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

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

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

Modified Tetrahedron Equations and Related 3D Integrable Models

Using a modified version of the tetrahedron equations we construct a new family of $N$-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 $k$ -- 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 $N$ colors. The case $N=2$ generalizes the elliptic model of our previous paper. The weight functions of the models satisfy modified tetrahedron equations with $N$ 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 $\eta$. 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

The modified tetrahedron equation and its solutions

A large class of 3-dimensional integrable lattice spin models is constructed. The starting point is an invertible canonical mapping operator in the space of a triple Weyl algebra. This operator is derived postulating a current branching principle together with a Baxter Z-invariance. The tetrahedron equation for this operator follows without further calculations. If the Weyl parameter is taken to be a root of unity, the mapping operator decomposes into a matrix conjugation and a C-number functional mapping. The operator of the matrix conjugation satisfies a modified tetrahedron equation (MTE) in which the "rapidities" are solutions of a classical integrable Hirota-type equation. The matrix elements of this operator can be represented in terms of the Bazhanov-Baxter Fermat curve cyclic functions, or alternatively in terms of Gauss functions. The paper summarizes several recent publications on the subject.Comment: 24 pages, 6 figures using epic/eepic package, Contribution to the proceedings of the 6th International Conference on CFTs and Integrable Models, Chernogolovka, Spetember 2002, reference adde

Briquetting the Carbon Phase from the Sludge Ponds at the Anzhersk Deposit

The briquetting of coal slurries from the Anzhersk deposit in the Kuznets Basin is investigated. Petroleum binder and sodium lignosulfonate are employed. The solid carbon phase from the sludge ponds (ash content up to 35%) has adequate briquetting properties when petroleum binder is added. The use of sulfite waste liquor at pressures of 80–100 MPa yields mechanically strong briquets that require additional water protection