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

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

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

Berezinians, Exterior Powers and Recurrent Sequences

We study power expansions of the characteristic function of a linear operator $A$ in a $p|q$-dimensional superspace $V$. We show that traces of exterior powers of $A$ satisfy universal recurrence relations of period $q$. `Underlying' recurrence relations hold in the Grothendieck ring of representations of \GL(V). They are expressed by vanishing of certain Hankel determinants of order $q+1$ in this ring, which generalizes the vanishing of sufficiently high exterior powers of an ordinary vector space. In particular, this allows to explicitly express the Berezinian of an operator as a rational function of traces. We analyze the Cayley--Hamilton identity in a superspace. Using the geometric meaning of the Berezinian we also give a simple formulation of the analog of Cramer's rule.Comment: 35 pages. LaTeX 2e. New version: paper substantially reworked and expanded, new results include

Highest weight modules over quantum queer Lie superalgebra U_q(q(n))

In this paper, we investigate the structure of highest weight modules over the quantum queer superalgebra $U_q(q(n))$. The key ingredients are the triangular decomposition of $U_q(q(n))$ and the classification of finite dimensional irreducible modules over quantum Clifford superalgebras. The main results we prove are the classical limit theorem and the complete reducibility theorem for $U_q(q(n))$-modules in the category $O_q^{\geq 0}$.Comment: Definition 1.5 and Definition 6.1 are changed, and a remark is added in the new versio

Ultrarelativistic nanoplasmonics as a new route towards extreme intensity attosecond pulses

The generation of ultra-strong attosecond pulses through laser-plasma interactions offers the opportunity to surpass the intensity of any known laboratory radiation source, giving rise to new experimental possibilities, such as quantum electrodynamical tests and matter probing at extremely short scales. Here we demonstrate that a laser irradiated plasma surface can act as an efficient converter from the femto- to the attosecond range, giving a dramatic rise in pulse intensity. Although seemingly similar schemes have been presented in the literature, the present setup deviates significantly from previous attempts. We present a new model describing the nonlinear process of relativistic laser-plasma interaction. This model, which is applicable to a multitude of phenomena, is shown to be in excellent agreement with particle-in-cell simulations. We provide, through our model, the necessary details for an experiment to be performed. The possibility to reach intensities above 10^26 W/cm^2, using upcoming 10 petawatt laser sources, is demonstrated.Comment: 15 pages, 5 figure

Corrigendum to "Time-varying magnetotail magnetic flux calculation: a test of the method" published in Ann. Geophys., 27, 1583–1591, 2009

No abstract available

Diurnal variations of cosmic ray geomagnetic cut-off threshold rigidities

The spectrographic global survey method was used to investigate the rigidity variations Rc of geomagnetic cut-off as a function of local time and the level of geomagnetic disturbance for a number of stations of the world wide network. It is shown that geomagnetic cut-off threshold rigidities undergo diurnal variations. The diurnal wave amplitude decreases with increasing threshold rigidity Rc, and the wave maximum occurs at 2 to 4 hr LT. The amplitude of diurnal variations increases with increasing geomagnetic activity. The results agree with those from trajectory calculations made for an asymmetric model of the magnetosphere during different geomagnetic disturbance conditions

Superanalogs of the Calogero operators and Jack polynomials

A depending on a complex parameter $k$ superanalog ${\mathcal S}{\mathcal L}$ of Calogero operator is constructed; it is related with the root system of the Lie superalgebra ${\mathfrak{gl}}(n|m)$. For $m=0$ we obtain the usual Calogero operator; for $m=1$ we obtain, up to a change of indeterminates and parameter $k$ the operator constructed by Veselov, Chalykh and Feigin [2,3]. For $k=1, \frac12$ the operator ${\mathcal S}{\mathcal L}$ is the radial part of the 2nd order Laplace operator for the symmetric superspaces corresponding to pairs $(GL(V)\times GL(V), GL(V))$ and $(GL(V), OSp(V))$, respectively. We will show that for the generic $m$ and $n$ the superanalogs of the Jack polynomials constructed by Kerov, Okunkov and Olshanskii [5] are eigenfunctions of ${\mathcal S}{\mathcal L}$; for $k=1, \frac12$ they coinside with the spherical functions corresponding to the above mentioned symmetric superspaces. We also study the inner product induced by Berezin's integral on these superspaces