9,973 research outputs found
Universal Time Scale for Thermalization in Two-dimensional Systems
The Fermi-Pasta-Ulam-Tsingou problem, i.e., the problem of energy
equipartition among normal modes in a weakly nonlinear lattice, is here studied
in two types of two-dimensional (2D) lattices, more precisely in lattices with
square cell and triangular cell. We apply the wave-turbulence approach to
describe the dynamics and find multi-wave resonances play a major role in the
transfer of energy among the normal modes. We show that, in general, the
thermalization time in 2D systems is inversely proportional to the squared
perturbation strength in the thermodynamic limit. Numerical simulations confirm
that the results are consistent with the theoretical prediction no matter
systems are translation-invariant or not. It leads to the conclusion that such
systems can always be thermalized by arbitrarily weak many-body interactions.
Moreover, the validity for disordered lattices implies that the localized
states are unstable.Comment: 6 pages, 4 figure
State-independent contextuality sets for a qutrit
We present a generalized set of complex rays for a qutrit in terms of
parameter , a -th root of unity. Remarkably, when ,
the set reduces to two well known state-independent contextuality (SIC) sets:
the Yu-Oh set and the Bengtsson-Blanchfield-Cabello set. Based on the
Ramanathan-Horodecki criterion and the violation of a noncontextuality
inequality, we have proven that the sets with and are SIC, while
the set with is not. Our generalized set of rays will theoretically
enrich the study of SIC proof, and experimentally stimulate the novel
application to quantum information processing.Comment: 4 pages, 2 figures; revised versio
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