Conformal Mapping and Bound States in Bent Waveguides

Is it possible to trap a quantum particle in an open geometry? In this work we deal with the boundary value problem of the stationary Schroedinger (or Helmholtz) equation within a waveguide with straight segments and a rectangular bending. The problem can be reduced to a one dimensional matrix Schroedinger equation using two descriptions: oblique modes and conformal coordinates. We use a corner-corrected WKB formalism to find the energies of the one dimensional problem. It is shown that the presence of bound states is an effect due to the boundary alone, with no classical counterpart for this geometry. The conformal description proves to be simpler, as the coupling of transversal modes is not essential in this case.Comment: 16 pages, 10 figures. To appear in the Proceedings of the Symposium "Symmetries in Nature, in memoriam Marcos Moshinsky

Efecte de l'aplicació d'ultrasons en l'enfosquiment enzimàtic de la patata (Solanum Tuberosum L.)

Different chemicals and physicals processes can be used to satisfy the consumer and obtain a high organoleptic quality and healthy safe food. Among the new physical processes we find pulsating electric fields, high hydrostatic pressures or ultrasounds.Per satisfer al consumidor i obtenir aliments amb una bona qualitat organolèptica i sanitàriament segurs es poden utilitzar diferents processos químics i físics. Entre els nous processos físics trobem els tractaments amb camps elèctrics polsants (CEP), les altes pressions hidrostàtiques o els ultrasons.Para satisfacer al consumidor y obtener alimentos con una buena calidad organoléptica y sanitariamente seguros se pueden utilizar diferentes procesos químicos y físicos. Entre los nuevos procesos físicos encontramos los tratamientos con campos eléctricos pulsantes, las altas presiones hidrostáticas o los ultrasonidos

Inverse problems in quantum graphs and accidental degeneracy

A general treatment of the spectral problem of quantum graphs and tight-binding models in finite Hilbert spaces is given. The direct spectral problem and the inverse spectral problem are written in terms of simple algebraic equations containing information on the topology of a quantum graph. The inverse problem is shown to be combinatorial, and some low dimensional examples are explicitly solved. For a {\it window\ }graph, a commutator and anticommutator algebra (superalgebra) is identified as the culprit behind accidental degeneracy in the form of triplets, where configurational symmetry {\it alone\ }fails to explain the result. For a M\"obius cycloacene graph, it is found that the accidental triplet cannot be explained with a superalgebra, but that the graph can be built unambiguously from the spectrum using combinatorial methods. These examples are compared with a more symmetric but less degenerate system, i.e. a {\it car wheel\ } graph which possesses neither triplets, nor superalgebra.Comment: 18 pages, 6 figure

Deregulations of RNA Pol II Subunits in Cancer

Deregulated transcription is a well-known characteristic of cancer cells, with differentially expressed genes being a common feature of several cancers. Often, deregulated transcription is a consequence of alterations in transcription factors (TFs), which play a crucial role in gene expression and can act as tumour suppressors or proto-oncogenes. In eukaryotic organisms, transcription is carried out by three distinct RNA polymerase complexes: Pol I, Pol II, and Pol III. Pol II, specifically, is responsible for transcribing messenger RNA (mRNA), the protein coding part of the genome, as well as long non-coding RNAs (lncRNAs). While there is considerable research on the impact of specific deregulated transcription factors in cancer development, there is a lack of studies focusing on defects within the RNA polymerase complexes and their subunits. This review aims to shed light in particular on the Pol II complex and highlight the deregulation of its subunits that have a significant impact on tumour development, prognosis, and survival. By providing a comprehensive overview of our current understanding of Pol II subunits in cancer, this review emphasizes the importance of further research in this area. It suggests that exploring these subunits’ deregulations could lead to the identification of valuable biomarkers and potential therapeutic targets, making it a topic of collective interest

Alternative Method for Determining the Feynman Propagator of a Non-Relativistic Quantum Mechanical Problem

A direct procedure for determining the propagator associated with a quantum mechanical problem was given by the Path Integration Procedure of Feynman. The Green function, which is the Fourier Transform with respect to the time variable of the propagator, can be derived later. In our approach, with the help of a Laplace transform, a direct way to get the energy dependent Green function is presented, and the propagator can be obtained later with an inverse Laplace transform. The method is illustrated through simple one dimensional examples and for time independent potentials, though it can be generalized to the derivation of more complicated propagators.Comment: This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ In v2 misprints are correcte

Two interacting atoms in a cavity: exact solutions, entanglement and decoherence

We address the problem of two interacting atoms of different species inside a cavity and find the explicit solutions of the corresponding eigenvalues and eigenfunctions using a new invariant. This model encompasses various commonly used models. By way of example we obtain closed expressions for concurrence and purity as a function of time for the case where the cavity is prepared in a number state. We discuss the behaviour of these quantities and and their relative behaviour in the concurrence-purity plane.Comment: 10 pages, 3 figure