Explicit Free Parameterization of the Modified Tetrahedron Equation

The Modified Tetrahedron Equation (MTE) with affine Weyl quantum variables at N-th root of unity is solved by a rational mapping operator which is obtained from the solution of a linear problem. We show that the solutions can be parameterized in terms of eight free parameters and sixteen discrete phase choices, thus providing a broad starting point for the construction of 3-dimensional integrable lattice models. The Fermat curve points parameterizing the representation of the mapping operator in terms of cyclic functions are expressed in terms of the independent parameters. An explicit formula for the density factor of the MTE is derived. For the example N=2 we write the MTE in full detail. We also discuss a solution of the MTE in terms of bosonic continuum functions.Comment: 28 pages, 3 figure

Ground states of Heisenberg evolution operator in discrete three-dimensional space-time and quantum discrete BKP equations

In this paper we consider three-dimensional quantum q-oscillator field theory without spectral parameters. We construct an essentially big set of eigenstates of evolution with unity eigenvalue of discrete time evolution operator. All these eigenstates belong to a subspace of total Hilbert space where an action of evolution operator can be identified with quantized discrete BKP equations (synonym Miwa equations). The key ingredients of our construction are specific eigenstates of a single three-dimensional R-matrix. These eigenstates are boundary states for hidden three-dimensional structures of U_q(B_n^1) and U_q(D_n^1)$.Comment: 13 page

Comment on "Giant Nernst Effect due to Fluctuating Cooper Pairs in Superconductors" by M.N. Serbyn, M.A. Skvortsov, A.A. Varlamov, and V. Galitski

In a recent Letter, Serbyn et al. [A] investigated thermomagnetic effects above the superconducting transition and generalized previous works for arbitrary magnetic fields and temperatures. While the results of [A] have been confirmed in [B], we have strong objections: (i) According to our results [C], the linear response calculation does not require any correction from the magnetization currents; (ii) The result of [A,B] is giant, because unlike the normal Fermi liquid, it is of zero order in the particle-hole asymmetry. Changing the interaction constant in the Cooper channel leads to ridiculously large results even for nonsuperconducting metals; (iii)Derived in [A] the Einstein-type relation for thermomagnetic coefficient contradicts to text-book results. [A] M.N. Serbyn, M.A. Skvortsov, A.A. Varlamov, V. Galitski, Phys. Rev. Lett. 102, 067001 (2009). [B] K. Michaeli and A.M. Finkel'stein, EPL 86, 27007 (2009). [C] A. Sergeev et al., Phys. Rev. B 77, 064501 (2008)

Diagnostic of electromagnetic conditions in space using cosmic rays

The method of spectrographic global survey was used to study the time variations in parameters of cosmic ray (CR) pitch angle anisotropy and their relationship with the variations of some solar wind characteristics under different electromagnetic conditions in interplanetary space. A classification is made of the conditions that are accompanied by the increase in CR anisotropy

Multi-Cascade Proton Acceleration by Superintense Laser Pulse in the Regime of Relativistically Induced Slab Transparency

A regime of multi-cascade proton acceleration in the interaction of $10^{21}-10^{22}$ W/cm$^2$ laser pulse with a structured target is proposed. The regime is based on the electron charge displacement under the action of laser ponderomotive force and on the effect of relativistically induced slab transparency which allows to realize idea of multi-cascade acceleration. It is shown that a target comprising several properly spaced apart thin foils can optimize the acceleration process and give at the output quasi-monoenergetic beams of protons with energies up to hundreds of MeV with energy spread of just few percent.Comment: 5 pages with 4 figure

Quantum 2+1 evolution model

A quantum evolution model in 2+1 discrete space - time, connected with 3D fundamental map R, is investigated. Map R is derived as a map providing a zero curvature of a two dimensional lattice system called "the current system". In a special case of the local Weyl algebra for dynamical variables the map appears to be canonical one and it corresponds to known operator-valued R-matrix. The current system is a kind of the linear problem for 2+1 evolution model. A generating function for the integrals of motion for the evolution is derived with a help of the current system. The subject of the paper is rather new, and so the perspectives of further investigations are widely discussed.Comment: LaTeX, 37page