The holographic correspondence predicts that certain strongly coupled
quantum systems describe an emergent, higher-dimensional bulk spacetime
in which excitations enjoy local dynamics. We consider a general
holographic state dual to an asymptotically AdS bulk spacetime, and
study boundary correlation functions of local fields integrated against
wavepackets. We derive a factorization...
Computing the spectrum of the Laplace operator on a compact Riemannian manifold is a classic problem in mathematical physics. For this presentation, we consider the four-dimensional Einstein metric on the non-trivial $S^2-$bundle over $S^2$ discovered by Page. A pseudospectral method is used to approximate the spectrum of the scalar Laplacian. We show our numerical results match well with...
Frobenius algebras and Hopf algebras generalize algebras of functions and Lie groups/Lie algebras, respectively. Appropriate constructions involving these two types of algebras link together concepts from functional analysis with those from Lie theory. As quantum field theories often involve a mixture of analytic and algebraic structures (for instance, performing analysis on operator-valued...
Classical mechanics can be cast in a framework that represents observables as operators and states as vectors in some Hilbert space, as shown by Koopman and von Neumann. In such a formulation, noncommuting operators naturally arise and the question of their physical interpretation is relevant for understanding both classical and quantum mechanics. We describe a general map from ordinary...
We use simple spectral perturbation theory to show that the positive partial transpose property is stable under bounded perturbations of the Hamiltonian, for equilibrium states in infinite dimensions. The result holds provided the temperature is high enough, or equivalently, provided the perturbation is small enough.
Despite the development in Engineering, the structure such as bridge continue to collapse due to fluid loads effects. Their combination on a bridge pier can also induced catastrophic damages. Less attention in literature has been given to bridge pier dynamics under transversal flow. This work describes the dynamic vibration, including theoretical non-linear dynamics analysis, of a bridge pier...
