Effective Hamiltonian approach to the exact dynamics of open system by complex discretization approximation for environment

• URL: http://arxiv.org/abs/2303.06584v4
• Date: Mon, 27 May 2024 09:50:05 GMT
• Title: Effective Hamiltonian approach to the exact dynamics of open system by complex discretization approximation for environment
• Authors: H. T. Cui, Y. A. Yan, M. Qin, X. X. Yi,
• Abstract summary: This paper proposes a noval generalization of the discretization approximation method in the complex plane using complex Gauss quadratures. The effective Hamiltonian can be constructed by this way, which is non-Hermitian and demonstrates the complex energy modes with negative imaginary part.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: The discretization approximation method commonly used to simulate the open dynamics of system coupled to the environment in continuum often suffers from the recurrence. To address this issue, this paper proposes a noval generalization of the discretization approximation method in the complex plane using complex Gauss quadratures. The effective Hamiltonian can be constructed by this way, which is non-Hermitian and demonstrates the complex energy modes with negative imaginary part, describing accurately the dissipative dynamics of the system. This method is applied to examine the dynamics in two exactly solvable models: the dephasing model and the single-excitation open dynamics in the Aubry-Andr\'{e}-Harper model. This approach not only significantly reduces recurrence and improve the effectiveness of calculation, but also provide the microscopic viewpoint on the dynamics of system through the effective Hamiltonian. In addition, a simple relationship between the parameters in computation and the effectiveness of evaluation is also established.

Related papers

• Reconstruction of dynamic systems using genetic algorithms with dynamic search limits [0.0]
  evolutionary computing techniques are presented to estimate the governing equations of a dynamical system using time-series data. Some of the main contributions of the present study are an adequate modification of the genetic algorithm to remove terms with minimal contributions, and a mechanism to escape local optima. Our results demonstrate a reconstruction with an Integral Square Error below 0.22 and a coefficient of determination R-squared of 0.99 for all systems.
  arXiv  Detail & Related papers  (2024-12-03T22:58:25Z)
• Statistical Mechanics of Dynamical System Identification [2.8820361301109365]
  We develop a statistical mechanics approach to analyze sparse equation discovery algorithms. We provide a method for closed-loop inference, estimating the noise in a given model. This perspective of sparse equation discovery is versatile and can be adapted to various other equation discovery algorithms.
  arXiv  Detail & Related papers  (2024-03-04T04:32:28Z)
• Response Theory via Generative Score Modeling [0.0]
  We introduce an approach for analyzing the responses of dynamical systems to external perturbations that combines score-based generative modeling with the Generalized Fluctuation-Dissipation Theorem (GFDT) The methodology enables accurate estimation of system responses, including those with non-Gaussian statistics.
  arXiv  Detail & Related papers  (2024-02-01T21:38:10Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• Structure-Preserving Learning Using Gaussian Processes and Variational Integrators [62.31425348954686]
  We propose the combination of a variational integrator for the nominal dynamics of a mechanical system and learning residual dynamics with Gaussian process regression. We extend our approach to systems with known kinematic constraints and provide formal bounds on the prediction uncertainty.
  arXiv  Detail & Related papers  (2021-12-10T11:09:29Z)
• Hybridized Methods for Quantum Simulation in the Interaction Picture [69.02115180674885]
  We provide a framework that allows different simulation methods to be hybridized and thereby improve performance for interaction picture simulations. Physical applications of these hybridized methods yield a gate complexity scaling as $log2 Lambda$ in the electric cutoff. For the general problem of Hamiltonian simulation subject to dynamical constraints, these methods yield a query complexity independent of the penalty parameter $lambda$ used to impose an energy cost.
  arXiv  Detail & Related papers  (2021-09-07T20:01:22Z)
• Multiplicative noise and heavy tails in stochastic optimization [62.993432503309485]
  empirical optimization is central to modern machine learning, but its role in its success is still unclear. We show that it commonly arises in parameters of discrete multiplicative noise due to variance. A detailed analysis is conducted in which we describe on key factors, including recent step size, and data, all exhibit similar results on state-of-the-art neural network models.
  arXiv  Detail & Related papers  (2020-06-11T09:58:01Z)
• On dissipative symplectic integration with applications to gradient-based optimization [77.34726150561087]
  We propose a geometric framework in which discretizations can be realized systematically. We show that a generalization of symplectic to nonconservative and in particular dissipative Hamiltonian systems is able to preserve rates of convergence up to a controlled error.
  arXiv  Detail & Related papers  (2020-04-15T00:36:49Z)
• Generalized Kernel-Based Dynamic Mode Decomposition [0.0]
  We devise an algorithm based on low rank constraint optimization and kernel-based computation that generalizes a recent approach called " Kernel-based dynamic mode decomposition" This new algorithm is characterized by a gain in approximation accuracy, as evidenced by numerical simulations, and in computational complexity.
  arXiv  Detail & Related papers  (2020-02-11T13:50:00Z)
• Analysis of Bayesian Inference Algorithms by the Dynamical Functional Approach [2.8021833233819486]
  We analyze an algorithm for approximate inference with large Gaussian latent variable models in a student-trivial scenario. For the case of perfect data-model matching, the knowledge of static order parameters derived from the replica method allows us to obtain efficient algorithmic updates.
  arXiv  Detail & Related papers  (2020-01-14T17:22:02Z)

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.