Model Device for Detection of Narcotics Transported Inside Human Body

A model device for detection of small solid inclusions in liquid phases on the basis of nuclear magnetic resonance methods is developed. Elements of magnetic resonance imaging technique are used in order to decrease the radio-frequency power necessary for solving the problem. The results of control experiments are presented. They demonstrate the effectiveness of the suggested methods. Possibilities of the methods for detection of narcotics inside the human body are discussed. Authors' address: Edward B. Fel'dman, Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka 142432, Moscow Region, Russian Federation     

The master T-operator for vertex models with trigonometric R-matrices as a classical τ-function

We apply the recently proposed construction of the master T-operator to integrable vertex models and the associated quantum spin chains with trigonometric R-matrices. The master T-operator is a generating function for commuting transfer matrices of integrable vertex models depending on infinitely many parameters. It also turns out to be the τ-function of an integrable hierarchy of classical soliton equations in the sense that it satisfies the same bilinear Hirota equations. We characterize the class of solutions of the Hirota equations that correspond to eigenvalues of the master T-operator and discuss its relation to the classical Ruijsenaars-Schneider system of particles.     

Elliptic Solutions to Difference Non-Linear Equations and Related Many-Body Problems

We study algebro-geometric (finite-gap) and elliptic solutions of fully discretized KP or 2D Toda equations. In bilinear form they are Hirota's difference equation for τ-functions. Starting from a given algebraic curve, we express the τ-function and the Baker–Akhiezer function in terms of the Riemann theta function. We show that the elliptic solutions, when the τ-function is an elliptic polynomial, form a subclass of the general algebro-geometric solutions. We construct the algebraic curves of the elliptic solutions. The evolution of zeros of the elliptic solutions is governed by the discrete time generalization of the Ruijsenaars-Schneider many body system. The zeros obey equations which have the form of nested Bethe-ansatz equations, known from integrable quantum field theories. We discuss the Lax representation and the action-angle-type variables for the many body system. We also discuss elliptic solutions to discrete analogues of KdV, sine-Gordon and 1D Toda equations and describe the loci of the zeros. Received: 15 May 1997 / Accepted: 7 September 1997     

Quantum transfer matrices for discrete and continuous quasi-exactly solvable problems

We clarify the algebraic structure of continuous and discrete quasi-exactly solvable spectral problems by embedding them in the framework of the quantum inverse scattering method. The quasi-exactly solvable hamiltonians in one dimension are identified with traces of quantum monodromy matrices for specific integrable systems with nonperiodic boundary conditions. Applications to the Azbel-Hofstadter problem are outlined.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 1, pp. 8–24, July, 1995.     

Machines for physicomechanical testing of polymeric materials

Two tensile-testing machines are described for physicomechanical tests of polymeric materials with deformation up to 100 and 1,000% in which the conditions of deformation are assigned directly to the measurement base of the specimen by using an automatically regulated electric drive, ensuring parity of the measured quantity (force, elongation, or stress) with the requisite preset functional controller.     

Non-archimedean strings and Bruhat-Tits trees

It is shown that the Bruhat-Tits tree for thep-adic linear groupGL(2) is a natural non-archimedean analog of the open string world sheet. The boundary of the tree can be identified with the field ofp-adic numbers. We construct a lattice quantum field theory on the Bruhat-Tits tree with a simple local lagrangian and show that it leads to the Freund-Olson amplitudes for emission processes of the particle states from the boundary.     

Multiloop calculations inp-adic string theory and Bruhat-Tits trees

We treat the openp-adic string world sheet as a coset spaceF=T/, whereT is the Bruhat-Tits tree for thep-adic linear groupGL(2, _p ) and PGL(2, _p ) is some Schottky group. The boundary of this world sheet corresponds to ap-adic Mumford curve of finite genus. The string dynamics is governed by the local gaussian action on the coset spaceF. The tachyon amplitudes expressed in terms ofp-adic -functions are proposed for the Mumford curve of arbitrary genus. We compare them with the corresponding usual archimedean amplitudes. The sum over moduli space of the algebraic curves is conjectured to be expressed in the arithmetic surface terms. We also give the necessary mathematical background including the Mumford approach top-adic algebraic curves. The connection of the problem of closedp-adic strings with the considered topics is discussed.