Abstract:
Parquet equations, describing the competition between superconducting and density-wave instabilities, are solved for a three-dimensional isotropic metal in a high magnetic field when only the lowest Landau level is filled. In the case of a repulsive interaction between electrons, a phase transition to the density-wave state is found at finite temperature. In the opposite case of attractive interaction, no phase transition is found. With decreasing temperature $T$, the effective vertex of interaction between electrons renormalizes toward a one-dimensional limit in a self-similar way with the characteristic length (transverse to the magnetic field) decreasing as $\ln^{-1/6}(\omega_c/T)$ ($\omega_c$ is a cutoff). Correlation functions have new forms, previously unknown for conventional one-dimensional or three-dimensional Fermi-liquids.

Abstract:
The second order correction to free energy due to the interaction between electrons is calculated for a quasi-one-dimensional conductor exposed to a magnetic field perpendicular to the chains. It is found that specific heat, magnetization and torque oscillate when the magnetic field is rotated in the plane perpendicular to the chains or when the magnitude of magnetic filed is changed. This new mechanism of thermodynamic magnetic oscillations in metals, which is not related to the presence of any closed electron orbits, is applied to explain behavior of the organic conductor (TMTSF)$_2$ClO$_4$.

Abstract:
This paper presents a novel principle for photovoltaic (PV) energy conversion using surface acoustic waves (SAWs) in piezoelectric semiconductors. A SAW produces a periodically modulated electric potential, which spatially segregates photoexcited electrons and holes to the maxima and minima of the SAW potential. The moving SAW collectively transports the carriers with the speed of sound to the electrodes made of different materials, which extract electrons and holes separately and generate dc output. The proposed active design is expected to have higher efficiency than passive designs of the existing PV devices and to produce enough energy to sustain the SAW.

Abstract:
Renormalization group equations and a phase diagram are derived for a system of two chains with a single-electron hopping between chains in order to correct the results of a recent paper by F.~V.~Kusmartsev, A.~Luther, and A.~Nersesyan, Pis'ma v Zh.\ Exp.\ Teor.\ Fiz.\ {\bf 55}, 692 (1992) [JETP Lett.\ {\bf 55}, 724 (1992)].

Abstract:
General topologically invariant microscopical expressions for quantum numbers of particle-like solitons ("skyrmions") are derived for a class of (2+1)D models. Skyrmions are either half-integer spin fermions with odd electric charge or integer spin bosons with even charge. So they cannot be Anderson's spinons or holons. General results are exemplified by a square lattice model reminiscenting high-Tc models.

Abstract:
This is a review article for Encyclopedia of Complexity and System Science, to be published by Springer http://refworks.springer.com/complexity/. The paper reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since late 1990s.

Abstract:
The paper briefly surveys theoretical models for the polar Kerr effect (PKE) and time-reversal symmetry breaking in the pseudogap phase of cuprate superconductors. By elimination, the most promising candidate is the tilted loop-current model, obtained from the Simon-Varma model by tilting one triangular loop up and another one down toward the apical oxygens. The model is consistent with the PKE, spin-polarized neutron scattering, and optical anisotropy measurements. Spontaneous currents in this model flow between the in-plane and apical oxygens in such a manner that each oxygen belongs to one current loop. This loop-current pattern is similar to the spin order in the magnetoelectric antiferromagnet Cr2O3, where the PKE is observed experimentally. By analogy, it should be possible to train the PKE sign in the cuprates magnetoelectrically. Several experiments are proposed to confirm the loop-current order: the magnetic-field-induced polarity, the nonlinear anomalous Hall effect, and the second-harmonic generation.

Abstract:
The optical Hall conductivity and the polar Kerr angle are calculated as functions of temperature for a two-dimensional chiral p_x+ip_y superconductor, where the time-reversal symmetry is spontaneously broken. The theoretical estimate for the polar Kerr angle agrees by the order of magnitude with the recent experimental measurement in Sr2RuO4 by Xia et al. cond-mat/0607539. The theory predicts that the Kerr angle is proportional to the square of the superconducting energy gap and is inversely proportional to the cube of frequency, which can be verified experimentally.

Abstract:
This is a theoretical review of the quantum Hall effect observed in quasi-one-dimensional organic conductors such as (TMTSF)2X. It is written for a book "Physics of Organic Superconductors and Conductors" to be published by Springer and edited by A. G. Lebed.

Abstract:
This Chapter is written for the Festschrift celebrating the 70th birthday of the distinguished economist Duncan Foley from the New School for Social Research in New York. This Chapter reviews applications of statistical physics methods, such as the principle of entropy maximization, to the probability distributions of money, income, and global energy consumption per capita. The exponential probability distribution of wages, predicted by the statistical equilibrium theory of a labor market developed by Foley in 1996, is supported by empirical data on income distribution in the USA for the majority (about 97%) of population. In addition, the upper tail of income distribution (about 3% of population) follows a power law and expands dramatically during financial bubbles, which results in a significant increase of the overall income inequality. A mathematical analysis of the empirical data clearly demonstrates the two-class structure of a society, as pointed out Karl Marx and recently highlighted by the Occupy Movement. Empirical data for the energy consumption per capita around the world are close to an exponential distribution, which can be also explained by the entropy maximization principle.