Exact diagonalization of the quantum supersymmetric SUq(n|m) model

We use the algebraic nested Bethe ansatz to solve the eigenvalue and eigenvector problem of the supersymmetric SU_q(n|m) model with open boundary conditions. Under an additional condition this model is related to a multicomponent supersymmetric t-J model. We also prove that the transfer matrix with open boundary conditions is SU_q(n|m) invariant.     

Quasiclassical calculation of the levels in a weakly asymmetric potential well corresponding to arbitrary quantum numbers m andl » n

The levels in a three-dimensional potential well are calculated in the case of asymmetric perturbations corresponding to arbitrary quantum numbers m andl » n; the results transform to zero oscillations whenl is small, and are also a generalization of the rotational levels of a rigid rotator in an external field. The results are used for Stark-effect calculation in diatomic molecules.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 11–15, December, 1978.It remains to thank G. V. Dubrovskii for wide-ranging discussion and comments on the work.     

q-Oscillator realizations of the quantum superalgebrassl q (m,n) andosp q (m, 2n)

Realizations of the quantum superalgebras corresponding to theA(m, n), B(m, n), C(n+1), andD(m, n) series are given in terms of the creation and annihilation operators ofq-deformed Bose and Fermi oscillators.     

On the assumption of initial factorization in the master equation for weakly coupled systems I: General framework

We analyze the dynamics of a quantum mechanical system in interaction with a reservoir when the initial state is not factorized. In the weak-coupling (van Hove) limit, the dynamics can be properly described in terms of a master equation, but a consistent application of Nakajima-Zwanzig’s projection method requires that the reference (not necessarily equilibrium) state of the reservoir be endowed with the mixing property.     

Irreducible Representations of the Quantum Group Uq(m + n) in Uq(m)⊕ Uq(n) Basis

Irreducible represen tations of U_q(m + n) in U_q(m) ⊕ U_q(n) basis are discussed. The noncanonical basis of U_q(m + n) are expanded in terms of its canonical basis. The expansion coefficients or subduction coefficients of U_q (m + n)↓ U_q(m) ⊕ U_q(n) are derived from the subduction coefficients of Hecke algebras.     

Exact theory of the (Einstein) gravitational field in an arbitrary background space-time

The Lagrangian based theory of the gravitational field and its sources at the arbitrary background space-time is developed. The equations of motion and the energy-momentum tensor of the gravitational field are derived by applying the variational principle. The gauge symmetries of the theory and the associated conservation laws are investigated. Some properties of the energymomentum tensor of the gravitational field are described in detail and the examples of its application are given. The desire to have the total energymomentum tensor as a source for the linear part of the gravitational field leads to the universal coupling of gravity with other fields (as well as to the self-interaction) and finally to the Einstein theory.     

The geometry structures and electronic properties of Li_mB_n(m+n=12) clusters

The geometric structures, electronic properties, total and binding energies, harmonic frequencies, the highest occupied molecular orbital to the lowest unoccupied molecular orbital energy gaps, and the vertical ionization potential energies of small LimBn （m＋ n = 12） clusters were investigated by the density functional theory B3LYP with a 6-31 I＋G （2d, 2p） basis set. All the calculations were performed using the Gaussian09 program. For the study of the LimBn clusters, the global minimum of the B 12 cluster was chosen as the starting point and the boron atoms were gradually replaced by Li atoms. The results showed that as the number of Li atoms increased, the stability of the LimBn cluster decreased and the physical and chemical properties became more active. In addition, on average there was a large charge transfer from the Li atoms to the B atoms.     

Exact solution of the O(n) model on a random lattice

We present an exact solution of the O(n) model on a random lattice. The coupling constant space of our model is parametrized in terms of a set of moment variables and the same type of universality with respect to the potential as observed for the one-matrix model is found. In addition we find a large degree of universality with respect to n; namely for n gE ] − 2,2[ the solution can be presented in a form which is valid not only for any potential, but also for any n (not necessarily rational). The cases n = ±2 are treated separately. We give explicit expressions for the genus-zero contribution to the one- and two-loop correlators as well as for the genus-one contribution to the one-loop correlator and the free energy. It is shown how one can obtain from these results any multi-loop correlator and the free energy to any genus and the structure of the higher-genera contributions is described. Furthermore we describe how the calculation of the higher-genera contributions can be pursued in the scaling limit.     

