Metastability in the BCS model

We discuss metastable states in the mean-field version of the strong coupling BCS-model and study the evolution of a superconducting equilibrium state subjected to a dynamical semi-group with Lindblad generator in detailed balance w.r.t. another equilibrium state. The intermediate states are explicitly constructed and their stability properties are derived. The notion of metastability in this genuine quantum system, is expressed by means of energy-entropy balance inequalities and canonical coordinates of observables

Constraint-based sequence mining using constraint programming

The goal of constraint-based sequence mining is to find sequences of symbols that are included in a large number of input sequences and that satisfy some constraints specified by the user. Many constraints have been proposed in the literature, but a general framework is still missing. We investigate the use of constraint programming as general framework for this task. We first identify four categories of constraints that are applicable to sequence mining. We then propose two constraint programming formulations. The first formulation introduces a new global constraint called exists-embedding. This formulation is the most efficient but does not support one type of constraint. To support such constraints, we develop a second formulation that is more general but incurs more overhead. Both formulations can use the projected database technique used in specialised algorithms. Experiments demonstrate the flexibility towards constraint-based settings and compare the approach to existing methods.Comment: In Integration of AI and OR Techniques in Constraint Programming (CPAIOR), 201

Statistics and Quantum Chaos

We use multi-time correlation functions of quantum systems to construct random variables with statistical properties that reflect the degree of complexity of the underlying quantum dynamics.Comment: 12 pages, LateX, no figures, restructured versio

Multi-distributed Entanglement in Finitely Correlated Chains

The entanglement-sharing properties of an infinite spin-chain are studied when the state of the chain is a pure, translation-invariant state with a matrix-product structure. We study the entanglement properties of such states by means of their finitely correlated structure. These states are recursively constructed by means of an auxiliary density matrix \rho on a matrix algebra B and a completely positive map E: A \otimes B -> B, where A is the spin 2\times 2 matrix algebra. General structural results for the infinite chain are therefore obtained by explicit calculations in (finite) matrix algebras. In particular, we study not only the entanglement shared by nearest-neighbours, but also, differently from previous works, the entanglement shared between connected regions of the spin-chain. This range of possible applications is illustrated and the maximal concurrence C=1/\sqrt{2} for the entanglement of connected regions can actually be reached.Comment: 7 pages, 2 figures, to be published in Eur.Phys.Let

Zeno Dynamics in Quantum Statistical Mechanics

We study the quantum Zeno effect in quantum statistical mechanics within the operator algebraic framework. We formulate a condition for the appearance of the effect in W*-dynamical systems, in terms of the short-time behaviour of the dynamics. Examples of quantum spin systems show that this condition can be effectively applied to quantum statistical mechanical models. Further, we derive an explicit form of the Zeno generator, and use it to construct Gibbs equilibrium states for the Zeno dynamics. As a concrete example, we consider the X-Y model, for which we show that a frequent measurement at a microscopic level, e.g. a single lattice site, can produce a macroscopic effect in changing the global equilibrium.Comment: 15 pages, AMSLaTeX; typos corrected, references updated and added, acknowledgements added, style polished; revised version contains corrections from published corrigend

Matrix Product Density Operators: Simulation of finite-T and dissipative systems

We show how to simulate numerically both the evolution of 1D quantum systems under dissipation as well as in thermal equilibrium. The method applies to both finite and inhomogeneous systems and it is based on two ideas: (a) a representation for density operators which extends that of matrix product states to mixed states; (b) an algorithm to approximate the evolution (in real or imaginary time) of such states which is variational (and thus optimal) in nature.Comment: See also M. Zwolak et al. cond-mat/040644

Asymptotic distinguishability measures for shift-invariant quasi-free states of fermionic lattice systems

We apply the recent results of F. Hiai, M. Mosonyi and T. Ogawa [arXiv:0707.2020, to appear in J. Math. Phys.] to the asymptotic hypothesis testing problem of locally faithful shift-invariant quasi-free states on a CAR algebra. We use a multivariate extension of Szego's theorem to show the existence of the mean Chernoff and Hoeffding bounds and the mean relative entropy, and show that these quantities arise as the optimal error exponents in suitable settings.Comment: Results extended to higher dimensional lattices, title changed. Submitted versio