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

Bound States in Sharply Bent Waveguides: Analytical and Experimental Approach

Quantum wires and electromagnetic waveguides possess common features since their physics is described by the same wave equation. We exploit this analogy to investigate experimentally with microwave waveguides and theoretically with the help of an effective potential approach the occurrence of bound states in sharply bent quantum wires. In particular, we compute the bound states, study the features of the transition from a bound to an unbound state caused by the variation of the bending angle and determine the critical bending angles at which such a transition takes place. The predictions are confirmed by calculations based on a conventional numerical method as well as experimental measurements of the spectra and electric field intensity distributions of electromagnetic waveguides

Playing relativistic billiards beyond graphene

The possibility of using hexagonal structures in general and graphene in particular to emulate the Dirac equation is the basis of our considerations. We show that Dirac oscillators with or without restmass can be emulated by distorting a tight binding model on a hexagonal structure. In a quest to make a toy model for such relativistic equations we first show that a hexagonal lattice of attractive potential wells would be a good candidate. First we consider the corresponding one-dimensional model giving rise to a one-dimensional Dirac oscillator, and then construct explicitly the deformations needed in the two-dimensional case. Finally we discuss, how such a model can be implemented as an electromagnetic billiard using arrays of dielectric resonators between two conducting plates that ensure evanescent modes outside the resonators for transversal electric modes, and describe an appropriate experimental setup.Comment: 23 pages, 8 figures. Submitted to NJ

Bound states in open coupled asymmetrical waveguides and quantum wires

The behavior of bound states in asymmetric cross, T and L shaped configurations is considered. Because of the symmetries of the wavefunctions, the analysis can be reduced to the case of an electron localized at the intersection of two orthogonal crossed wires of different width. Numerical calculations show that the fundamental mode of this system remains bound for the widths that we have been able to study directly; moreover, the extrapolation of the results obtained for finite widths suggests that this state remains bound even when the width of one arm becomes infinitesimal. We provide a qualitative argument which explains this behavior and that can be generalized to the lowest energy states in each symmetry class. In the case of odd-odd states of the cross we find that the lowest mode is bounded when the width of the two arms is the same and stays bound up to a critical value of the ratio between the widths; in the case of the even-odd states we find that the lowest mode is unbound up to a critical value of the ratio between the widths. Our qualitative arguments suggest that the bound state survives as the width of the vertical arm becomes infinitesimal.Comment: 11 pages, 19 figures, 3 table

A longitudinal study of gene expression in first-episode schizophrenia; exploring relapse mechanisms by co-expression analysis in peripheral blood

Little is known about the pathophysiological mechanisms of relapse in first-episode schizophrenia, which limits the study of potential biomarkers. To explore relapse mechanisms and identify potential biomarkers for relapse prediction, we analyzed gene expression in peripheral blood in a cohort of first-episode schizophrenia patients with less than 5 years of evolution who had been evaluated over a 3-year follow-up period. A total of 91 participants of the 2EPs project formed the sample for baseline gene expression analysis. Of these, 67 provided biological samples at follow-up (36 after 3 years and 31 at relapse). Gene expression was assessed using the Clariom S Human Array. Weighted gene co-expression network analysis was applied to identify modules of co-expressed genes and to analyze their preservation after 3 years of follow-up or at relapse. Among the 25 modules identified, one module was semi-conserved at relapse (DarkTurquoise) and was enriched with risk genes for schizophrenia, showing a dysregulation of the TCF4 gene network in the module. Two modules were semi-conserved both at relapse and after 3 years of follow-up (DarkRed and DarkGrey) and were found to be biologically associated with protein modification and protein location processes. Higher expression of DarkRed genes was associated with higher risk of suffering a relapse and early appearance of relapse (p = 0.045). Our findings suggest that a dysregulation of the TCF4 network could be an important step in the biological process that leads to relapse and suggest that genes related to the ubiquitin proteosome system could be potential biomarkers of relapse. © 2021, The Author(s)

A longitudinal study of gene expression in first-episode schizophrenia; exploring relapse mechanisms by co-expression analysis in peripheral blood

Little is known about the pathophysiological mechanisms of relapse in first-episode schizophrenia, which limits the study of potential biomarkers. To explore relapse mechanisms and identify potential biomarkers for relapse prediction, we analyzed gene expression in peripheral blood in a cohort of first-episode schizophrenia patients with less than 5 years of evolution who had been evaluated over a 3-year follow-up period. A total of 91 participants of the 2EPs project formed the sample for baseline gene expression analysis. Of these, 67 provided biological samples at follow-up (36 after 3 years and 31 at relapse). Gene expression was assessed using the Clariom S Human Array. Weighted gene co-expression network analysis was applied to identify modules of co-expressed genes and to analyze their preservation after 3 years of follow-up or at relapse. Among the 25 modules identified, one module was semi-conserved at relapse (DarkTurquoise) and was enriched with risk genes for schizophrenia, showing a dysregulation of the TCF4 gene network in the module. Two modules were semi-conserved both at relapse and after 3 years of follow-up (DarkRed and DarkGrey) and were found to be biologically associated with protein modification and protein location processes. Higher expression of DarkRed genes was associated with higher risk of suffering a relapse and early appearance of relapse (p = 0.045). Our findings suggest that a dysregulation of the TCF4 network could be an important step in the biological process that leads to relapse and suggest that genes related to the ubiquitin proteosome system could be potential biomarkers of relapse.This study was supported by the Carlos III Healthcare Institute, the Spanish Ministry of Science, Innovation and Universities, the European Regional Development Fund (ERDF/FEDER) (PI08/0208, PI11/00325, PI14/00612); Centro de Investigacion Biomedica en Red de Salud Mental (CIBERSAM); CERCA Program; Catalan Government, the Secretariat of Universities and Research of the Department of Enterprise and Knowledge (2017SGR1562 and 2017SGR1355); and Institut de Neurociencies, Universitat de Barcelona. The authors thank the Language Advisory Service at the University of Barcelona for manuscript revision. The authors also thank all subjects and their families for the time and effort spent on this study as well as Ana Meseguer for sample collection assistance