Exact solution of the spin-1/2 Ising model on the Shastry–Sutherland (orthogonal-dimer) lattice

A star-triangle mapping transformation is used to establish an exact correspondence between the spin-1/2 Ising model on the Shastry–Sutherland (orthogonal-dimer) lattice and respectively, the spin-1/2 Ising model on a bathroom tile (4–8) lattice. Exact results for the critical temperature and spontaneous magnetization are obtained and compared with corresponding results on the regular Ising lattices.     

Laser ultraviolet fragmentation of homogeneous (CF3I) n clusters in a molecular beam and (CF3I) n clusters inside of large (Xe) m clusters or on their surface

The fragmentation of homogeneous (CF₃I) _n clusters (where n ≤ 45 is the average number of molecules in a cluster) in a molecular beam, as well as (CF₃I) _n clusters inside of large (Xe) _m clusters (where m ≥ 100 is the average number of atoms in a cluster) or on their surface, by laser ultraviolet radiation has been studied. It has been found that the indicated three types of (CF₃I) _n clusters have different stabilities with respect to fragmentation and strongly different dependences of the fragmentation probability on the energy of ultraviolet radiation. Fragmentation at low energies and the weakest energy dependence of the probability of fragmentation are observed for homogeneous clusters, a stronger dependence is characteristic of (CF₃I) _n clusters localized inside (Xe) _m clusters, and the strongest dependence is observed for (CF₃I) _n clusters on the surface of (Xe) _m clusters. Possible reasons for such a character of the observed dependences have been discussed.     

A study of the127I(n, γ)128I reaction

The reaction¹²⁷I(n, γ)¹²⁸I has been investigated at the tangential facility of the McMaster University Nuclear Reactor using a pair spectrometer. A total of 248 transitions were observed in the photon energy range 4.5–6.8 MeV. Below an excitation energy of 1 MeV more than 50 levels have been inferred. Through use of 28 levels with well established energies, a neutron separation energy of 6826.12±0.05 keV was determined. The level density up to an excitation of 2.5 MeV was examined on the basis of a statistical model and found to agree with current parameter values. TheE1 andM1 strength functions were determined and the influence of the giant dipole resonance on the former investigated.     

On the tensor product of supersingleton representations ofosp(1, 2n)

The tensor product of two supersingleton representations _n of the Lie superalgebraosp (1, 2n) is studied forn2. The main results are as follows: (a) anticommutators and commutators of the odd generators in _{n n} form a skew-symmetric representation of the Lie algebrau(n, n); (b) simple explicit form of all irreducible components of _{n n}, which are labelled by a single parameterJ=0, 1, ..., has been found. Each of them is a^*-representation ofosp (1, 2n) for which assertion (a) is valid. The dimension of its vacuum subspace equals , i.e., the nondegenerate vacuum occurs for J=0 only. Basic property of this family of irreducible^*-representations of osp(1, 2n) are analogous to those of massless representations of osp(1, 4).Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday.     

The low-lying states of127I from the (n,n′ γ) reaction

Using time-of-flight methods to discriminate against neutron induced backgrounds, a 40 cm³ Ge(Li) detector was used to observe the γ-rays from the¹²⁷I(n, n′ γ) reaction. Based on these γ-rays, energy level and decay schemes are derived up to an excitation of 1780 keV in¹²⁷I. This scheme shows seventeen new levels, whilst the existence of two levels recently determined in Coulomb excitation studies are confirmed. The level scheme is compared with the intermediate coupling unified model predictions.     

Discontinuity of the dynamic critical exponents ofO(n)-symmetric systems

Then-component model of Sasvári, Schwabl, and Szépfalusy is analyzed by means of renormalized field theory to two-loop order. Singular two-loop contributions have a significant effect on the nature of the stability boundary of the dynamic scaling region in then—d plane. Along this boundary the dynamic critical exponents exhibit unexpected discontinuities.