Exact Bethe Ansatz solution for An−1A_{n-1} chains with non-SUq(n)SU_{q}(n) invariant open boundary conditions

The Nested Bethe Ansatz is generalized to open and independent boundary conditions depending on two continuous and two discrete free parameters. This is used to find the exact eigenvectors and eigenvalues of the $A_{n-1}$ vertex models and $SU(n)$ spin chains with such boundary conditions. The solution is found for all diagonal families of solutions to the reflection equations in all possible combinations. The Bethe ansatz equations are used to find de first order finite size correction.Comment: Two references adde

Combinatorics of lattice paths with and without spikes

We derive a series of results on random walks on a d-dimensional hypercubic lattice (lattice paths). We introduce the notions of terse and simple paths corresponding to the path having no backtracking parts (spikes). These paths label equivalence classes which allow a rearrangement of the sum over paths. The basic combinatorial quantities of this construction are given. These formulas are useful when performing strong coupling (hopping parameter) expansions of lattice models. Some applications are described.Comment: Latex. 25 page

Mesoscopic entanglement induced by spontaneous emission in solid-state quantum optics

Implementations of solid-state quantum optics provide us with devices where qubits are placed at fixed positions in photonic or plasmonic one-dimensional waveguides. We show that solely by controlling the position ofthe qubits and withthe help of a coherent driving, collective spontaneous decay may be engineered to yield an entangled mesoscopic steady state. Our scheme relies on the realization of pure superradiant Dicke models by a destructive interference that cancels dipole-dipole interactions in one dimension

Evidence of several dipolar quasi-invariants in Liquid Crystals

In a closed quantum system of N coupled spins with magnetic quantum number I, there are about (2I + 1)^N constants of motion. However, the possibility of observing such quasi-invariant (QI) states in solid-like spin systems in Nuclear Magnetic Resonance (NMR) is not a strictly exact prediction. The aim of this work is to provide experimental evidence of several QI, in the proton NMR of small spin clusters, besides those already known Zeeman, and dipolar orders (strong and weak). We explore the spin states prepared with the Jeener-Broekaert pulse sequence by analyzing the time-domain signals yielded by this sequence as a function of the preparation times, in a variety of dipolar networks. We observe that the signals can be explained with two dipolar QIs only within a range of short preparation times. At longer times the time-domain signals have an echo-like behaviour. We study their multiple quantum coherence content on a basis orthogonal to the z-basis and see that such states involve a significant number of correlated spins. Then we show that the whole preparation time-scale can only be reconstructed by assuming the occurrence of multiple QI which we isolate experimentally

Large N reduction on a twisted torus

We consider SU(N) lattice gauge theory at infinite N defined on a torus with a CP invariant twist. Massless fermions are incorporated in an elegant way, while keeping them quenched. We present some numerical results which suggest that twisting can make numerical simulations of planar QCD more efficient.Comment: 14 pages, 2 figures, 1 tabl

A new class of highly efficient exact stochastic simulation algorithms for chemical reaction networks

We introduce an alternative formulation of the exact stochastic simulation algorithm (SSA) for sampling trajectories of the chemical master equation for a well-stirred system of coupled chemical reactions. Our formulation is based on factored-out, partial reaction propensities. This novel exact SSA, called the partial propensity direct method (PDM), is highly efficient and has a computational cost that scales at most linearly with the number of chemical species, irrespective of the degree of coupling of the reaction network. In addition, we propose a sorting variant, SPDM, which is especially efficient for multiscale reaction networks.Comment: 23 pages, 3 figures, 4 tables; accepted by J. Chem. Phy