Optical transformation from chirplet to fractional Fourier transformation kernel

We find a new integration transformation which can convert a chirplet function to fractional Fourier transformation kernel, this new transformation is invertible and obeys Parseval theorem. Under this transformation a new relationship between a phase space function and its Weyl-Wigner quantum correspondence operator is revealed.Comment: 3 pages, no figur

Introduction to Quantum Thermodynamics: History and Prospects

Quantum Thermodynamics is a continuous dialogue between two independent theories: Thermodynamics and Quantum Mechanics. Whenever the two theories addressed the same phenomena new insight has emerged. We follow the dialogue from equilibrium Quantum Thermodynamics and the notion of entropy and entropy inequalities which are the base of the II-law. Dynamical considerations lead to non-equilibrium thermodynamics of quantum Open Systems. The central part played by completely positive maps is discussed leading to the Gorini-Kossakowski-Lindblad-Sudarshan GKLS equation. We address the connection to thermodynamics through the system-bath weak-coupling-limit WCL leading to dynamical versions of the I-law. The dialogue has developed through the analysis of quantum engines and refrigerators. Reciprocating and continuous engines are discussed. The autonomous quantum absorption refrigerator is employed to illustrate the III-law. Finally, we describe some open questions and perspectives

Partial Hamiltonian reduction of relativistic extended objects in light-cone gauge

The elimination of the non-transversal field in the standard light-cone formulation of higher-dimensional extended objects is formulated as a Hamiltonian reduction.Comment: 11 page

Conformal symmetry transformations and nonlinear Maxwell equations

We make use of the conformal compactification of Minkowski spacetime $M^{\#}$ to explore a way of describing general, nonlinear Maxwell fields with conformal symmetry. We distinguish the inverse Minkowski spacetime $[M^{\#}]^{-1}$ obtained via conformal inversion, so as to discuss a doubled compactified spacetime on which Maxwell fields may be defined. Identifying $M^{\#}$ with the projective light cone in $(4+2)$-dimensional spacetime, we write two independent conformal-invariant functionals of the $6$-dimensional Maxwellian field strength tensors -- one bilinear, the other trilinear in the field strengths -- which are to enter general nonlinear constitutive equations. We also make some remarks regarding the dimensional reduction procedure as we consider its generalization from linear to general nonlinear theories.Comment: 12 pages, Based on a talk by the first author at the International Conference in Mathematics in honor of Prof. M. Norbert Hounkonnou (October 29-30, 2016, Cotonou, Benin). To be published in the Proceedings, Springer 201

On Some Open Problems in Many-Electron Theory

Mel Levy and Elliott Lieb are two of the most prominent researchers who have dedicated their efforts to the investigation of fundamental questions in many-electron theory. Their results have not only revolutionized the theoretical approach of the field, but, directly or indirectly, allowed for a quantum jump in the computational treatment of realistic systems as well. For this reason, at the conclusion of our book where the subject is treated across different disciplines, we have asked Mel Levy and Elliott Lieb to provide us with some open problems, which they believe will be a worth challenge for the future also in the perspective of a synergy among the various disciplines.Comment: "Epilogue" chapter in "Many-Electron Approaches in Physics, Chemistry and Mathematics: A Multidisciplinary View", Volker Bach and Luigi Delle Site Eds. pages 411-416; Book Series: Mathematical Physics Studies, Springer International Publishing Switzerland, 2014. The original title has been modified in order to clarify the subject of the chapter out of the context of the boo

Optical Absorption Characteristics of Silicon Nanowires for Photovoltaic Applications

Solar cells have generated a lot of interest as a potential source of clean renewable energy for the future. However a big bottleneck in wide scale deployment of these energy sources remain the low efficiency of these conversion devices. Recently the use of nanostructures and the strategy of quantum confinement have been as a general approach towards better charge carrier generation and capture. In this article we have presented calculations on the optical characteristics of nanowires made out of Silicon. Our calculations show these nanowires form excellent optoelectronic materials and may yield efficient photovoltaic devices

de Sitter symmetry of Neveu-Schwarz spinors

We study the relations between Dirac fields living on the 2-dimensional Lorentzian cylinder and the ones living on the double-covering of the 2-dimensional de Sitter manifold, here identified as a certain coset space of the group $SL(2,R)$. We show that there is an extended notion of de Sitter covariance only for Dirac fields having the Neveu-Schwarz anti-periodicity and construct the relevant cocycle. Finally, we show that the de Sitter symmetry is naturally inherited by the Neveu-Schwarz massless Dirac field on the cylinder.Comment: 24 page

Symmetries of Snyder--de Sitter space and relativistic particle dynamics

We study the deformed conformal-Poincare symmetries consistent with the Snyder--de Sitter space. A relativistic particle model invariant under these deformed symmetries is given. This model is used to provide a gauge independent derivation of the Snyder--de Sitter algebra. Our results are valid in the leading order in the parameters appearing in the model.Comment: 12 pages, LaTeX, version appearing in JHEP, minor changes to match published versio

Chiral zero-mode for abelian BPS dipoles

We present an exact normalisable zero-energy chiral fermion solution for abelian BPS dipoles. For a single dipole, this solution is contained within the high temperature limit of the SU(2) caloron with non-trivial holonomy.Comment: 9 pages, 1 figure (in 2 parts), presented at the workshop on "Confinement, Topology, and other Non-Perturbative Aspects of QCD", 21-27 Jan. 2002, Stara Lesna, Slovaki

Positive tension 3-branes in an AdS5AdS_{5} bulk

In this work, we review and extend the so-called consistency conditions for the existence of a braneworld scenario in arbitrary dimensions in the Brans-Dicke (BD) gravitational theory. After that, we consider the particular case of a five-dimensional scenario which seems to have phenomenological interesting implications. We show that, in the BD framework, it is possible to achieve necessary conditions pointing to the possibility of accommodating branes with positive tensions in an AdS bulk by the presence of the additional BD scalar field, avoiding in this way the necessity of including unstable objects in the compactification scheme. Furthermore, in the context of time variable brane tension, it is shown that the brane tension may change its sign, following the bulk cosmological constant sign.Comment: 15 pages, new version to appear in JHE