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

Simple Estimation of X- Trion Binding Energy in Semiconductor Quantum Wells

A simple illustrative wave function with only three variational parameters is suggested to calculate the binding energy of negatively charged excitons (X-) as a function of quantum well width. The results of calculations are in agreement with experimental data for GaAs, CdTe and ZnSe quantum wells, which differ considerably in exciton and trion binding energy. The normalized X- binding energy is found to be nearly independent of electron-to-hole mass ratio for any quantum well heterostructure with conventional parameters. Its dependence on quantum well width follows an universal curve. The curve is described by a simple phenomenological equation.Comment: 8 pages, 3 Postscript figure

Coupling of intrinsic Josephson oscillations in layered superconductors by charge fluctuations

The coupling of Josephson oscillations in layered superconductors is studied with help of a tunneling Hamiltonian formalism. The general form of the current density across the barriers between the superconducting layers is derived. The induced charge fluctuations on the superconducting layers lead to a coupling of the Josephson oscillations in different junctions. A simplified set of equations is then used to study the non-linear dynamics of the system. In particular the influence of the coupling on the current-voltage characteristics is investigated and upper limits for the coupling strength are estimated from a comparison with experiments on cuprate superconductors.Comment: To be published in proceedings of SPIE conference San Diego 199

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

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

Visualizing Pure Quantum Turbulence in Superfluid 3^{3}He: Andreev Reflection and its Spectral Properties

Superfluid $^3$He-B in the zero-temperature limit offers a unique means of studying quantum turbulence by the Andreev reflection of quasiparticle excitations by the vortex flow fields. We validate the experimental visualization of turbulence in $^3$He-B by showing the relation between the vortex-line density and the Andreev reflectance of the vortex tangle in the first simulations of the Andreev reflectance by a realistic 3D vortex tangle, and comparing the results with the first experimental measurements able to probe quantum turbulence on length scales smaller than the inter-vortex separation.Comment: 5 pages, 4 figures, and Supplemental Material (2 pages, 2 figures

Cross-sections of Andreev scattering by quantized vortex rings in 3He-B

We studied numerically the Andreev scattering cross-sections of three-dimensional isolated quantized vortex rings in superfluid 3He-B at ultra-low temperatures. We calculated the dependence of the cross-section on the ring's size and on the angle between the beam of incident thermal quasiparticle excitations and the direction of the ring's motion. We also introduced, and investigated numerically, the cross-section averaged over all possible orientations of the vortex ring; such a cross-section may be particularly relevant for the analysis of experimental data. We also analyzed the role of screening effects for Andreev reflection of quasiparticles by systems of vortex rings. Using the results obtained for isolated rings we found that the screening factor for a system of unlinked rings depends strongly on the average radius of the vortex ring, and that the screening effects increase with decreasing the rings' size.Comment: 11 pages, 8 figures ; submitted to Physical Review

Casimir eigenvalues for universal Lie algebra

For two different natural definitions of Casimir operators for simple Lie algebras we show that their eigenvalues in the adjoint representation can be expressed polynomially in the universal Vogel's parameters $\alpha, \beta, \gamma$ and give explicit formulae for the generating functions of these eigenvalues.Comment: Slightly revised versio