2,015 research outputs found
Ansatz of Hans Bethe for a two-dimensional Bose gas
The method of q-oscillator lattices, proposed recently in [hep-th/0509181],
provides the tool for a construction of various integrable models of quantum
mechanics in 2+1 dimensional space-time. In contrast to any one dimensional
quantum chain, its two dimensional generalizations -- quantum lattices -- admit
different geometrical structures. In this paper we consider the q-oscillator
model on a special lattice. The model may be interpreted as a two-dimensional
Bose gas. The most remarkable feature of the model is that it allows the
coordinate Bethe Ansatz: the p-particles' wave function is the sum of plane
waves. Consistency conditions is the set of 2p equations for p one-particle
wave vectors. These "Bethe Ansatz" equations are the main result of this paper.Comment: LaTex2e, 12 page
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
Modified Tetrahedron Equations and Related 3D Integrable Models
Using a modified version of the tetrahedron equations we construct a new
family of -state three-dimensional integrable models with commuting
two-layer transfer-matrices. We investigate a particular class of solutions to
these equations and parameterize them in terms of elliptic functions. The
corresponding models contain one free parameter -- an elliptic modulus.Comment: 26 pages, LaTeX fil
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
On invariance of specific mass increment in the case of non-equilibrium growth
It is the first time invariance of specific mass increments of crystalline
structures that co-exist in the case of non-equilibrium growth is grounded
using the maximum entropy production principle. Based on the hypothesis of the
existence of a universal growth equation, with the use of dimensional analysis,
an explicit form of the dependence of specific mass increment on time is
proposed. Applicability of the obtained results for describing growth in
animate nature is discussed.Comment: 5 page
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