Stochastic Schr\"odinger equation approach to real-time dynamics of Anderson-Holstein impurities: an open quantum system perspective

• URL: http://arxiv.org/abs/2309.08890v1
• Date: Sat, 16 Sep 2023 06:03:54 GMT
• Title: Stochastic Schr\"odinger equation approach to real-time dynamics of Anderson-Holstein impurities: an open quantum system perspective
• Authors: Zhen Huang, Limin Xu and Zhennan Zhou
• Abstract summary: We develop a framework to simulate dynamics of Anderson-Holstein impurities coupled to a continuous fermionic bath. We show that such an SSE treatment provides a middle ground between numerically expansive microscopic simulations and master equations.
• Score: 3.105656247358225
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop a stochastic Schr\"odinger equation (SSE) framework to simulate real-time dynamics of Anderson-Holstein (AH) impurities coupled to a continuous fermionic bath. The bath degrees of freedom are incorporated through fluctuating terms determined by exact system-bath correlations, which is derived in an ab initio manner. We show that such an SSE treatment provides a middle ground between numerically expansive microscopic simulations and macroscopic master equations. Computationally, the SSE model enables efficient numerical methods for propagating stochastic trajectories. We demonstrate that this approach not only naturally provides microscopically-detailed information unavailable from reduced models, but also captures effects beyond master equations, thus serves as a promising tool to study open quantum dynamics emerging in physics and chemistry.

Related papers

• Post-Markovian master equation à la microscopic collisional model [0.0]
  We derive a positive post-Markovian master equation (PMME) from a microscopic Markovian collisional model framework. We also investigate thermalization using the derived equation, revealing that the post-Markovian dynamics accelerates the thermalization process.
  arXiv  Detail & Related papers  (2024-11-25T19:18:10Z)
• 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)
• Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation [59.45669299295436]
  We propose a Monte Carlo PDE solver for training unsupervised neural solvers. We use the PDEs' probabilistic representation, which regards macroscopic phenomena as ensembles of random particles. Our experiments on convection-diffusion, Allen-Cahn, and Navier-Stokes equations demonstrate significant improvements in accuracy and efficiency.
  arXiv  Detail & Related papers  (2023-02-10T08:05:19Z)
• An efficient method for quantum impurity problems out of equilibrium [0.0]
  We introduce an efficient method to simulate dynamics of an interacting quantum impurity coupled to non-interacting fermionic reservoirs. We apply our method to study quantum quenches and transport in an Anderson impurity model, including highly non-equilibrium setups. This approach will provide new insights into dynamical properties of mesoscopic devices and correlated materials.
  arXiv  Detail & Related papers  (2022-11-18T14:57:29Z)
• Non-equilibrium quantum impurity problems via matrix-product states in the temporal domain [0.0]
  We propose an approach to analyze impurity dynamics based on the matrix-product state (MPS) representation of the Feynman-Vernon influence functional (IF) We obtain explicit expressions of the wave function for a family of one-dimensional reservoirs, and analyze the scaling of TE with the evolution time for different reservoir's initial states. The approach can be applied to a number of experimental setups, including highly non-equilibrium transport via quantum dots and real-time formation of impurity-reservoir correlations.
  arXiv  Detail & Related papers  (2022-05-10T16:05:25Z)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• 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)
• Visualizing spinon Fermi surfaces with time-dependent spectroscopy [62.997667081978825]
  We propose applying time-dependent photo-emission spectroscopy, an established tool in solid state systems, in cold atom quantum simulators. We show in exact diagonalization simulations of the one-dimensional $t-J$ model that the spinons start to populate previously unoccupied states in an effective band structure. The dependence of the spectral function on the time after the pump pulse reveals collective interactions among spinons.
  arXiv  Detail & Related papers  (2021-05-27T18:00:02Z)
• Generalized Discrete Truncated Wigner Approximation for Nonadiabtic Quantum-Classical Dynamics [0.0]
  We introduce a linearized semiclassical method, the generalized discrete truncated Wigner approximation (GDTWA) GDTWA samples the electron degrees of freedom in a discrete phase space, and forbids an unphysical growth of electronic state populations. Our results suggest that the method can be very adequate to treat challenging nonadiabatic dynamics problems in chemistry and related fields.
  arXiv  Detail & Related papers  (2021-04-14T21:53:35Z)
• Quantum Markov Chain Monte Carlo with Digital Dissipative Dynamics on Quantum Computers [52.77024349608834]
  We develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. We evaluate the algorithm by simulating thermal states of the transverse Ising model.
  arXiv  Detail & Related papers  (2021-03-04T18:21:00Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)

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.