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

Weak Decays of Doubly Heavy Baryons: the 1/2→1/21/2\to 1/2 case

Very recently, the LHCb collaboration has observed in the final state $\Lambda_c^+ K^-\pi^+\pi^+$ a resonant structure that is identified as the doubly-charmed baryon $\Xi_{cc}^{++}$. Inspired by this observation, we investigate the weak decays of doubly heavy baryons $\Xi_{cc}^{++}$, $\Xi_{cc}^{+}$, $\Omega_{cc}^{+}$, $\Xi_{bc}^{(\prime)+}$, $\Xi_{bc}^{(\prime)0}$, $\Omega_{bc}^{(\prime)0}$, $\Xi_{bb}^{0}$, $\Xi_{bb}^{-}$ and $\Omega_{bb}^{-}$ and focus on the decays into spin $1/2$ baryons in this paper. At the quark level these decay processes are induced by the $c\to d/s$ or $b\to u/c$ transitions, and the two spectator quarks can be viewed as a scalar or axial vector diquark. We first derive the hadronic form factors for these transitions in the light-front approach and then apply them to predict the partial widths for the semi-leptonic and non-leptonic decays of doubly heavy baryons. We find that a number of decay channels are sizable and can be examined in future measurements at experimental facilities like LHC, Belle II and CEPC.Comment: 40 pages, 4 figures, to appear in EPJ