Stochastic Representation of Non-Markovian Fermionic Quantum Dissipation

Abstract

Quantum Brownian motion plays a fundamental role in many areas of modern physics. In the path-integral formulation, the environmental quantum fluctuations driving the system dynamics can be characterized by auxiliary stochastic fields. For fermion bath environment the stochastic fields are Grassmann-valued, and cannot be represented by conventional classical numbers. In this Letter, we propose a strategy to map the nonclassical Grassmann fields onto Gaussian white noises along with a set of quantized pseudo-states. This results in a numerically feasible stochastic equation of motion (SEOM) method for fermionic open systems. The SEOM yields exact physical observables for noninteracting systems, and accurate approximate results for interacting systems. The practicality and accuracy of the proposed SEOM are exemplified by direct stochastic simulations conducted on a single-impurity Anderson model.

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Cited by in corpus (12)

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• Local Temperatures Out of Equilibrium
• Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. I. Formalism
• A quantum-classical decomposition of Gaussian quantum environments: a stochastic pseudomode model
• Towards Quantum Simulation of Non-Markovian Open Quantum Dynamics: A Universal and Compact Theory
• Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. II. Numerical Implementation
• Modeling the unphysical pseudomode model with physical ensembles: simulation, mitigation, and restructuring of non-Markovian quantum noise
• About the performance of perturbative treatments of the spin-boson dynamics within the hierarchical equations of motion approach
• High-order strong methods for stochastic differential equations with colored noises
• Machine learning meets $\mathfrak{su}(n)$ Lie algebra: Enhancing quantum dynamics learning with exact trace conservation
• Input-Output Hierarchical Equations Of Motion
• Toward Quantum-Aware Machine Learning: Improved Prediction of Quantum Dissipative Dynamics via Complex Valued Neural Networks