M.Sc Student | Klempner Anat |
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Subject | Thermalization in Open Quantum Systems and Density Matrix in Steady States far from Equilibrium |

Department | Department of Physics |

Supervisor | Professor Daniel Podolsky |

Full Thesis text |

We study the statistical mechanics of
open quantum systems coupled to external baths locally near the edges of the
system. We consider the Lindblad formalism to treat the dynamics of such
systems, and focus on a class of problems that allow for analytical solutions
of the steady state and equilibration properties. In particular, we examine the
quantum XY Model and the transverse field Ising model in 1D, with the outer
spins coupled to external baths. We obtain the steady state properties of this
system using Third Quantization, which provides an analytical method for solving
the Lindblad equation. Numerical methods, Exact Diagonalization and Density
Matrix Renormalization Group, are used as benchmarks for this method. We
develop a method to extract the exact steady state density matrix, and examine
the system for different sets of parameters and different couplings to the
external baths. In the case of the XY model coupled to a bath on one side only,
we found that the density matrix in steady-state factorizes into a product of
density matrices in individual sites. For more general cases the structure of
the density matrix is more complex. For instance, when the XY model is driven
asymmetrically on both ends, we find correlations that are restricted to
nearest neighbor sites. We provide a systematic study of current and its fluctuations
in the driven XY model. Finally, we examine the relaxation time of the system
to steady-state. We find that when both edges of the Ising model are coupled to
baths the relaxation time exhibits *L*^{3} behavior, where L is
the number of spins. However when only one edge is coupled to a bath, we find a
transition between *L*^{3} and exponential behavior. This
transition occurs at the critical field of the model in zero temperature. We
provide a simple toy model to explain this result.