7 June 2022 Tue 4.20 pm

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In my presentation I will summarize my work devoted to the subject of weakly nonintegrable dynamics of systems with macroscopic number of degrees of freedom. The main points of interest is identifying the classes of weak nonintegrability, characterizing the relevant thermalization and chaotization timescals.

Typically the thermalization is studied by testing the ergodic hypothesis; the timescales of ergodization are identified as those when the time averages of observables attain values close enough to the phase space averages. Naturally the question regarding the choice of observables arises. 

I will discuss the ambiguity which may come along with the certain choices of observables, the ways to overcome this ambiguity and the ways to classify the dynamics according to the network structure formed by the equations of motion of the properly chosen observables.

I will expand on the latter by discussing the characteristics of the Lyapunov spectra and tangent vectors depending on the structure of the underlying network of observables. In most of my studies the unitary circuit maps are chosen as a test bed model. I will introduce the model and discuss its features and advantages for the study of large timescale/system size dynamics. At the same time I will touch on the universality of the results and observations in the Hamiltonian systems such as the Klein-Gordon model.

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