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Title:  Classical and quantum integrability out of equilibrium
Author:  Yuan Miao
As Contributor:   (not claimed)
Type: Ph.D.
Field: Physics
Specialties:
  • Mathematical Physics
Approach: Theoretical
URL:  https://hdl.handle.net/11245.1/b9f84ee2-152c-4e9d-a925-33de979066e8
Degree granting institution:  University of Amsterdam
Supervisor(s): Jean-S├ębastien Caux
Defense date:  2021-09-15

Abstract:

In this thesis we study the out-of-equilibrium physics of classical and quantum integrable models, which are a particular set of models that can be solved exactly. The thesis is devoted to two main topics. For the first part, we obtained the exact results for the domain-wall quench problem in classical Landau-Lifshitz field theory, i.e. the semi-classical limit of quantum spin-1/2 XXZ model using classical integrability. We discovered the classical-quantum correspondence of spin transport in the domain-wall quench. In order to develop a quantitative method for the correspondence, we studied the quantisation of magnetic solitons in classical Landau-Lifshitz field theory that directly related to some eigenstates of the quantum XXZ model. In the second part of the thesis, we studied the exact spectrum of the quantum XXZ model with anisotropy parameter at root of unity value. We used the underlying algebraic structure of quantum integrability to elucidate the exponential degeneracies in the spectrum. This result motivated us to conjecture about the hidden Onsager algebra symmetries of the quantum XXZ model with anisotropy parameter at root of unity value, which reveals possible connection between the quantum group structure and the spectrum.

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