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

A note on a canonical dynamical r-matrix

It is well known that a classical dynamical $r$-matrix can be associated with every finite-dimensional self-dual Lie algebra \G by the definition $R(\omega):= f(\mathrm{ad} \omega)$, where \omega\in \G and $f$ is the holomorphic function given by $f(z)={1/2}\coth \frac{z}{2}-\frac{1}{z}$ for z\in \C\setminus 2\pi i \Z^*. We present a new, direct proof of the statement that this canonical $r$-matrix satisfies the modified classical dynamical Yang-Baxter equation on \G.Comment: 17 pages, LaTeX2

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

Probes of Lorentz Violation in Neutrino Propagation

It has been suggested that the interactions of energetic particles with the foamy structure of space-time thought to be generated by quantum-gravitational (QG) effects might violate Lorentz invariance, so that they do not propagate at a universal speed of light. We consider the limits that may be set on a linear or quadratic violation of Lorentz invariance in the propagation of energetic neutrinos, v/c=[1 +- (E/M_\nuQG1)] or [1 +- (E/M_\nu QG2}^2], using data from supernova explosions and the OPERA long-baseline neutrino experiment. Using the SN1987a neutrino data from the Kamioka II, IMB and Baksan experiments, we set the limits M_\nuQG1 > 2.7(2.5)x10^10 GeV for subluminal (superluminal) propagation, respectively, and M_\nuQG2 >4.6(4.1)x10^4 GeV at the 95% confidence level. A future galactic supernova at a distance of 10 kpc would have sensitivity to M_\nuQG1 > 2(4)x10^11 GeV for subluminal (superluminal) propagation, respectively, and M_\nuQG2 > 2(4)x10^5 GeV. With the current CNGS extraction spill length of 10.5 micro seconds and with standard clock synchronization techniques, the sensitivity of the OPERA experiment would reach M_\nuQG1 ~ 7x10^5 GeV (M_\nuQG2 ~ 8x10^3 GeV) after 5 years of nominal running. If the time structure of the SPS RF bunches within the extracted CNGS spills could be exploited, these figures would be significantly improved to M_\nuQG1 ~ 5x10^7 GeV (M_\nuQG2 ~ 4x10^4 GeV). These results can be improved further if similar time resolution can be achieved with neutrino events occurring in the rock upstream of the OPERA detector: we find potential sensitivities to M_\nuQG1 ~ 4x10^8 GeV and M_\nuQG2 ~ 7x10^5 GeV.Comment: 33 pages, 22 figures, version accepted for publication in Physical Review

Nonmonotonic magnetoresistance of a two-dimensional viscous electron-hole fluid in a confined geometry

Ultra-pure conductors may exhibit hydrodynamic transport where the collective motion of charge carriers resembles the flow of a viscous fluid. In a confined geometry (e.g., in ultra-high quality nanostructures) the electronic fluid assumes a Poiseuille-like flow. Applying an external magnetic field tends to diminish viscous effects leading to large negative magnetoresistance. In two-component systems near charge neutrality the hydrodynamic flow of charge carriers is strongly affected by the mutual friction between the two constituents. At low fields, the magnetoresistance is negative, however at high fields the interplay between electron-hole scattering, recombination, and viscosity results in a dramatic change of the flow profile: the magnetoresistance changes its sign and eventually becomes linear in very high fields. This novel non-monotonic magnetoresistance can be used as a fingerprint to detect viscous flow in two-component conducting systems.Comment: 10 pages, 8 figure

Counterflows in viscous electron-hole fluid

In ultra-pure conductors, collective motion of charge carriers at relatively high temperatures may become hydrodynamic such that electronic transport may be described similarly to a viscous flow. In confined geometries (e.g., in ultra-high quality nanostructures), the resulting flow is Poiseuille-like. When subjected to a strong external magnetic field, the electric current in semimetals is pushed out of the bulk of the sample towards the edges. Moreover, we show that the interplay between viscosity and fast recombination leads to the appearance of counterflows. The edge currents possess a non-trivial spatial profile and consist of two stripe-like regions: the outer stripe carrying most of the current in the direction of the external electric field and the inner stripe with the counterflow.Comment: 10 pages, 5 figure

Resummations in the Bloch-Nordsieck model

We studied different levels of resummations of the exactly solvable Bloch-Nordsieck model in order to be able to compare the approximations with an exact result. We studied one-loop perturbation theory, 2PI resummation and Schwinger-Dyson equations truncated in a way to maintain Ward-identities. At all levels we carefully performed renormalization. We found that although the 2PI resummation does not exhibit infrared sensitivity at the mass shell (the one-loop perturbation theory does), but it is still far from the exact solution. The method of truncated Schwinger-Dyson equations, however, is exact in this model, so it provides a new way of solving the Bloch-Nordsieck model. This method can also be generalized to other, more complicated theories.Comment: 12 pages, 3 figures, revtex

Nonperturbative Contributions in an Analytic Running Coupling of QCD

In the framework of analytic approach to QCD the nonperturbative contributions in running coupling of strong interaction up to 4-loop order are obtained in an explicit form. For all $Q>\Lambda$ they are shown to be represented in the form of an expansion in inverse powers of Euclidean momentum squared. The expansion coefficients are calculated for different numbers of active quark flavors $n_f$ and for different number of loops taken into account. On basis of the stated expansion the effective method for precise calculation of the analytic running coupling can be developed.Comment: 9 pages, LaTeX, 1 table, 1 eps figur

Magnetoresistance of compensated semimetals in confined geometries

Two-component conductors -- e.g., semi-metals and narrow band semiconductors -- often exhibit unusually strong magnetoresistance in a wide temperature range. Suppression of the Hall voltage near charge neutrality in such systems gives rise to a strong quasiparticle drift in the direction perpendicular to the electric current and magnetic field. This drift is responsible for a strong geometrical increase of resistance even in weak magnetic fields. Combining the Boltzmann kinetic equation with sample electrostatics, we develop a microscopic theory of magnetotransport in two and three spatial dimensions. The compensated Hall effect in confined geometry is always accompanied by electron-hole recombination near the sample edges and at large-scale inhomogeneities. As the result, classical edge currents may dominate the resistance in the vicinity of charge compensation. The effect leads to linear magnetoresistance in two dimensions in a broad range of parameters. In three dimensions, the magnetoresistance is normally quadratic in the field, with the linear regime restricted to rectangular samples with magnetic field directed perpendicular to the sample surface. Finally, we discuss the effects of heat flow and temperature inhomogeneities on the magnetoresistance.Comment: 22 pages, 7 figures, published versio

Magnetoresistance in two-component systems

Two-component systems with equal concentrations of electrons and holes exhibit non-saturating, linear magnetoresistance in classically strong magnetic fields. The effect is predicted to occur in finite-size samples at charge neutrality in both disorder- and interaction-dominated regimes. The phenomenon originates in the excess quasiparticle density developing near the edges of the sample due to the compensated Hall effect. The size of the boundary region is of the order of the electron-hole recombination length that is inversely proportional to the magnetic field. In narrow samples and at strong enough magnetic fields, the boundary region dominates over the bulk leading to linear magnetoresistance. Our results are relevant for semimetals and narrow-band semiconductors including most of the topological insulators.Comment: 11 pages, 3 figure