Young measures in a nonlocal phase transition problem

A nonlocal variational problem modelling phase transitions is studied in the framework of Young measures. The existence of global minimisers among functions with internal layers on an infinite tube is proved by combining a weak convergence result for Young measures and the principle of concentration-compactness. The regularity of such global minimisers is discussed, and the nonlocal variational problem is also considered on asymptotic tubes

Vanishing Integral Relations and Expectation Values for Bloch Functions in Finite Domains

Integral identities for particular Bloch functions in finite periodic systems are derived. All following statements are proven for a finite domain consisting of an integer number of unit cells. It is shown that matrix elements of particular Bloch functions with respect to periodic differential operators vanish identically. The real valuedness, the time-independence and a summation property of the expectation values of periodic differential operators applied to superpositions of specific Bloch functions are derived.Comment: 10 page

Quench Dynamics of Entanglement in an Opened Anisotropic Spin-1/2 Heisenberg Chain

The quantum entanglement dynamics of a one-dimensional spin-1/2 anisotropic XXZ model is studied using the method of the adaptive time-dependent density-matrix renormalization-group when two cases of quenches are performed in the system. An anisotropic interaction quench and the maximum number of domain walls of staggered magnetization quench are considered. The dynamics of pairwise entanglement between the nearest two qubits in the spin chain is investigated. The entanglement of the two-spin qubits can be created and oscillates in both cases of the quench. The anisotropic interaction has a strong influence on the oscillation frequency of entanglement.Comment: 13 pages, 4 figure

Quasinormal Modes of Self-Dual Warped AdS3_3 Black Hole in Topological Massive Gravity

We consider the various perturbations of self-dual warped AdS$_3$ black hole and obtain the exact expressions of quasinormal modes by imposing the vanishing Dirichlet boundary condition at asymptotic infinity. It is expected that the quasinormal modes agree with the poles of retarded Green's functions of the dual CFT. Our results provide a quantitative test of the warped AdS/CFT correspondence.Comment: 10 pages, no figure, some references and comments on gravitational perturbations are adde