Relaxations in few-body systems

D. Blume

Lawrence Phillips

M. Pelc, David Dams, Abhishek Ghosh +6 more

This paper addresses the challenge of modeling relaxation dynamics in quantum many-body systems, specifically focusing on electrons in graphene nanoflakes. While quantum many-body techniques effectively describe dynamics up to a few particles, these approaches become computationally intractable for large systems. Larger systems may be tackled with a single-particle approach that, however, struggles to incorporate relaxation effects. Existing relaxation models encounter issues such as an inability to capture system complexity and violation of the Pauli principle. In this paper, we propose a single-particle model that accounts for various relaxation effects at the crossroads of quantum optics and solid-state photonics, that overcomes the limitations of previous models. Our approach is rooted in the quantum-optical Lindblad model, where relaxation rates are deactivated once the target levels saturate due to the Pauli principle. This approach is referred to as the saturated-Lindblad model. To validate the predictions of the saturated-Lindblad model, we confront them against phenomenological and many-body physics models in low-dimensional systems, including atomic chains and graphene nanoflakes. Remarkably, the saturated-Lindblad model exhibits excellent agreement with few-body calculations, distinguishing itself from other existing approaches. Moreover, by assigning different relaxation rates to different transitions, we successfully reproduce cascade deexcitation dynamics and predict emission spectra. The saturated-Lindblad model offers the ability to describe dynamics in systems of practical sizes, encompassing a wide range of structures that can be effectively captured within the single-particle description.

Petar Stipanović, Leandra Vranješ Markić, Andrii Gudyma +1 more

Parvinder Solanki, Igor Lesanovsky, Gabriele Perfetto

Speeding up the relaxation dynamics of many-body quantum systems is important in a variety of contexts, including quantum computation and state preparation. We demonstrate that such acceleration can be universally achieved via transient stochastic resetting. This means that during an initial time interval of finite duration, the dynamics is interrupted by resets that take the system to a designated state at randomly selected times. We illustrate this idea for few-body open systems and also for a challenging many-body case, where a first-order phase transition leads to a divergence of relaxation time. In all scenarios, a significant and sometimes even exponential acceleration in reaching the stationary state is observed, similar to the so-called Mpemba effect. The universal nature of this speedup lies in the fact that the design of the resetting protocol only requires knowledge of a few macroscopic properties of the target state, such as the order parameter of the phase transition, while it does not necessitate any fine-tuned manipulation of the initial state.

Eduardo Jonathan Torres-Herrera, Davida Kollmar, Léa Ferreira dos Santos

We provide an overview of our numerical and analytical studies of isolated interacting quantum systems that are abruptly quenched out of equilibrium instantaneously. We describe the relaxation process to a new equilibrium and obtain lower bounds for the relaxation time of full random matrices and realistic systems with two-body interactions. We show that the size of the time fluctuations after relaxation decays exponentially with system size for systems without too many degeneracies. We also discuss the conditions for thermalization and demonstrate that it can happen after local and global quenches in space. The analyses are developed for systems, initial states, and few-body observables accessible to experiments with optical lattices.