We introduce and fully analyze a new commutation relation $\overline{K} L_1 = L_2 K$ between finite convolution integral operator $K$ differential operators $L_1$ $L_{2}$, that has implications for spectral properties of $K$. This work complements our explicit characterization commuting pairs $KL=LK$ provides an exhaustive list kernels admitting or sesquicommuting operators.

For continuous-time Markov chains, we provide criteria for non-ergodicity, non-algebraic ergodicity, non-exponential and non-strong ergodicity. discrete-time ergodicity are given. Our in terms of the existence solutions to inequalities involving Q-matrix (or transition matrix P time-discrete case) chain. Meanwhile, these practical applied some examples, including a special class single birth pr...

Eigenstate thermalization hypothesis (ETH) has played a pivotal role in understanding ergodicity and its breaking isolated quantum many-body systems. The recent experiment on 51-atom Rydberg simulator by Bernien et al. [Nature (London) 551, 579 (2017)] subsequent theoretical analysis have shown that hardcore kinetic constraint can lead to weak breaking. In this work, we demonstrate, using $1d$ ...

We consider a class of semi-linear differential Volterra equations with memory terms, polynomial nonlinearities and random perturbation. For broad nonlinearities, we show that the system in concern admits unique weak solution. Also, any statistically steady state must possess regularity compatible Moreover, if sufficiently many directions are stochastically forced, employ generalized coupling a...

Models with mixed origins of anomalous subdiffusion have been considered important for understanding transport in biological systems. Here one such mixed model, the quenched-trap model (QTM) on fractal lattices, is investigated. It is shown that both ensemble- and time-averaged mean-square displacements (MSDs) show subdiffusion with different scaling exponents, i.e., this system shows weak ergo...

The calculation of the conductance of ballistic rings requires a theory that goes well beyond the Kubo-Drude formula. Assuming “mesoscopic” circumstance of very weak environmental relaxation, the conductance is much smaller compared with the naive expectation. Namely, the electro-motiveforce induces an energy absorption with a rate that depends crucially on the possibility to make connected seq...

A mean–field formulation is used to investigate the bifurcation diagram for globally coupled tent maps by means of an analytical approach. It is shown that the period doubling sequence of the single site map induces a continuous family of periodic states in the coupled system. This type of collective motion breaks the ergodicity of the coupled map lattice. The stability analysis suggests that t...