The 1/N-expansion, quantum-classical correspondence and nonclassical states generation in dissipative higher-order anharmonic oscillators

We develop a method for the determination of thecdynamics of dissipative quantum systems in the limit of large number of quanta N, based on the 1/N-expansion of Heidmann et al. [ Opt. Commun. 54, 189 (1985) ] and the quantum-classical correspondence. Using this method, we find analytically the dynamics of nonclassical states generation in the higher-order anharmonic dissipative oscillators for an arbitrary temperature of a reservoir. We show that the quantum correction to the classical motion increases with time quadratically up to some maximal value, which is dependent on the degree of nonlinearity and a damping constant, and then it decreases. Similarities and differences with the corresponding behavior of the quantum corrections to the classical motion in the Hamiltonian chaotic systems are discussed. We also compare our results obtained for some limiting cases with the results obtained by using other semiclassical tools and discuss the conditions for validity of our approach.Comment: 15 pages, RevTEX (EPSF-style), 3 figs. Replaced with final version (stylistic corrections

Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups

In this paper, we construct a Lagrangian submanifold of the moduli space associated to the fundamental group of a punctured Riemann surface (the space of representations of this fundamental group into a compact connected Lie group). This Lagrangian submanifold is obtained as the fixed-point set of an anti-symplectic involution defined on the moduli space. The notion of decomposable representation provides a geometric interpretation of this Lagrangian submanifold

Nested T-duality

We identify the obstructions for T-dualizing the boundary WZW model and make explicit how they depend on the geometry of branes. In particular, the obstructions disappear for certain brane configurations associated to non-regular elements of the Cartan torus. It is shown in this case that the boundary WZW model is "nested" in the twisted boundary WZW model as the dynamical subsystem of the latter.Comment: 13 page

Nonlinear dynamics and band transport in a superlattice driven by a plane wave

A quantum particle transport induced in a spatially-periodic potential by a propagating plane wave has a number important implications in a range of topical physical systems. Examples include acoustically driven semiconductor superlattices and cold atoms in optical crystal. Here we apply kinetic description of the directed transport in a superlattice beyond standard linear approximation, and utilize exact path-integral solutions of the semiclassical transport equation. We show that the particle drift and average velocities have non-monotonic dependence on the wave amplitude with several prominent extrema. Such nontrivial kinetic behaviour is related to global bifurcations developing with an increase of the wave amplitude. They cause dramatic transformations of the system phase space and lead to changes of the transport regime. We describe different types of phase trajectories contributing to the directed transport and analyse their spectral content

Physical Principles of the Amplification of Electromagnetic Radiation Due to Negative Electron Masses in a Semiconductor Superlattice

In a superlattice placed in crossed electric and magnetic fields, under certain conditions, the inversion of electron population can appear at which the average energy of electrons is above the middle of the miniband and the effective mass of the electron is negative. This is the implementation of the negative effective mass amplifier and generator (NEMAG) in the superlattice. It can result in the amplification and generation of terahertz radiation even in the absence of negative differential conductivity.Comment: 5 pages, 3 figure

Fractional and unquantized dc voltage generation in THz-driven semiconductor superlattices

We consider the spontaneous creation of a dc voltage across a strongly coupled semiconductor superlattice subjected to THz radiation. We show that the dc voltage may be approximately proportional either to an integer or to a half- integer multiple of the frequency of the applied ac field, depending on the ratio of the characteristic scattering rates of conducting electrons. For the case of an ac field frequency less than the characteristic scattering rates, we demonstrate the generation of an unquantized dc voltage.Comment: 6 pages, 3 figures, RevTEX, EPSF. Revised version v3: corrected typo

Monodromy-data parameterization of spaces of local solutions of integrable reductions of Einstein's field equations

For the fields depending on two of the four space-time coordinates only, the spaces of local solutions of various integrable reductions of Einstein's field equations are shown to be the subspaces of the spaces of local solutions of the ``null-curvature'' equations constricted by a requirement of a universal (i.e. solution independent) structures of the canonical Jordan forms of the unknown matrix variables. These spaces of solutions of the ``null-curvature'' equations can be parametrized by a finite sets of free functional parameters -- arbitrary holomorphic (in some local domains) functions of the spectral parameter which can be interpreted as the monodromy data on the spectral plane of the fundamental solutions of associated linear systems. Direct and inverse problems of such mapping (``monodromy transform''), i.e. the problem of finding of the monodromy data for any local solution of the ``null-curvature'' equations with given canonical forms, as well as the existence and uniqueness of such solution for arbitrarily chosen monodromy data are shown to be solvable unambiguously. The linear singular integral equations solving the inverse problems and the explicit forms of the monodromy data corresponding to the spaces of solutions of the symmetry reduced Einstein's field equations are derived.Comment: LaTeX, 33 pages, 1 figure. Typos, language and reference correction

Symmetry-breaking and chaos in electron transport in semiconductor superlattices

We study the motion of electrons in a single miniband of a semiconductor superlattice driven by THz electric field polarized along the growth direction. We work in the semiclassical balance-equation model, including different elastic and inelastic scattering rates, and incorporating the self-consistent electric field generated by electron motion. We explore regions of complex dynamics, which can include chaotic behaviour and symmetry-breaking. We estimate the magnitudes of dc current and dc voltage that spontaneously appear in regions of broken-symmetry for parameters characteristic of modern semiconductor superlattices. This work complements PRL 80(1998)2669 [ cond-mat/9709026 ].Comment: 4 pages, 3 figures, RevTEX, EPS

Dynamical Instabilities and Deterministic Chaos in Ballistic Electron Motion in Semiconductor Superlattices

We consider the motion of ballistic electrons within a superlattice miniband under the influence of an alternating electric field. We show that the interaction of electrons with the self-consistent electromagnetic field generated by the electron current may lead to the transition from regular to chaotic dynamics. We estimate the conditions for the experimental observation of this deterministic chaos and discuss the similarities of the superlattice system with the other condensed matter and quantum optical systems.Comment: 6 pages, RevTEX; 4 fig