1,938 research outputs found
Truth, Beauty, Freedom, and Money: Technology-Based Art and the Dynamics of Sustainability
Proposes innovative new approaches and models for art and technology institutions, and provides details for an "Arts Lab," a unique hybrid art center and research lab
Perturbative Analysis of Spectral Singularities and Their Optical Realizations
We develop a perturbative method of computing spectral singularities of a
Schreodinger operator defined by a general complex potential that vanishes
outside a closed interval. These can be realized as zero-width resonances in
optical gain media and correspond to a lasing effect that occurs at the
threshold gain. Their time-reversed copies yield coherent perfect absorption of
light that is also known as an antilaser. We use our general results to
establish the exactness of the n-th order perturbation theory for an arbitrary
complex potential consisting of n delta-functions, obtain an exact expression
for the transfer matrix of these potentials, and examine spectral singularities
of complex barrier potentials of arbitrary shape. In the context of optical
spectral singularities, these correspond to inhomogeneous gain media.Comment: 13 pages, 2 figures, one table, a reference added, typos correcte
Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies
Spectral singularities are spectral points that spoil the completeness of the
eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify
spectral singularities of complex scattering potentials with the real energies
at which the reflection and transmission coefficients tend to infinity, i.e.,
they correspond to resonances having a zero width. We show that a wave guide
modeled using such a potential operates like a resonator at the frequencies of
spectral singularities. As a concrete example, we explore the spectral
singularities of an imaginary PT-symmetric barrier potential and demonstrate
the above resonance phenomenon for a certain electromagnetic wave guide.Comment: Published versio
Is the CPT-norm always positive?
We give an explicit example of an exactly solvable PT-symmetric Hamiltonian
with the unbroken PT symmetry which has one eigenfunction with the zero
PT-norm. The set of its eigenfunctions is not complete in corresponding Hilbert
space and it is non-diagonalizable. In the case of a regular Sturm-Liouville
problem any diagonalizable PT-symmetric Hamiltonian with the unbroken PT
symmetry has a complete set of positive CPT-normalazable eigenfunctions. For
non-diagonalizable
Hamiltonians a complete set of CPT-normalazable functions is possible but the
functions belonging to the root subspace corresponding to multiple zeros of the
characteristic determinant are not eigenfunctions of the Hamiltonian anymore
Optical realization of relativistic non-Hermitian quantum mechanics
Light propagation in distributed feedback optical structures with gain/loss
regions is shown to provide an accessible laboratory tool to visualize in
optics the spectral properties of the one-dimensional Dirac equation with
non-Hermitian interactions. Spectral singularities and PT symmetry breaking of
the Dirac Hamiltonian are shown to correspond to simple observable physical
quantities and related to well-known physical phenomena like resonance
narrowing and laser oscillation.Comment: 4 page
Elastic–Plastic Transition in Iron: Structural and Thermodynamic Features
The structural and thermodynamic features of the elastic–plastic transition in armco iron and its plastic deformation are studied. Energy storage in iron is shown to have a nonlinear character and be accompanied by wavelike heat dissipation. To describe the energy balance in the plastically deformed metal, a theoretical model is proposed based on a statistical description of the evolution of an ensemble of typical mesodefects (microshears). Moreover, a procedure is developed to experimentally determine the dependence of the potential of the medium on the mesodefect density using infrared scanning data.This work was supported in part by the Russian Foundation for Basic Research, project nos. 05-08- 33652, 07-08-96001, and 07-01-0-96004
Unidirectional Invisibility and PT-Symmetry with Graphene
We investigate the reflectionlessness and invisibility properties in the
transverse electric (TE) mode solution of a linear homogeneous optical system
which comprises the -symmetric structures covered by graphene
sheets. We derive analytic expressions, indicate roles of each parameter
governing optical system with graphene and justify that optimal conditions of
these parameters give rise to broadband and wide angle invisibility. Presence
of graphene turns out to shift the invisible wavelength range and to reduce the
required gain amount considerably, based on its chemical potential and
temperature. We substantiate that our results yield broadband reflectionless
and invisible configurations for realistic materials of small refractive
indices, usually around , and of small thickness sizes with graphene
sheets of rather small temperatures and chemical potentials. Finally, we
demonstrate that pure -symmetric graphene yields invisibility at
small temperatures and chemical potentials.Comment: 20 pages, 1 table 17 figure
Scaling Invariance of Fatigue Crack Growth in Gigacycle Loading Regime
The role of the collective behavior of defect ensembles at the crack tip and the laws of fatigue crack propagation in R4 high strength steel have been studied under conditions of symmetric tension–compression gigacycle loading at 20 kHz. At every stage of the fatigue crack growth, replicas from the sample side surface were taken and studied by the method of three dimensional relief profilometry (using NewView interferometer profilometer) so as to study the scaling invariant laws of defect related structure evolution.This study was supported in part by the Russian Foundation for Basic Research, Project nos. 08-01-00699, 09-01-92005-NNS_a, and 09-01-92441-KE-
Relativistic Harmonic Oscillator Revisited
The familiar Fock space commonly used to describe the relativistic harmonic
oscillator, for example as part of string theory, is insufficient to describe
all the states of the relativistic oscillator. We find that there are three
different vacua leading to three disconnected Fock sectors, all constructed
with the same creation-annihilation operators. These have different spacetime
geometric properties as well as different algebraic symmetry properties or
different quantum numbers. Two of these Fock spaces include negative norm
ghosts (as in string theory) while the third one is completely free of ghosts.
We discuss a gauge symmetry in a worldline theory approach that supplies
appropriate constraints to remove all the ghosts from all Fock sectors of the
single oscillator. The resulting ghost free quantum spectrum in d+1 dimensions
is then classified in unitary representations of the Lorentz group SO(d,1).
Moreover all states of the single oscillator put together make up a single
infinite dimensional unitary representation of a hidden global symmetry
SU(d,1), whose Casimir eigenvalues are computed. Possible applications of these
new results in string theory and other areas of physics and mathematics are
briefly mentioned.Comment: 41 pages, 2 figures, LaTe
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