Christine Khripkov's Personal Information

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Christine Khripkov


Office: 54/317

PhD Information

Advisor: Amichay Vardi

Title: Chaos and thermodynamics in few-site Bose-Hubbard systems

My thesis describes the efforts to understand and quantify the transition from reversible microscopic mechanics to irreversible macroscopic thermodynamics, using small quantum systems for which a complete description of their many-body dynamics is possible. A particular point of interest is the possibility of unique $hbar$-dependent features that may appear in quantum thermalization, yet are necessarily absent in the semiclassical case where $hbar$ goes to zero.

The canonical approach to thermalization is based on the idea of a large bath of fluctuations and a small test system. By contrast, the thesis considered an isolated system with two subunits of similar size, one of which is clasically chaotic. Using a Bose-Hubbard model of N nonlinearly interacting particles in M sites, the simplest scheme was constructed where thermalization is expected to appear: a four-mode system, consisting of a trimer weakly coupled to a monomer. The isolated trimer contains two degrees of freedom and thus satisfies the minimal requirement for a classical chaos in the absence of time-dependent forces. The weak coupling was chosen to ensure a classical linear response, which predicts a diffusive energy transfer between the subunits.

A full many-body analysis of the four-mode system has presented a formidable numerical task due to the large dimension of the respective Hilbert space even for a small number of particles. Therefore the work proceeded by first studying smaller configurations of the Bose-Hubbard model, both integrable and chaotic, in an attempt to increase our understanding of the generic model, and to identify $hbar$-dependent anomalies. Following that, the behavior of the minimal self-thermalizing model was examined, and it was confirmed that energy indeed diffuses between the subunits, at a rate slower than the predictions of standard linear response theory. A complete ergodization was prevented by both semiclassical and many-body localization effects, indicating that the Eigenstate Thermalization Hypothesis does not hold for this model.

MSc Information

Advisor: Amichay Vardi

Title: Chaos and thermodynamics in few-site Bose-Hubbard systems (combined MSc-PhD thesis)