Twisted quantum affine superalgebra Uq[gl(m|n)(2)] and new Uq[osp(m|n)] invariant R-matrices

The minimal irreducible representations of U-q[gl(m|n)], i.e. those irreducible representations that are also irreducible under U-q[osp(m|n)] are investigated and shown to be affinizable to give irreducible representations of the twisted quantum affine superalgebra U-q[gl(m|n)((2))]. The U-q[osp(m|n)] invariant R-matrices corresponding to the tensor product of any two minimal representations are constructed, thus extending our twisted tensor product graph method to the supersymmetric case. These give new solutions to the spectral-dependent graded Yang-Baxter equation arising from U-q[gl(m|n)((2))], which exhibit novel features not previously seen in the untwisted or non-super cases.

Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process

Quasi-birth-and-death (QBD) processes with infinite “phase spaces” can exhibit unusual and interesting behavior. One of the simplest examples of such a process is the two-node tandem Jackson network, with the “phase” giving the state of the first queue and the “level” giving the state of the second queue. In this paper, we undertake an extensive analysis of the properties of this QBD. In particular, we investigate the spectral properties of Neuts’s R-matrix and show that the decay rate of the stationary distribution of the “level” process is not always equal to the convergence norm of R. In fact, we show that we can obtain any decay rate from a certain range by controlling only the transition structure at level zero, which is independent of R. We also consider the sequence of tandem queues that is constructed by restricting the waiting room of the first queue to some finite capacity, and then allowing this capacity to increase to infinity. We show that the decay rates for the finite truncations converge to a value, which is not necessarily the decay rate in the infinite waiting room case. Finally, we show that the probability that the process hits level n before level 0 given that it starts in level 1 decays at a rate which is not necessarily the same as the decay rate for the stationary distribution.

Common multiples of complete graphs

A graph H is said to divide a graph G if there exists a set S of subgraphs of G, all isomorphic to H, such that the edge set of G is partitioned by the edge sets of the subgraphs in S. Thus, a graph G is a common multiple of two graphs if each of the two graphs divides G.

Integrability of the Russian doll BCS model

We show that integrability of the BCS model extends beyond Richardson's model (where all Cooper pair scatterings have equal coupling) to that of the Russian doll BCS model for which the couplings have a particular phase dependence that breaks time-reversal symmetry. This model is shown to be integrable using the quantum inverse scattering method, and the exact solution is obtained by means of the algebraic Bethe ansatz. The inverse problem of expressing local operators in terms of the global operators of the monodromy matrix is solved. This result is used to find a determinant formulation of a correlation function for fluctuations in the Cooper pair occupation numbers. These results are used to undertake exact numerical analysis for small systems at half-filling.

Gauge fields, geometric phases, and quantum adiabatic pumps

Quantum adiabatic pumping of charge and spin between two reservoirs (leads) has recently been demonstrated in nanoscale electronic devices. Pumping occurs when system parameters are varied in a cyclic manner and sufficiently slowly that the quantum system always remains in its ground state. We show that quantum pumping has a natural geometric representation in terms of gauge fields (both Abelian and non-Abelian) defined on the space of system parameters. Tunneling from a scanning tunneling microscope tip through a magnetic atom could be used to demonstrate the non-Abelian character of the gauge field.

A unified and complete construction of all finite dimensional irreducible representations of gl(2|2)

Representations of the non-semisimple superalgebra gl(2/2) in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All finite-dimensional irreducible typical and atypical representations and lowest weight (indecomposable) Kac modules of gl(2/2) are constructed explicity through the explicit construction of all gl(2) circle plus gl(2) particle states (multiplets) in terms of boson and fermion creation operators in the super-Fock space. This gives a unified and complete treatment of finite-dimensional representations of gl(2/2) in explicit form, essential for the construction of primary fields of the corresponding current superalgebra at arbitrary level.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. II. The two-shell nonzero shift ACCs and U(2n) generator MEs

This is the second in a series of articles whose ultimate goal is the evaluation of the matrix elements (MEs) of the U(2n) generators in a multishell spin-orbit basis. This extends the existing unitary group approach to spin-dependent configuration interaction (CI) and many-body perturbation theory calculations on molecules to systems where there is a natural partitioning of the electronic orbital space. As a necessary preliminary to obtaining the U(2n) generator MEs in a multishell spin-orbit basis, we must obtain a complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The zero-shift coefficients were obtained in the first article of the series. in this article, we evaluate the nonzero shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. We then demonstrate that the one-shell versions of these coefficients may be obtained by taking the Gelfand-Tsetlin limit of the two-shell formulas. These coefficients,together with the zero-shift types, then enable us to write down formulas for the U(2n) generator matrix elements in a two-shell spin-orbit basis. Ultimately, the results of the series may be used to determine the many-electron density matrices for a partitioned system. (C) 1998 John Wiley & Sons, Inc.

