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

Null boundary gravitational charges from local Lorentz symmetries

In this paper, we revisit the null boundary gravitational charge in the Newman-Penrose formalism with special emphasis on the charges from local Lorentz transformations. We find that there is one more charge derived from the local Lorentz transformation and the new charge is purely from the Holst term. This reveals a remarkable fact that trivial terms which do not change classical equations of motion can not only affect the boundary degrees of freedom through their contributions to the boundary charges but also have their own rights to create new boundary degrees of freedom.Comment: 10 page

Notes on self-dual gravity

In this paper, we study self-dual gravity in the Newman-Penrose formalism. We specify the self-dual solution space from the Newman-Unti solutions. We show that the asymptotic symmetries of the self-dual gravity are still the (extended) BMS symmetries. We transform the self-dual Taub-NUT solution into the Newman-Unti gauge in analytical form.Comment: 11+4 page

Nonintegrability-driven Transition from Kinetics to Hydrodynamics

Nonintegrability plays a crucial role in thermalization and transport processes in many-body Hamiltonian systems, yet its quantitative effects remain unclear. To reveal the connection between the macroscopic relaxation properties and the underlying dynamics, the one-dimensional diatomic hard-point model as an illustrating example was studied analytically and numerically. We demonstrate how the system transitions from kinetic behavior to hydrodynamic behavior as the nonintegrability strength increases. Specifically, for the thermalization dynamics, we find a power-law relationship between the thermalization time and the perturbation strength near integrable regime, whereas in the far from integrable regime, the hydrodynamics dominates and the thermalization time becomes independent of the perturbation strength and exhibits a strong size-dependent behavior. Regarding transport behavior, our results further establish a threshold for the nonintegrable strength of this transition. Consequently, we can predict which behavior dominates the transport properties of the system. Especially, an explicit expression of the thermal conductivity contributed by the kinetics is given. Finally, possible applications were briefly discussed.Comment: 6 pages;5figure

Accurate Time-segmented Loss Model for SiC MOSFETs in Electro-thermal Multi-Rate Simulation

Compared with silicon (Si) power devices, Silicon carbide (SiC) devices have the advantages of fast switching speed and low on-resistance. However, the effects of non-ideal characteristics of SiC MOSFETs and stray parameters (especially parasitic inductance) on switching losses need to be further evaluated. In this paper, a transient loss model based on SiC MOSFET and SiC Schottky barrier diode (SBD) switching pairs is proposed. The transient process analysis is simplified by time segmentation of the transient process of power switching devices. The electro-thermal simulation calculates the junction temperature and updates the temperature-related parameters with the proposed loss model and the thermal network model. A multi-rate data exchange strategy is proposed to solve the problem of disparity in timescales between circuit simulation and thermal network simulation. The CREE CMF20120D SiC MOSFET device is used for the experimental verification. The experimental results verify the accuracy of the model which provides guidance for the circuit design of SiC MOSFETs. All the parameters of the loss model can be extracted from the datasheet, which is practical in power electronics design