Control of the geometric phase and pseudo-spin dynamics on coupled Bose-Einstein condensates

We describe the behavior of two coupled Bose-Einstein condensates in time-dependent (TD) trap potentials and TD Rabi (or tunneling) frequency, using the two-mode approach. Starting from Bloch states, we succeed to get analytical solutions for the TD Schroedinger equation and present a detailed analysis of the relative and geometric phases acquired by the wave function of the condensates, as well as their population imbalance. We also establish a connection between the geometric phases and constants of motion which characterize the dynamic of the system. Besides analyzing the affects of temporality on condensates that differs by hyperfine degrees of freedom (internal Josephson effect), we also do present a brief discussion of a one specie condensate in a double-well potential (external Josephson effect).Comment: 1 tex file and 11 figures in pdf forma

Nonadiabatic coherent evolution of two-level systems under spontaneous decay

In this paper we extend current perspectives in engineering reservoirs by producing a time-dependent master equation leading to a nonstationary superposition equilibrium state that can be nonadiabatically controlled by the system-reservoir parameters. Working with an ion trapped inside a nonindeal cavity we first engineer effective Hamiltonians that couple the electronic states of the ion with the cavity mode. Subsequently, two classes of decoherence-free evolution of the superposition of the ground and decaying excited levels are achieved: those with time-dependent azimuthal or polar angle. As an application, we generalise the purpose of an earlier study [Phys. Rev. Lett. 96, 150403 (2006)], showing how to observe the geometric phases acquired by the protected nonstationary states even under a nonadiabatic evolution.Comment: 5 pages, no figure

Dynamical invariants and nonadiabatic geometric phases in open quantum systems

We introduce an operational framework to analyze non-adiabatic Abelian and non-Abelian, cyclic and non-cyclic, geometric phases in open quantum systems. In order to remove the adiabaticity condition, we generalize the theory of dynamical invariants to the context of open systems evolving under arbitrary convolutionless master equations. Geometric phases are then defined through the Jordan canonical form of the dynamical invariant associated with the super-operator that governs the master equation. As a by-product, we provide a sufficient condition for the robustness of the phase against a given decohering process. We illustrate our results by considering a two-level system in a Markovian interaction with the environment, where we show that the non-adiabatic geometric phase acquired by the system can be constructed in such a way that it is robust against both dephasing and spontaneous emission.Comment: 9 pages, 3 figures. v2: minor corrections and subsection IV.D added. Published versio

G\"odel Type Metrics in Three Dimensions

We show that the G{\" o}del type Metrics in three dimensions with arbitrary two dimensional background space satisfy the Einstein-perfect fluid field equations. There exists only one first order partial differential equation satisfied by the components of fluid's velocity vector field. We then show that the same metrics solve the field equations of the topologically massive gravity where the two dimensional background geometry is a space of constant negative Gaussian curvature. We discuss the possibility that the G{\" o}del Type Metrics to solve the Ricci and Cotton flow equations. When the vector field $u^{\mu}$ is a Killing vector field we finally show that the stationary G{\" o}del Type Metrics solve the field equations of the most possible gravitational field equations where the interaction lagrangian is an arbitrary function of the electromagnetic field and the curvature tensors.Comment: 17 page

Urethral advancement procedure in the treatment of primary distal hypospadias: a series of 20 cases

Introduction: Distal hypospadias is the most common genital anomaly, occurring in almost 65% of all hypospadias cases. Although there are several surgical techniques for the treatment of distal hypospadias, it is clear that none can be used to correct all forms of hypospadias. The aim of the study was to evaluate urethral advancement in the repair of primary distal penile hypospadias with regard to feasibility, complication rates and the final cosmetic outcome.Patients and methods: Between October 2014 and June 2015, the urethral mobilization technique was used in 20 patients who presented at the Pediatric Surgery Unit, Tanta University Hospital, with primary distal hypospadias. A submeatal crescent-like incision was performed a few millimeters proximal to the meatus with two vertical incisions from the lateral ends of the submeatal incisions. The urethra within the corpus spongiosum was dissected from the skin of the ventral surface and from the glans and corpora cavernosa for a distance of ~ 4 : 1. The urethra was advanced till the urethral meatus reached its normal position without any tension. Spongioplsty can be performed, and covering Buck’s or Dartos’ layers can be used. The follow-up was conducted on a weekly basis in the outpatient clinic in the first month, and then every month for 6 months.Results: The age of the patient at the time of operation ranged from 6 to 24 months, with a mean age of 10.5 months. The operative time ranged from 60 to 90 min, with a mean time of 73.5 min. Intraoperative urethral injury occurred only in one patient. In all patients, the catheter was removed immediately postoperatively except for one patient who had operative urethral injury. Deep wound infection was noticed in only one patient, followed by partial glanular disruption. Only one patient had urethrocutaneous fistula and two patients had meatal retraction.Conclusion: Urethral advancement can be used safely in the mobilization of the distal urethra with wide glanular dissection and wide lateral mobilization of glanular wings. However, it should be stressed that in the presence of hypoplastic distal urethra and/or persistent ventral curvature, another technique should be adopted. The majority of our patients had very good cosmetic results and minimal complication. However, the technique requires further studies with a larger number of patients and longer follow-up periods to draw more precise and final conclusions.Keywords: distal hypospidaus, primary, urethral advancemen

Black hole mass and angular momentum in topologically massive gravity

We extend the Abbott-Deser-Tekin approach to the computation of the Killing charge for a solution of topologically massive gravity (TMG) linearized around an arbitrary background. This is then applied to evaluate the mass and angular momentum of black hole solutions of TMG with non-constant curvature asymptotics. The resulting values, together with the appropriate black hole entropy, fit nicely into the first law of black hole thermodynamics.Comment: 20 pages, references added, version to appear in Classical and Quantum Gravit

Sums of hermitian squares and the BMV conjecture

Recently Lieb and Seiringer showed that the Bessis-Moussa-Villani conjecture from quantum physics can be restated in the following purely algebraic way: The sum of all words in two positive semidefinite matrices where the number of each of the two letters is fixed is always a matrix with nonnegative trace. We show that this statement holds if the words are of length at most 13. This has previously been known only up to length 7. In our proof, we establish a connection to sums of hermitian squares of polynomials in noncommuting variables and to semidefinite programming. As a by-product we obtain an example of a real polynomial in two noncommuting variables having nonnegative trace on all symmetric matrices of the same size, yet not being a sum of hermitian squares and commutators.Comment: 21 pages; minor changes; a companion Mathematica notebook is now available in the source fil