
components for manipulating light in unusual ways. Here, we propose and
demonstrate the concept of a planar immersion lens based on metasurfaces. The
resulting planar device, when placed near an interface between air and
dielectric material, can focus electromagnetic radiation incident from air to a
spot in material smaller than the free-space wavelength. As an experimental
demonstration, we fabricate an ultrathin and flexible microwave lens and
further show that it achieves wireless energy transfer in material mimicking
biological tissue
Polarization and frequency disentanglement of photons via stochastic polarization mode dispersion
We investigate the quantum decoherence of frequency and polarization
variables of photons via polarization mode dispersion in optical fibers. By
observing the analogy between the propagation equation of the field and the
Schr\"odinger equation, we develop a master equation under Markovian
approximation and analytically solve for the field density matrix. We identify
distinct decay behaviors for the polarization and frequency variables for
single-photon and two-photon states. For the single photon case, purity
functions indicate that complete decoherence for each variable is possible only
for infinite fiber length. For entangled two-photon states passing through
separate fibers, entanglement associated with each variable can be completely
destroyed after characteristic finite propagation distances. In particular, we
show that frequency disentanglement is independent of the initial polarization
status. For propagation of two photons in a common fiber, the evolution of a
polarization singlet state is addressed. We show that while complete
polarization disentanglement occurs at a finite propagation distance, frequency
entanglement could survive at any finite distance for gaussian states.Comment: 2 figure
Determining system Hamiltonian from eigenstate measurements without correlation functions
Local Hamiltonians arise naturally in physical systems. Despite its seemingly
`simple' local structure, exotic features such as nonlocal correlations and
topological orders exhibit in eigenstates of these systems. Previous studies
for recovering local Hamiltonians from measurements on an eigenstate
require information of nonlocal correlation functions. In this
work, we develop an algorithm to determine local Hamiltonians from only local
measurements on , by reformulating the task as an unconstrained
optimization problem of certain target function of Hamiltonian parameters, with
only polynomial number of parameters in terms of system size. We also develop a
machine learning-based-method to solve the first-order gradient used in the
algorithm. Our method is tested numerically for randomly generated local
Hamiltonians and returns promising reconstruction in the desired accuracy. Our
result shed light on the fundamental question on how a single eigenstate can
encode the full system Hamiltonian, indicating a somewhat surprising answer
that only local measurements are enough without additional assumptions, for
generic cases.Comment: 11 pages, 10 figure
Relation Between First Arrival Time and Permeability in Self-Affine Fractures with Areas in Contact
We demonstrate that the first arrival time in dispersive processes in
self-affine fractures are governed by the same length scale characterizing the
fractures as that which controls their permeability. In one-dimensional channel
flow this length scale is the aperture of the bottle neck, i.e., the region
having the smallest aperture. In two dimensions, the concept of a bottle neck
is generalized to that of a minimal path normal to the flow. The length scale
is then the average aperture along this path. There is a linear relationship
between the first arrival time and this length scale, even when there is strong
overlap between the fracture surfaces creating areas with zero permeability. We
express the first arrival time directly in terms of the permeability.Comment: EPL (2012)
- …