טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentReichental Israel
SubjectThermalization in Open Quantum Systems
DepartmentDepartment of Physics
Supervisor Professor Daniel Podolsky


Abstract

We perform a theoretical study of thermalization in open quantum systems. A common tool for that is the Lindblad formalism: a linear equation of motion for the system density matrix which encapsulates the influence of the environment. In addition to the unitary evolution, the system undergoes dissipation and decoherence, via Lindblad operators which act on part of the system or wholly. The Lindblad equation is commonly used to describe transport, for example conductance between two heat reservoirs. But to keep in line with statistical mechanics principles, any use of the Lindblad equation to model coupling to thermal reservoirs must be conditioned by the following: if the system is coupled to one reservoir, it reaches a thermal equilibrium state with the same control intensive parameters (temperature, chemical potential etc.) of the reservoir. A configuration known to satisfy that rigorously requires the Lindblad operators to act on the whole system. However, it can be shown that due to this global coupling property, it is limited to the weak coupling regime. Other configurations, where the Lindblad operators act locally on a part of the system, are not limited to the weak coupling limit but have not proved to satisfy the thermalization condition. To the extent of our knowledge, no systematic study has been done on this issue. Here, we introduce a method that leads to thermalization while acting only at the edges of the system. Our method leads to a Gibbs state of the system, satisfies fluctuation-dissipation relations, and applies both to integrable and non integrable systems. Possible applications of the method include an analytical method to compute of the rate of equilibration, and the study of systems coupled locally to multiple reservoirs. Our analysis highlights the limits of applicability of the common Lindblad approaches to study strongly driven systems. Whether our method can be applied to study this regime or not is an open question.