20.500.12556/RUL-182239 Transfer matrix approach to quantum systems subject to certain Lindblad evolution Solving for the time evolution of a many particle system whose dynamics is governed by Lindblad equation is hard. We extend the use of the transfer matrix approach to a class of Lindblad equations that admit a closed hierarchy of two point correlators. An example that we treat is the XX spin chain, i.e., free fermions, subject to the local onsite dephasing, but can be extended to other Hermitian dissipators, e.g., nonlocal dephasing. We find a simple expression of the Green's function in the Laplace domain. The method can be used to get analytical results in the thermodynamic limit, for instance, to get the evolution of the magnetization density and to explicitly see the crossover between ballistic and diffusive behavior, or to show that the correlations between operators at distance l decay with time as $1/t^{[l/2]+1/2}$. It also provides a fast numerical method to determine the evolution of the density with a complexity scaling with the system size more favorably than in previous methods, easily allowing one to study systems with $\sim 10^6$ spins. quantum mechanics quantum many-body systems 1-dimensional spin chains diffusion kvantna mehanika kvantni večdelčni sistemi enodimenzionalne spinske verige difuzija true false true Angleški jezik Slovenski jezik Članek v reviji 2026-05-05 08:58:50 2026-05-05 08:58:52 2026-05-06 04:29:06 0000-00-00 00:00:00 2025 0 0 Str. 174306-1-174306-11 iss. 17 Vol. 111 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 530.145 2469-9950 10.1103/PhysRevB.111.174306 276512515 https://journals.aps.org/prb/abstract/10.1103/PhysRevB.111.174306 1 97aa1dd0-484f-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=233311 PhysRevB.111.174306.pdf PhysRevB.111.174306.pdf 1 217F8A9A4509FD5DD1E36D36CD81C4E0 ea6ceaf47fa2291364ff4883f7bf13458182cb2723f2726890a669cd2e7b43f8 63af051d-4850-11f1-b0ab-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=233313 Fakulteta za matematiko in fiziko 0 0 0