Long-range Kitaev chain in a thermal bath: Analytic techniques for time-dependent systems and environments
arXiv:2204.07595 · doi:10.1140/epjs/s11734-025-01788-5
Abstract
We construct and solve a "minimal model" with which nonequilibrium phenomena in many-body open quantum systems can be studied analytically under time-dependent parameter changes in the system and/or the bath. Coupling a suitable configuration of baths to a Kitaev chain, we self-consistently derive a Lindblad master equation which, at least in the absence of explicit time dependencies, leads to thermalization. Using the method of Third Quantization we derive time-evolution equations for the correlation matrix, which we relate to the occupation of the system's quasiparticle modes. These results permit analytic and efficient numeric descriptions of the nonequilibrium dynamics of open Kitaev chains under a wide range of driving protocols, which in turn facilitate the investigation of the interplay between bath-induced dissipation and the generation of coherent excitations by nonadiabatic driving. We advertise this minimal model of maximum simplicity for the study of finite-temperature generalizations of Kibble-Zurek ramps, Floquet physics, and many other nonequilibrium protocols of quantum many-body systems driven by time-varying parameters and/or temperatures.
12 pages, 4 figures; companion paper to "Universal cooling dynamics towards a quantum critical point" by the same authors and submitted on the same day
References in corpus (8)
- Third quantization: a general method to solve master equations for quadratic open Fermi systems
- Adiabatic dynamics in open quantum critical many-body systems
- Self-consistent microscopic derivation of Markovian master equations for open quadratic quantum systems
- Time-dependent Correlation Functions in Open Quadratic Fermionic Systems
- Kibble-Zurek scaling due to environment temperature quench in the transverse field Ising model
- Universal cooling dynamics toward a quantum critical point
- Reducing defect production in random transverse-field Ising chains by inhomogeneous driving fields
- Universal Quench Dynamics of an Open Quantum System