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

Highly viscous electron fluid in GaAs quantum wells

A fluid in which shear-stress transverse waves, being character for solids, can propagate is usually referred as a highly viscous fluid. Hydrodynamics of the fluid formed by conduction electrons has been recently discovered in graphene, ultra-pure Weyl and layered metals, and high-mobility GaAs quantum wells. Here we construct a theory of magnetotransport in a highly viscous two-dimensional (2D) electron fluid in moderate magnetic fields, accounting its viscoelastic dynamics and the memory effects in the interparticle scattering. In addition to the properties of the microwave-induced resistance oscillations (MIRO) in photoresistance explained by theories for non-interacting 2D electrons, our theory predicts an irregular shape of MIRO at certain sample sizes, a peak in photoresistance near the doubled electron cyclotron frequency, and no dependence of MIRO on the helicity of the circular polarization of radiation. These effects, which are the evidences of the excitation of the transverse magnetosonic waves, were observed in magnetotransport experiments on ultra-high-quality GaAs quantum wells. We conclude that 2D electrons in such structures in magnetic field form a highly viscous fluid.Comment: 26 pages, 10 figure