We address the existence and stability of spatial localized modes supported by a parity-time-symmetric complex potential in the presence of power-law nonlinearity. The analytical expressions of the localized modes, which are Gaussian in nature, are obtained in both (1+1) and (2+1) dimensions. A linear stability analysis corroborated by the direct numerical simulations reveals that these analytical localized modes can propagate stably for a wide range of the potential parameters and for various order nonlinearities. Some dynamical characteristics of these solutions, such as the power and the transverse power-flow density, are also examined.

http://arxiv.org/abs/1404.7322
Quantum Physics (quant-ph); Pattern Formation and Solitons (nlin.PS); Exactly Solvable and Integrable Systems (nlin.SI)

We use super-fermion representation of quantum kinetic equation to develop nonequilibrium perturbation theory for inelastic electron current through quantum dot. We derive Lindblad type kinetic equation for an embedded quantum dot (i.e. a quantum dot connected to Lindblad dissipators through a buffer zone). The kinetic equation is converted to non-Hermitian field theory in Liouville-Fock space. The general nonequilibrium many-body perturbation theory is developed and applied to the quantum dot with electron-vibron and electron-electron interactions. Our perturbation theory becomes equivalent to Keldysh nonequilibrium Green’s functions perturbative treatment provided that the buffer zone is large enough to alleviate the problems associated with approximations of the Lindblad kinetic equation.

http://arxiv.org/abs/1201.1230
Mesoscale and Nanoscale Physics (cond-mat.mes-hall)