5,577 research outputs found
n+1 Dimensional Gravity duals to quantum criticalities with spontaneous symmetry breaking
We reexamine the charged AdS domain wall solution to the
Einstein-Abelian-Higgs model proposed by Gubser et al as holographic
superconductors at quantum critical points and comment on their statement about
the uniqueness of gravity solutions. We generalize their explorations from 3+1
dimensions to arbitrary Ds and find that the D charged AdS
domain walls are unstable against electric perturbations.Comment: version to appear in commun. theor. phy
Pseudorandom States, Non-Cloning Theorems and Quantum Money
We propose the concept of pseudorandom states and study their constructions,
properties, and applications. Under the assumption that quantum-secure one-way
functions exist, we present concrete and efficient constructions of
pseudorandom states. The non-cloning theorem plays a central role in our
study---it motivates the proper definition and characterizes one of the
important properties of pseudorandom quantum states. Namely, there is no
efficient quantum algorithm that can create more copies of the state from a
given number of pseudorandom states. As the main application, we prove that any
family of pseudorandom states naturally gives rise to a private-key quantum
money scheme.Comment: 20 page
Jantzen filtration of Weyl modules, product of Young symmetrizers and denominator of Young's seminormal basis
Let be a connected reductive algebraic group over an algebraically closed
field of characteristic , denote the Weyl module of
of highest weight and be the canonical -morphism. We study the
split condition for over , and apply
this as an approach to compare the Jantzen filtrations of the Weyl modules
and . In the case when is of type
, we show that the split condition is closely related to the product of
certain Young symmetrizers and, under some mild conditions, is further
characterized by the denominator of a certain Young's seminormal basis vector.
We obtain explicit formulas for the split condition in some cases
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