Abstract We propose a gedanken experiment on realizing thermofield double state (TFD) by using analog black holes and provide an approach to test the scrambling time. Through this approach, we demonstrate clearly how shock wave changes TFD as time evolves. As whole system evolves forward in time, perturbation of space-time geometry will increase exponentially. Finally, it destroy entanglement b...

For X a topological space let expk X be the set of all non-empty finite subsets of X of cardinality at most k. There is a map from the Cartesian product of k copies of X with itself to expk X which sends x1 xk to x1 xk . The quotient topology gives expk X the structure of a topological space. Notice that for any m k the space expmX is canonically embedded into expk X . Clearly, exp1X X . The si...

We propose an alternative to Kendall’s shape space for reflection shapes of configurations in Rm with k labelled vertices, where reflection shape consists of all the geometric information that is invariant under compositions of similarity and reflection transformations. The proposed approach embeds the space of such shapes into the space P(k − 1) of (k − 1) × (k − 1) real symmetric positive sem...