1,738 research outputs found
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
New series of 3D lattice integrable models
In this paper we present a new series of 3-dimensional integrable lattice
models with colors. The case generalizes the elliptic model of our
previous paper. The weight functions of the models satisfy modified tetrahedron
equations with states and give a commuting family of two-layer
transfer-matrices. The dependence on the spectral parameters corresponds to the
static limit of the modified tetrahedron equations and weights are
parameterized in terms of elliptic functions. The models contain two free
parameters: elliptic modulus and additional parameter . Also we briefly
discuss symmetry properties of weight functions of the models.Comment: 17 pages, IHEP-93-126, Late
New solution of vertex type tetrahedron equations
In this paper we formulate a new N-state spin integrable model on a
three-dimensional lattice with spins interacting round each elementary cube of
the lattice. This model can be also reformulated as a vertex type model. Weight
functions of the model satisfy tetrahedron equations.Comment: 12 pages, LaTeX, IHEP-94-10
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
Functional Tetrahedron Equation
We describe a scheme of constructing classical integrable models in
2+1-dimensional discrete space-time, based on the functional tetrahedron
equation - equation that makes manifest the symmetries of a model in local
form. We construct a very general "block-matrix model" together with its
algebro-geometric solutions, study its various particular cases, and also
present a remarkably simple scheme of quantization for one of those cases.Comment: LaTeX, 16 page
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 . The key ingredients are the
triangular decomposition of 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 -modules in the category .Comment: Definition 1.5 and Definition 6.1 are changed, and a remark is added
in the new versio
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