565 research outputs found
Lifshitz quasinormal modes and relaxation from holography
We obtain relaxation times for field theories with Lifshitz scaling and with
holographic duals Einstein-Maxwell-Dilaton gravity theories. This is done by
computing quasinormal modes of a bulk scalar field in the presence of Lifshitz
black branes. We determine the relation between relaxation time and dynamical
exponent z, for various values of boundary dimension d and operator scaling
dimension. It is found that for d>z+1, at zero momenta, the modes are
non-overdamped, whereas for d<=z+1 the system is always overdamped. For d=z+1
and zero momenta, we present analytical results.Comment: 16 pages and 5 figure
Krylov complexity in a natural basis for the Schr\"odinger algebra
We investigate operator growth in quantum systems with two-dimensional
Schr\"odinger group symmetry by studying the Krylov complexity. While feasible
for semisimple Lie algebras, cases such as the Schr\"odinger algebra which is
characterized by a semi-direct sum structure are complicated. We propose to
compute Krylov complexity for this algebra in a natural orthonormal basis,
which produces a pentadiagonal structure of the time evolution operator,
contrasting the usual tridiagonal Lanczos algorithm outcome. The resulting
complexity behaves as expected. We advocate that this approach can provide
insights to other non-semisimple algebras.Comment: 18 pages, 4 figures. v2: Typos corrected and references added. v3:
Restructured some sentence
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