52 research outputs found
The band spectrum of periodic potentials with PT-symmetry
A real band condition is shown to exist for one dimensional periodic complex
non-hermitian potentials exhibiting PT-symmetry. We use an exactly solvable
ultralocal periodic potential to obtain the band structure and discuss some
spectral features of the model, specially those concerning the role of the
imaginary parameters of the couplings. Analytical results as well as some
numerical examples are provided.Comment: 14 pages, 19 included figures (13 coloured). Submitted to J. Phys.
Miura Transformation between two Non-Linear Equations in 2+1 dimensions
A Dispersive Wave Equation in 2+1 dimensions (2LDW) widely discussed by
different authors is shown to be nothing but the modified version of the
Generalized Dispersive Wave Equation (GLDW). Using Singularity Analysis and
techniques based upon the Painleve Property leading to the Double Singular
Manifold Expansion we shall find the Miura Transformation which converts the
2LDW Equation into the GLDW Equation. Through this Miura Transformation we
shall also present the Lax pair of the 2LDW Equation as well as some
interesting reductions to several already known integrable systems in 1+1
dimensions.Comment: 14 pages, latex. Journal of Mathematical Physics (to appear
An amplitude-phase (Ermakov-Lewis) approach for the Jackiw-Pi model of bilayer graphene
In the context of bilayer graphene we use the simple gauge model of Jackiw
and Pi to construct its numerical solutions in powers of the bias potential V
according to a general scheme due to Kravchenko. Next, using this numerical
solutions, we develop the Ermakov-Lewis approach for the same model. This leads
us to numerical calculations of the Lewis-Riesenfeld phases that could be of
forthcoming experimental interest for bilayer graphene. We also present a
generalization of the Ioffe-Korsch nonlinear Darboux transformationComment: FTC, 11 pp, 5 figure
Esquemes argumentatius i coneixement científic. Un estudi sobre la comprensió de la flotabilitat a diferents nivells educatius
Es presenta un estudi sobre les respostes escrites d’estudiants de diversos nivells educatius a una activitat presentada com una narrativa en forma de conte. L’anàlisi es basa en identificar arguments dels estudiants que són estudiats en base a teories d’argumentació. L’estudi dels elements dels arguments ens permet inferir sobre les concepcions científiques i alternatives dels estudiants i trobar esquemes o patrons argumentatius comuns. La comparació entre nivells educatius ens mostra que els tipus d’arguments no varien gaire entre nivells educatius però sí que es troben diferencies quant al tipus d’explicacions que poden ser animistes o que no tenir res a veure amb la física als nivells educatius més baixos
On the shape of spectra for non-self-adjoint periodic Schr\"odinger operators
The spectra of the Schr\"odinger operators with periodic potentials are
studied. When the potential is real and periodic, the spectrum consists of at
most countably many line segments (energy bands) on the real line, while when
the potential is complex and periodic, the spectrum consists of at most
countably many analytic arcs in the complex plane.
In some recent papers, such operators with complex -symmetric
periodic potentials are studied. In particular, the authors argued that some
energy bands would appear and disappear under perturbations. Here, we show that
appearance and disappearance of such energy bands imply existence of nonreal
spectra. This is a consequence of a more general result, describing the local
shape of the spectrum.Comment: 5 pages, 2 figure
Two-Dimensional Electron Gas in InGaAs/InAlAs Quantum Wells
We designed and performed low temperature DC transport characterization
studies on two-dimensional electron gases confined in lattice-matched
InGaAs/InAlAs quantum wells grown by
molecular beam epitaxy on InP substrates. The nearly constant mobility for
samples with the setback distance larger than 50nm and the similarity between
the quantum and transport life-time suggest that the main scattering mechanism
is due to short range scattering, such as alloy scattering, with a scattering
rate of 2.2 ps. We also obtain the Fermi level at the
InGaAs/InAlAs surface to be 0.36eV above
the conduction band, when fitting our experimental densities with a
Poisson-Schr\"odinger model.Comment: Accepted in Applied Physics Letter
The Chevreton Tensor and Einstein-Maxwell Spacetimes Conformal to Einstein Spaces
In this paper we characterize the source-free Einstein-Maxwell spacetimes
which have a trace-free Chevreton tensor. We show that this is equivalent to
the Chevreton tensor being of pure-radiation type and that it restricts the
spacetimes to Petrov types \textbf{N} or \textbf{O}. We prove that the trace of
the Chevreton tensor is related to the Bach tensor and use this to find all
Einstein-Maxwell spacetimes with a zero cosmological constant that have a
vanishing Bach tensor. Among these spacetimes we then look for those which are
conformal to Einstein spaces. We find that the electromagnetic field and the
Weyl tensor must be aligned, and in the case that the electromagnetic field is
null, the spacetime must be conformally Ricci-flat and all such solutions are
known. In the non-null case, since the general solution is not known on closed
form, we settle with giving the integrability conditions in the general case,
but we do give new explicit examples of Einstein-Maxwell spacetimes that are
conformal to Einstein spaces, and we also find examples where the vanishing of
the Bach tensor does not imply that the spacetime is conformal to a -space.
The non-aligned Einstein-Maxwell spacetimes with vanishing Bach tensor are
conformally -spaces, but none of them are conformal to Einstein spaces.Comment: 22 pages. Corrected equation (12
Spin dynamics in helical molecules with nonlinear interactions
It is widely admitted that the helical conformation of certain chiral molecules may induce a sizable spin selectivity observed in experiments. Spin selectivity arises as a result of the interplay between a helicity-induced spin-orbit coupling (SOC) and electric dipole fields in the molecule. From the theoretical point of view, different phenomena might affect the spin dynamics in helical molecules, such as quantum dephasing, dissipation and the role of metallic contacts. With a few exceptions, previous studies usually neglect the local deformation of the molecule about the carrier, but this assumption seems unrealistic to describe charge transport in molecular systems. We introduce an effective model describing the electron spin dynamics in a deformable helical molecule with weak SOC. We find that the electron-lattice interaction allows the formation of stable solitons such as bright solitons with well defined spin projection onto the molecule axis. We present a thorough study of these bright solitons and analyze their possible impact on the spin dynamics in deformable helical molecules
SU(1,1) symmetry of multimode squeezed states
We show that a class of multimode optical transformations that employ linear
optics plus two-mode squeezing can be expressed as SU(1,1) operators. These
operations are relevant to state-of-the-art continuous variable quantum
information experiments including quantum state sharing, quantum teleportation,
and multipartite entangled states. Using this SU(1,1) description of these
transformations, we obtain a new basis for such transformations that lies in a
useful representation of this group and lies outside the often-used restriction
to Gaussian states. We analyze this basis, show its application to a class of
transformations, and discuss its extension to more general quantum optical
networks
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