Macroscopic thermalization by unitary time-evolution in the weakly perturbed two-dimensional Ising model --- An application of the Roos-Teufel-Tumulka-Vogel theorem

• URL: http://arxiv.org/abs/2409.09395v1
• Date: Sat, 14 Sep 2024 10:07:01 GMT
• Title: Macroscopic thermalization by unitary time-evolution in the weakly perturbed two-dimensional Ising model --- An application of the Roos-Teufel-Tumulka-Vogel theorem
• Authors: Hal Tasaki,
• Abstract summary: We study thermalization in the two-dimensional Ising model in the low-temperature phase. It is proved that, for most choices of the random perturbation, the unitary time evolution $e-i(hatH_L+lambdahatV)t$ brings the initial state into thermal equilibrium.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: To demonstrate the implication of the recent important theorem by Roos, Teufel, Tumulka, and Vogel [1] in a simple but nontrivial example, we study thermalization in the two-dimensional Ising model in the low-temperature phase. We consider the Hamiltonian $\hat{H}_L$ of the standard ferromagnetic Ising model with the plus boundary conditions and perturb it with a small self-adjoint operator $\lambda\hat{V}$ drawn randomly from the space of self-adjoint operators on the whole Hilbert space. Suppose that the system is initially in a classical spin configuration with a specified energy that may be very far from thermal equilibrium. It is proved that, for most choices of the random perturbation, the unitary time evolution $e^{-i(\hat{H}_L+\lambda\hat{V})t}$ brings the initial state into thermal equilibrium after a sufficiently long and typical time $t$, in the sense that the measurement result of the magnetization density at time $t$ almost certainly coincides with the spontaneous magnetization expected in the corresponding equilibrium.

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