Measurement and state preparation via ion trap quantum computing

We investigate in detail the effects of a QND vibrational number measurement made on single ions in a recently proposed measurement scheme for the vibrational state of a register of ions in a linear rf trap [C. D'HELON and G. J. MILBURN, Phys Rev. A 54, 5141 (1996)]. The performance of a measurement shows some interesting patterns which are closely related to searching.

Three-dimensional quantum solitons with parametric coupling

We consider the quantum field theory of two bosonic fields interacting via both parametric (cubic) and quartic couplings. In the case of photonic fields in a nonlinear optical medium, this corresponds to the process of second-harmonic generation (via chi((2)) nonlinearity) modified by the chi((3)) nonlinearity. The quantum solitons or energy eigenstates (bound-state solutions) are obtained exactly in the simplest case of two-particle binding, in one, two, and three space dimensions. We also investigate three-particle binding in one space dimension. The results indicate that the exact quantum solitons of this field theory have a singular, pointlike structure in two and three dimensions-even though the corresponding classical theory is nonsingular. To estimate the physically accessible radii and binding energies of the bound states, we impose a momentum cutoff on the nonlinear couplings. In the case of nonlinear optical interactions, the resulting radii and binding energies of these photonic particlelike excitations in highly nonlinear parametric media appear to be close to physically observable values.

Multidimensional parametric quantum solitons

We consider the parametric quantum field theory involving cubic and quartic couplings of two bosonic fields. This is exactly soluble for the two-particle energy eigenstates (or quantum solitons) in one, two, and three space dimensions. We estimate the binding energies and corresponding radii in the case of photonic fields in nonlinear optical materials, and Bose-Einstein condensates. [S1050-2947(98)51110-9].

Measurements on trapped laser-cooled ions using quantum computations

There are some interesting connections between the theory of quantum computation and quantum measurement. As an illustration, we present a scheme in which an ion trap quantum computer can be used to make arbitrarily accurate measurements of the quadrature phase variables for the collective vibrational motion of the ion. We also discuss some more general aspects of quantum computation and measurement in terms of the Feynman-Deutsch principle.

Dynamical quantum noise in trapped Bose-Einstein condensates

We introduce the study of dynamical quantum noise in Bose-Einstein condensates through numerical simulation of stochastic partial differential equations obtained using phase-space representations. We derive evolution equations for a single trapped condensate in both the positive-P and Wigner representations and perform simulations to compare the predictions of the two methods. The positive-P approach is found to be highly susceptible to the stability problems that have been observed in other strongly nonlinear, weakly damped systems. Using the Wigner representation, we examine the evolution of several quantities of interest using from a variety of choices of initial stare for the condensate and compare results to those for single-mode models. [S1050-2947(98)06612-8].

Decomposing complete tripartite graphs into cycles of lengths 3 and 4

Necessary and sufficient conditions are given for the edge-disjoint decomposition of a complete tripartite graph K-r,K-s,K-t into exactly alpha 3-cycles and beta 4-cycles. (C) 1999 Elsevier Science B.V. All rights reserved.

The Heisenberg antiferromagnet on an anisotropic triangular lattice: linear spin-wave theory

We consider the effect of quantum spin fluctuations on the ground-state properties of the Heisenberg antiferromagnet on an anisotropic triangular lattice using linear spin-wave (LSW) theory. This model should describe the magnetic properties of the insulating phase of the kappa-(BEDT-TTF)(2)X family of superconducting molecular crystals. The ground-state energy, the staggered magnetization, magnon excitation spectra, and spin-wave velocities are computed as functions of the ratio of the antiferromagnetic exchange between the second and first neighbours, J(2)/J(1). We find that near J(2)/J(1) = 0.5, i.e., in the region where the classical spin configuration changes from a Neel-ordered phase to a spiral phase, the staggered magnetization vanishes, suggesting the possibility of a quantum disordered state. in this region, the quantum correction to the magnetization is large but finite. This is in contrast to the case for the frustrated Heisenberg model on a square lattice, for which the quantum correction diverges logarithmically at the transition from the Neel to the collinear phase. For large J(2)/J(1), the model becomes a set of chains with frustrated interchain coupling. For J(2) > 4J(1), the quantum correction to the magnetization, within LSW theory, becomes comparable to the classical magnetization, suggesting the possibility of a quantum disordered state. We show that, in this regime, the quantum fluctuations are much larger than for a set of weakly coupled chains with non-frustrated interchain coupling.

A new approach to current and noise in double quantum dot systems

We use a quantum master equation to describe transport in double-dot devices. The coherent dot-to-dot coupling affects the noise spectra strongly. For phonon-assisted tunneling, the calculated current spectra are consistent with those of experiments. The model shows that quantum stochastic theory may he applied to some advantage in mesoscopic electronic systems. (C) 2000 Elsevier Science B.V. All rights reserved.