How One can Repair Non-integrable Kahan Discretizations. II. A Planar System with Invariant Curves of Degree 6

Mathematical Physics, Analysis and Geometry - In this paper, we develop the dressing method to study the modified Camassa-Holm equation with the help of reciprocal transformation and the associated...     

Many-body effects in diffusion-limited kinetics

We review a novel approach to treating many-body effects in diffusion-limited kinetics. The derivation of the general expression for the survival probability of a Brownian particle in the presence of randomly distributed traps is given. The reduction of this expression to both the Smoluchowski solultion and the wellknown asymptotic behavior is demonstrated. It is shown that the Smoluchowski solution gives a lower bound for the particle survival probability. The correction to the Smoluchowski solution which takes into account the particle death slowdown in the initial process stage is described. The steady-state rate-constant concentration dependence and the reflection of many-body effects in it are discussed in detail.     

Absolute negative conductivity and zero-resistance states in two-dimensional electron systems: A plausible scenario

We present a model that provides a plausible explanation of the effect of zero-resistance and zero-conductance states in two-dimensional electron systems subjected to a magnetic field and irradiated with microwaves observed in a number of experiments and of the effect’s main features. The model is based on the concept of absolute negative conductivity associated with photon-assisted scattering of electrons on impurities. It is shown that the main features of the effect can be attributed to the interplay of different electron scattering mechanisms.     

Integrable Noncommutative Equations on Quad-graphs. The Consistency Approach

We extend integrable systems on quad-graphs, such as the Hirota equation and the cross-ratio equation, to the noncommutative context, when the fields take values in an arbitrary associative algebra. We demonstrate that the three-dimensional consistency property remains valid in this case. We derive the noncommutative zero curvature representations for these systems, based on the latter property. Quantum systems with their quantum zero curvature representations are particular cases of the general noncommutative ones.     

Effect of the microstructure of epitaxial YBa2Cu3O7 − x films on their electrophysical and nonlinear microwave properties

The local nonlinear microwave response of YBa₂Cu₃O_{7 ? x} films was measured by near-zone field microscopy with a spatial resolution of 50 μm, and YBa₂Cu₃O_{7 ? x} film microbridges were locally studied by low-temperature scanning microscopy with a spatial resolution of 4 μm. The microstructure of epitaxial YBa₂Cu₃O_{7 ? x} films was examined using x-ray diffraction and electron microscopy. A correlation is detected between the average crystallite size and the half-widths of the temperature dependences of the third-harmonic power (W _TH) and the electron-beam-induced voltage (W _EBIV). The experimental results are described in terms of a model of a two-phase medium taking into account the nonlinear I-V characteristic of the superconductor. For large crystallites, the nonlinear microwave response is shown to be caused by intracrystallite vortex pinning. As the average crystallite size decreases, an additional contribution to the nonlinear response appears due to the pinning of a magnetic flux by the Josephson network of crystallite boundaries. Calculations show that a three-fold increase in the crystallite size decreases the nonlinearity coefficient of YBa₂Cu₃O_{7 ? x} films by two orders of magnitude.     

On the bi-Hamiltonian structure of Toda and relativistic Toda lattices

We introduce a general quadratic Poisson bracket on the associative algebra equipped with non-degenerate scalar product. With the help of this bracket we obtain the interpretation of the Toda and relativistic Toda lattices as the restrictions of one and the same bi-Hamiltonian system to two different low-dimensional manifolds, which are Poisson submanifolds with respect to two brackets simultaneously.     

Photomagnetic effect in bilayer two-dimensional electron–hole systems

In tilted magnetic fields a bilayer electron–hole system is found to generate a photocurrent under terahertz radiation as the system is tuned to electron cyclotron resonance conditions. The photoinduced current amplitude oscillates with the magnetic field in correlation with Shubnikov–de Haas oscillations for electrons. The phenomenon is accounted for by a photomagnetic effect in electron–hole systems in the quantum Hall regime and has potentialities for terahertz detection and spectroscopy.     

On the Hamiltonian structure of Hirota‐Kimura discretization of the Euler top

This paper deals with a remarkable integrable discretization of the so (3) Euler top introduced by Hirota and Kimura. Such a discretization leads to an explicit map, whose integrability has been understood by finding two independent integrals of motion and a solution in terms of elliptic functions. Our goal is the construction of its Hamiltonian formulation. After giving a simplified and streamlined presentation of their results, we provide a bi‐Hamiltonian structure for this discretization, thus proving its integrability in the standard Liouville‐Arnold sense (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gas–crystal phase transition in a 2D dipolar exciton system

A system of dipolar excitons at temperatures exceeding the expected Bose–Einstein condensation temperature is considered. It is shown that a first-order phase transition with the formation of a phase close to the crystal of such excitons is possible at such temperatures. The phase diagram in the range of low concentrations and temperatures is constructed. The effect of this transition on the luminescence spectrum of the system is analyzed.