44,276 research outputs found
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
Quasinormal Modes of Self-Dual Warped AdS Black Hole in Topological Massive Gravity
We consider the various perturbations of self-dual warped AdS 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
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