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

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

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 $E(t)$ generated by a laser system \textbf{S} operated in an arbitrary regime can be perfectly absorbed by a CPA device $\bf{S'}$ 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.

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

Optical lattices with exceptional points in the continuum

The spectral, dynamical and topological properties of physical systems described by non-Hermitian (including $\mathcal{PT}$-symmetric) Hamiltonians are deeply modified by the appearance of exceptional points and spectral singularities. Here we show that exceptional points in the continuum can arise in non-Hermitian (yet admitting and entirely real-valued energy spectrum) optical lattices with engineered defects. At an exceptional point, the lattice sustains a bound state with an energy embedded in the spectrum of scattered states, similar to the von-Neumann Wigner bound states in the continuum of Hermitian lattices. However, the dynamical and scattering properties of the bound state at an exceptional point are deeply different from those of ordinary von-Neumann Wigner bound states in an Hermitian system. In particular, the bound state in the continuum at an exceptional point is an unstable state that can secularly grow by an infinitesimal perturbation. Such properties are discussed in details for transport of discretized light in a $\mathcal{PT}$-symmetric array of coupled optical waveguides, which could provide an experimentally accessible system to observe exceptional points in the continuum.Comment: 11 pages, 4 figures, slightly revised revision (corrected misprints in caption of Figs.2 and 4 from published version

Klein tunneling of two correlated bosons

Reflection of two strongly interacting bosons with long-rage interaction hopping on a one-dimensional lattice scattered off by a potential step is theoretically investigated in the framework of the extended Hubbard model. The analysis shows that, in the presence of unbalanced on-site and nearest-neighbor site interaction, two strongly correlated bosons forming a bound particle state can penetrate a high barrier, despite the single particle can not. Such a phenomenon is analogous to one-dimensional Klein tunneling of a relativistic massive Dirac particle across a potential step.Comment: 10 pages; Spring select paper; highlighted in: Science Daily, 29 May 2013 and in phys.org May 29, 201

Transparency at the interface between two isospectral crystals

Reflection at an interface separating two different media is a rather universal phenomenon which arises because of wave mismatching at the interface. By means of supersymmetric quantum mechanics methods, it is shown that a fully transparent interface can be realized, connecting two isospectral but different one-dimensional crystals. An example of reflectionless interface is presented for the sinusoidal (Mathieu) crystal connected to a non-sinusoidal potential by a transparent domain wall.Comment: 4 figures, to appear in EP

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 $\hat{H}_0$, induced by a time-dependent non-Hermitian interaction $f(t) \hat{P}$. 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 $f(t)$ 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 $\hat{H}_0$ and $\hat{P}$. 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