2,004 research outputs found
Collective and relative variables for a classical Klein-Gordon field
In this paper a set of canonical collective variables is defined for a
classical Klein-Gordon field and the problem of the definition of a set of
canonical relative variables is discussed. This last point is approached by
means of a harmonic analysis is momentum space. This analysis shows that the
relative variables can be defined if certain conditions are fulfilled by the
field configurations. These conditions are expressed by the vanishing of a set
of conserved quantities, referred to as supertranslations since as canonical
observables they generate a set of canonical transformations whose algebra is
the same as that which arises in the study of the asymptotic behaviour of the
metric of an isolated system in General Relativity.Comment: 47 pages, no figur
Coherent perfect absorbers for transient, periodic or chaotic optical fields: time-reversed lasers beyond threshold
Recent works [Y.D. Chong {\it et al.}, Phys. Rev. Lett. {\bf 105}, 053901
(2010); W. Wan {\it et al.}, Science {\bf 331}, 889 (2011)] have shown that the
time-reversed process of lasing at threshold realizes a coherent perfect
absorber (CPA). In a CPA, a lossy medium in an optical cavity with a specific
degree of dissipation, equal in modulus to the gain of the lasing medium, can
perfectly absorb coherent optical waves at discrete frequencies that are the
time-reversed counterpart of the lasing modes. Here the concepts of
time-reversal of lasing and CPA are extended for optical radiation emitted by a
laser operated in an arbitrary (and generally highly-nonlinear) regime, i.e.
for transient, chaotic or periodic coherent optical fields. We prove that any
electromagnetic signal generated by a laser system \textbf{S} operated
in an arbitrary regime can be perfectly absorbed by a CPA device
which is simply realized by placing inside \textbf{S} a broadband linear
absorber (attenuator) of appropriate transmittance. As examples, we discuss CPA
devices that perfectly absorb a chaotic laser signal and a frequency-modulated
optical wave.Comment: 9 pages, 3 figure; to appear in Phys. Rev.
Absence of Floquet scattering in oscillating non-Hermitian potential wells
Scattering of a quantum particle from an oscillating barrier or well does not
generally conserve the particle energy owing to energy exchange with the photon
field, and an incoming particle-free state is scattered into a set of outgoing
(transmitted and reflected) free states according to Floquet scattering theory.
Here we introduce two families of oscillating non-Hermitian potential wells in
which Floquet scattering is fully suppressed for any energy of the incident
particle. The scattering-free oscillating potentials are synthesized by
application of the Darboux transformation to the time-dependent Schr\"{o}dinger
equation. For one of the two families of scattering-free potentials, the
oscillating potential turns out to be fully invisible.Comment: 5 figure
Low-energy doublons in the ac-driven two-species Hubbard model
The hopping dynamics of two fermionic species with different effective masses
in the one-dimensional Hubbard model driven by an external field is
theoretically investigated. A multiple-time-scale asymptotic analysis of the
driven asymmetric Hubbard model shows that a high-frequency bichromatic
external field can sustain a new kind of low-energy particle bound state
(doublon), in which two fermions of different species occupy nearest neighbor
sites and co-tunnel along the lattice. The predictions of the asymptotic
analysis are confirmed by direct numerical simulations of the two-particle
Hubbard Hamiltonian.Comment: 4 figure
Invisible defects in complex crystals
We show that invisible localized defects, i.e. defects that can not be
detected by an outside observer, can be realized in a crystal with an
engineered imaginary potential at the defect site. The invisible defects are
synthesized by means of supersymmetric (Darboux) transformations of an ordinary
crystal using band-edge wave functions to construct the superpotential. The
complex crystal has an entire real-valued energy spectrum and Bragg scattering
is not influenced by the defects. An example of complex crystal synthesis is
presented for the Mathieu potential
Non-Hermitian time-dependent perturbation theory: asymmetric transitions and transitionless interactions
The ordinary time-dependent perturbation theory of quantum mechanics, that
describes the interaction of a stationary system with a time-dependent
perturbation, predicts that the transition probabilities induced by the
perturbation are symmetric with respect to the initial an final states. Here we
extend time-dependent perturbation theory into the non-Hermitian realm and
consider the transitions in a stationary Hermitian system, described by a
self-adjoint Hamiltonian , induced by a time-dependent non-Hermitian
interaction . In the weak interaction (perturbative) limit, the
transition probabilities generally turn out to be {\it asymmetric} for exchange
of initial and final states. In particular, for a temporal shape of the
perturbation with one-sided Fourier spectrum, i.e. with only positive (or
negative) frequency components, transitions are fully unidirectional, a result
that holds even in the strong interaction regime. Interestingly, we show that
non-Hermitian perturbations can be tailored to be transitionless, i.e. the
perturbation leaves the system unchanged as if the interaction had not occurred
at all, regardless the form of and . As an application of
the results, we discuss asymmetric (chiral) behavior of dynamical encircling of
an exceptional point in a two- and three-level system.Comment: final version, to appear in Annals of Physic
Workshop on Pristine Highlands Rocks and the early History of the Moon
Oxide composition of the Moon, evidence for an initially totally molten Moon, geophysical contraints on lunar composition, random sampling of a layered intrusion, lunar highland rocks, early evolution of the Moon, mineralogy and petrology of the pristine rocks, relationship of the pristine nonmore rocks to the highlands soils and breccias, ferroan anorthositic norite, early lunar igneous history, compositional variation in ferroan anosthosites, a lunar magma ocean, deposits of lunar pristine rocks, lunar and planetary compositions and early fractionation in the solar nebula, Moon composition models, petrogenesis in a Moon with a chondritic refractory lithophile pattern, a terrestrial analog of lunar ilmenite bearing camulates, and the lunar magma ocean are summarized
Optical analogue of population trapping in the continuum: classical and quantum interference effects
A quantum theory of light propagation in two optical channel waveguides
tunnelling-coupled to a common continuum of modes (such as those of a slab
waveguide) is presented, and classical and quantum interference effects are
investigated. For classical light, the photonic system realizes an optical
analogue of coherent population trapping in the continuum encountered in atomic
physics, where destructive interference between different light leakage
channels leads to the appearance of a trapped state embedded in the continuum.
For nonclassical light, two-photon interference effects are predicted, such as
the tendency of photon pairs to bunch when decaying into the continuum.Comment: 12 pages, 2 figure
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