Time dependent Markovian master equation beyond the adiabatic limit

• URL: http://arxiv.org/abs/2304.06166v1
• Date: Wed, 12 Apr 2023 21:33:12 GMT
• Title: Time dependent Markovian master equation beyond the adiabatic limit
• Authors: Giovanni Di Meglio, Martin B. Plenio, Susana F. Huelga
• Abstract summary: We develop a Markovian master equation that models the evolution of systems subject to arbitrary driving and control fields. We demonstrate the reliability and broad scope of our approach by benchmarking the solutions of the derived reduced time evolution against numerically exact simulations.
• Score: 1.6114012813668934
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a Markovian master equation that models the evolution of systems subject to arbitrary driving and control fields. Our approach combines time rescaling and weak-coupling limits for the system-environment interaction with a secular approximation. The derivation makes use of the adiabatic time evolution operator in a manner that allows for the efficient description of strong driving, while recovering the adiabatic master equation in the appropriate limit. To illustrate the effectiveness of our approach, we apply it to the paradigmatic case of a two-level (qubit) system subjected to a form of periodic driving that remains unsolvable using a Floquet representation. We demonstrate the reliability and broad scope of our approach by benchmarking the solutions of the derived reduced time evolution against numerically exact simulations using tensor networks. Our results provide rigorous conditions that must be satisfied by phenomenological master equations for driven systems that do not rely on first principles derivations.

Related papers

• Counterdiabatic Driving for Periodically Driven Systems [0.0]
  Periodically driven systems have emerged as a useful technique to engineer the properties of quantum systems. We develop a technique to capture nonperturbative photon resonances and obtain high-fidelity protocols.
  arXiv  Detail & Related papers  (2023-10-04T11:08:19Z)
• Semiclassical descriptions of dissipative dynamics of strongly interacting Bose gases in optical lattices [0.0]
  We develop methods for describing real-time dynamics of dissipative Bose-Hubbard systems in a strongly interacting regime. We numerically demonstrate that the discrete TWA approach is able to qualitatively capture the continuous quantum Zeno effect on dynamics.
  arXiv  Detail & Related papers  (2023-07-30T08:39:06Z)
• Finite-time Landauer principle beyond weak coupling [0.0]
  We develop a finite-time version of Landauer's principle for a bit encoded in the occupation of a single fermionic mode. We characterize a finite-time correction to Landauer's bound, fully taking into account non-markovian and strong coupling effects.
  arXiv  Detail & Related papers  (2022-11-03T18:00:13Z)
• Semi-supervised Learning of Partial Differential Operators and Dynamical Flows [68.77595310155365]
  We present a novel method that combines a hyper-network solver with a Fourier Neural Operator architecture. We test our method on various time evolution PDEs, including nonlinear fluid flows in one, two, and three spatial dimensions. The results show that the new method improves the learning accuracy at the time point of supervision point, and is able to interpolate and the solutions to any intermediate time.
  arXiv  Detail & Related papers  (2022-07-28T19:59:14Z)
• Canonically consistent quantum master equation [68.8204255655161]
  We put forth a new class of quantum master equations that correctly reproduce the state of an open quantum system beyond the infinitesimally weak system-bath coupling limit. Our method is based on incorporating the knowledge of the reduced steady state into its dynamics.
  arXiv  Detail & Related papers  (2022-05-25T15:22:52Z)
• Lindblad master equations for quantum systems coupled to dissipative bosonic modes [0.0]
  We derive Lindblad master equations for a subsystem whose dynamics is coupled to bosonic modes. We apply this formalism to the dissipative Dicke model and derive a Lindblad master equation for the atomic spins. This master equation accurately predicts the Dicke phase transition and gives the correct steady state.
  arXiv  Detail & Related papers  (2022-03-07T11:21:48Z)
• Deep Learning Approximation of Diffeomorphisms via Linear-Control Systems [91.3755431537592]
  We consider a control system of the form $dot x = sum_i=1lF_i(x)u_i$, with linear dependence in the controls. We use the corresponding flow to approximate the action of a diffeomorphism on a compact ensemble of points.
  arXiv  Detail & Related papers  (2021-10-24T08:57:46Z)
• Flow Renormalization and Emergent Prethermal Regimes of Periodically-Driven Quantum Systems [0.0]
  We develop a flow renormalization approach for periodically-driven quantum systems. We show that the renormalization flow has an elegant representation in terms of a flow of matrix product operators.
  arXiv  Detail & Related papers  (2021-03-12T19:02:20Z)
• Policy Analysis using Synthetic Controls in Continuous-Time [101.35070661471124]
  Counterfactual estimation using synthetic controls is one of the most successful recent methodological developments in causal inference. We propose a continuous-time alternative that models the latent counterfactual path explicitly using the formalism of controlled differential equations.
  arXiv  Detail & Related papers  (2021-02-02T16:07:39Z)
• Fast and differentiable simulation of driven quantum systems [58.720142291102135]
  We introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical methods. We show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
  arXiv  Detail & Related papers  (2020-12-16T21:43:38Z)
• Assessment of weak-coupling approximations on a driven two-level system under dissipation [58.720142291102135]
  We study a driven qubit through the numerically exact and non-perturbative method known as the Liouville-von equation with dissipation. We propose a metric that may be used in experiments to map the regime of validity of the Lindblad equation in predicting the steady state of the driven qubit.
  arXiv  Detail & Related papers  (2020-11-11T22:45:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.