In interacting quantum many-body systems, relaxation toward equilibrium reflects a competition between internal chaotic dynamics and environmental dissipation. While conventional Markovian baths typically produce exponential decay, non-Markovian dissipation can give rise to more intricate behavior, including algebraic relaxation. We study an open Sachdev-Ye-Kitaev (SYK) model coupled to a pseudogapped fermionic bath, using the Keldysh formalism to compute steady-state correlations in the large- $N$ limit. Our results uncover a rich dynamical phase diagram, with regimes of bath-driven power-law relaxation, chaos-driven exponential decay, and an intermediate pre-relaxation phase where exponential decay crosses over to algebraic decay. These findings demonstrate that non-Markovian environments can qualitatively reshape relaxation mechanisms in strongly correlated quantum many-body systems.In interacting quantum many-body systems, relaxation toward equilibrium reflects a competition between internal chaotic dynamics and environmental dissipation. While conventional Markovian baths typically produce exponential decay, non-Markovian dissipation can give rise to more intricate behavior, including algebraic relaxation. We study an open Sachdev-Ye-Kitaev (SYK) model coupled to a pseudogapped fermionic bath, using the Keldysh formalism to compute steady-state correlations in the large-$N$ limit. Our results uncover a rich dynamical phase diagram, with regimes of bath-driven power-law relaxation, chaos-driven exponential decay, and an intermediate pre-relaxation phase where exponential decay crosses over to algebraic decay. These findings demonstrate that non-Markovian environments can qualitatively reshape relaxation mechanisms in strongly correlated quantum many-body systems.

cond-mat.stat-mechCross-listedarXiv:2603.10815Physical review. B./Physical review. BMar 12, 20260 citations

Non-Markovian quantum dynamics from environmental relaxation

Stefan K. Possanner, Benjamin A. Stickler

We consider the dynamics of composite quantum systems in the particular case that the state operator relaxes towards the Born approximation. For this we augment the von Neumann equation by a relaxation operator imposing a finite relaxation time ${\ensuremath{\tau}}_{r}$. Under the premise that the relaxation is the dominant process we obtain a hierarchy of non-Markovian master equations. The latter arises from an expansion of the total state operator in powers of the relaxation time ${\ensuremath{\tau}}_{r}$. In the Born-Markov limit ${\ensuremath{\tau}}_{r}\ensuremath{\rightarrow}0$ the Lindblad master equation is recovered. Higher-order contributions enable a systematic treatment of correlations and non-Markovian dynamics in a recursive manner.We consider the dynamics of composite quantum systems in the particular case that the state operator relaxes towards the Born approximation. For this we augment the von Neumann equation by a relaxation operator imposing a finite relaxation time ${\ensuremath{\tau}}_{r}$. Under the premise that the relaxation is the dominant process we obtain a hierarchy of non-Markovian master equations. The latter arises from an expansion of the total state operator in powers of the relaxation time ${\ensuremath{\tau}}_{r}$. In the Born-Markov limit ${\ensuremath{\tau}}_{r}\ensuremath{\rightarrow}0$ the Lindblad master equation is recovered. Higher-order contributions enable a systematic treatment of correlations and non-Markovian dynamics in a recursive manner.

Physical Review AJun 20, 20123 citations

Non-Markovian dynamics of quantum systems

Z. Kanokov

Nov 1, 20120 citations

Controle da não Markovianidade em sistemas quânticas abertos

Rafael Bruno Barbosa Lima

Open quantum systems have been aim of several theoretical and experimental studies over the last years.In particular, research related to non-Markovianity and how it influences the dynamics of the system has become relatively important, because this way we can have the return the initial quantum characteristics present in the system.In this thesis two related works were developed about the influence of non-Markovianity in open quantum systems.In the first, it was used a one qubit system in contact with a bosonic reservoir and also under the influence of a classic stochastic pumping, thus generating an effective coupling of the system with the stochastic noise and the thermal reservoir.Thus, it was investigated how the dynamics of the qubit is modified through the production of non-Markovianity in the system due to the effective coupling and also how the mean system energy, with and without pumping, behaves in both Markovian and non-Markovian regime.Additionally, an analysis of non-Markovianity production was performed using exponential, Gaussian and power law stochastic noises.Applying the Andersson, Cresser, Hall and Li (ACHL) measure, it was possible to make a comparison of how much non-Markovianity was produced for each stochastic noise.In the second work, a study was performed on how it is possible to generate the transition between Markovian to non-Markovian regimes through the control of the spin-lattice relaxation time of an ancillary qubit, which acts as an environment.The decoherence of the system was simulated through the formulation of quantum channels.In addition, it was discussed how the relaxation mechanism is modified by the action of an external magnetic field.Finally, an experimental demonstration of the model is presented and the experimental data were compared with the theoretically simulated ones.Open quantum systems have been aim of several theoretical and experimental studies over the last years.In particular, research related to non-Markovianity and how it influences the dynamics of the system has become relatively important, because this way we can have the return the initial quantum characteristics present in the system.In this thesis two related works were developed about the influence of non-Markovianity in open quantum systems.In the first, it was used a one qubit system in contact with a bosonic reservoir and also under the influence of a classic stochastic pumping, thus generating an effective coupling of the system with the stochastic noise and the thermal reservoir.Thus, it was investigated how the dynamics of the qubit is modified through the production of non-Markovianity in the system due to the effective coupling and also how the mean system energy, with and without pumping, behaves in both Markovian and non-Markovian regime.Additionally, an analysis of non-Markovianity production was performed using exponential, Gaussian and power law stochastic noises.Applying the Andersson, Cresser, Hall and Li (ACHL) measure, it was possible to make a comparison of how much non-Markovianity was produced for each stochastic noise.In the second work, a study was performed on how it is possible to generate the transition between Markovian to non-Markovian regimes through the control of the spin-lattice relaxation time of an ancillary qubit, which acts as an environment.The decoherence of the system was simulated through the formulation of quantum channels.In addition, it was discussed how the relaxation mechanism is modified by the action of an external magnetic field.Finally, an experimental demonstration of the model is presented and the experimental data were compared with the theoretically simulated ones.

Apr 3, 20200 citations

NON-MARKOVIAN DYNAMICS OF QUANTUM SYSTEMS

Dariusz Chruściński, Andrzej Kossakowski

QP-PQ, quantum probability and white noise analysisJan 1, 20110 citations

N

limit. Our results uncover a rich dynamical phase diagram, with regimes of bath-driven power-law relaxation, chaos-driven exponential decay, and an intermediate pre-relaxation phase where exponential decay crosses over to algebraic decay. These findings demonstrate that non-Markovian environments can qualitatively reshape relaxation mechanisms in strongly correlated quantum many-body systems.