Darboux transformations for a twisted derivation and quasideterminant solutions to the super KdV equation

This paper is concerned with a generalized type of Darboux transformations defined in terms of a twisted derivation $D$ satisfying $D(AB)=D(A)+\sigma(A)B$ where $\sigma$ is a homomorphism. Such twisted derivations include regular derivations, difference and $q$-difference operators and superderivatives as special cases. Remarkably, the formulae for the iteration of Darboux transformations are identical with those in the standard case of a regular derivation and are expressed in terms of quasideterminants. As an example, we revisit the Darboux transformations for the Manin-Radul super KdV equation, studied in Q.P. Liu and M. Ma\~nas, Physics Letters B \textbf{396} 133--140, (1997). The new approach we take enables us to derive a unified expression for solution formulae in terms of quasideterminants, covering all cases at once, rather than using several subcases. Then, by using a known relationship between quasideterminants and superdeterminants, we obtain expressions for these solutions as ratios of superdeterminants. This coincides with the results of Liu and Ma\~nas in all the cases they considered but also deals with the one subcase in which they did not obtain such an expression. Finally, we obtain another type of quasideterminant solutions to the Main-Radul super KdV equation constructed from its binary Darboux transformations. These can also be expressed as ratios of superdeterminants and are a substantial generalization of the solutions constructed using binary Darboux transformations in earlier work on this topic

Dissipative Binding of Lattice Bosons through Distance-Selective Pair Loss

We show that in a gas of ultra cold atoms distance selective two-body loss can be engineered via the resonant laser excitation of atom pairs to interacting electronic states. In an optical lattice this leads to a dissipative Master equation dynamics with Lindblad jump operators that annihilate atom pairs with a specific interparticle distance. In conjunction with coherent hopping between lattice sites this unusual dissipation mechanism leads to the formation of coherent long-lived complexes that can even exhibit an internal level structure which is strongly coupled to their external motion. We analyze this counterintuitive phenomenon in detail in a system of hard-core bosons. While current research has established that dissipation in general can lead to the emergence of coherent features in many-body systems our work shows that strong non-local dissipation can effectuate a binding mechanism for particles

From Coulomb blockade to the Kondo regime in a Rashba dot

We investigate the electronic transport in a quantum wire with localized Rashba interaction. The Rashba field forms quasi-bound states which couple to the continuum states with an opposite spin direction. The presence of this Rashba dot causes Fano-like antiresonances and dips in the wire's linear conductance. The Fano lineshape arises from the interference between the direct transmission channel along the wire and the hopping through the Rashba dot. Due to the confinement, we predict the observation of large charging energies in the local Rashba region which lead to Coulomb-blockade effects in the transport properties of the wire. Importantly, the Kondo regime can be achieved with a proper tuning of the Rashba interaction, giving rise to an oscillating linear conductance for a fixed occupation of the Rashba dot.Comment: 6 pages, 3 figures; presentation improved, discussions extended. Published versio

An improved single particle potential for transport model simulations of nuclear reactions induced by rare isotope beams

Taking into account more accurately the isospin dependence of nucleon-nucleon interactions in the in-medium many-body force term of the Gogny effective interaction, new expressions for the single nucleon potential and the symmetry energy are derived. Effects of both the spin(isospin) and the density dependence of nuclear effective interactions on the symmetry potential and the symmetry energy are examined. It is shown that they both play a crucial role in determining the symmetry potential and the symmetry energy at supra-saturation densities. The improved single nucleon potential will be useful for simulating more accurately nuclear reactions induced by rare isotope beams within transport models.Comment: 6 pages including 6 figures

An adaptive mutation operator for particle swarm optimization

Copyright @ 2008 MICParticle swarm optimization (PSO) is an effcient tool for optimization and search problems. However, it is easy to betrapped into local optima due to its in-formation sharing mechanism. Many research works have shown that mutation operators can help PSO prevent prema- ture convergence. In this paper, several mutation operators that are based on the global best particle are investigated and compared for PSO. An adaptive mutation operator is designed. Experimental results show that these mutation operators can greatly enhance the performance of PSO. The adaptive mutation operator shows great advantages over non-adaptive mutation operators on a set of benchmark test problems.This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/1

Dirichlet Boundary State in Linear Dilaton Background

Dirichlet-branes have emerged as important objects in studying nonperturbative string theory. It is important to generalize these objects to more general backgrounds other than the usual flat background. The simplest case is the linear dilaton condensate. The usual Dirichlet boundary condition violates conformal invariance in such a background. We show that by switching on a certain boundary interaction, conformal invariance is restored. An immediate application of this result is to two dimensional string theory.Comment: 6 pages, harvmac, some remarks are modified and one reference is added, formulas remain the sam

From Heisenberg matrix mechanics to EBK quantization: theory and first applications

Despite the seminal connection between classical multiply-periodic motion and Heisenberg matrix mechanics and the massive amount of work done on the associated problem of semiclassical (EBK) quantization of bound states, we show that there are, nevertheless, a number of previously unexploited aspects of this relationship that bear on the quantum-classical correspondence. In particular, we emphasize a quantum variational principle that implies the classical variational principle for invariant tori. We also expose the more indirect connection between commutation relations and quantization of action variables. With the help of several standard models with one or two degrees of freedom, we then illustrate how the methods of Heisenberg matrix mechanics described in this paper may be used to obtain quantum solutions with a modest increase in effort compared to semiclassical calculations. We also describe and apply a method for obtaining leading quantum corrections to EBK results. Finally, we suggest several new or modified applications of EBK quantization.Comment: 37 pages including 3 poscript figures, submitted to Phys. Rev.