Stochastic simulation of dissipative quantum oscillators

Abstract

Generic open quantum systems are notoriously difficult to simulate unless one looks at specific regimes. In contrast, classical dissipative systems can often be effectively described by stochastic processes, which are generally less computationally expensive. Here, we use the paradigmatic case of a dissipative quantum oscillator to give a pedagogic introduction into the modelling of open quantum systems using quasiclassical methods, i.e. classical stochastic methods that use a 'quantum' noise spectrum to capture the influence of the environment on the system. Such quasiclassical methods have the potential to offer insights into the impact of the quantum nature of the environment on the dynamics of the system of interest whilst still being computationally tractable.

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References in corpus (26)

• Quantum thermal transport in nanostructures
• Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials
• Fundamental Aspects of Quantum Brownian Motion
• Nuclear quantum effects in solids using a colored-noise thermostat
• Markovian Master Equations: A Critical Study
• Colored-noise thermostats à la carte
• Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities
• Accelerating the convergence of path integral dynamics with a generalized Langevin equation
• Heat transport in harmonic lattices
• Open quantum system dynamics and the mean force Gibbs state
• Quantum thermal transport from classical molecular dynamics
• Current-induced atomic dynamics, instabilities, and Raman signals: Quasi-classical Langevin equation approach
• Exact analytical solutions to the master equation of quantum Brownian motion for a general environment
• The equilibrium states of open quantum systems in the strong coupling regime
• Decoherence in a scalable adiabatic quantum computer
• Generalized Gibbs state with modified Redfield solution: Exact agreement up to second order
• Exact dynamics of non-additive environments in non-Markovian open quantum systems
• Weak and ultrastrong coupling limits of the quantum mean force Gibbs state
• Fundamental limits for cooling of linear quantum refrigerators
• New analytic solution for the heat flow through a general harmonic network
• Hamiltonian of mean force in the weak-coupling and high-temperature approximations and refined quantum master equations
• Dynamics of Open Quantum Systems II, Markovian Approximation
• Numerical evaluation and robustness of the quantum mean force Gibbs state
• Temperature-dependent thermal transport of single molecular junctions from semi-classical Langevin molecular dynamics
• Accounting for Quantum Effects in Atomistic Spin Dynamics
• SpiDy.jl: open-source Julia package for the study of non-Markovian stochastic dynamics

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• Simulating spin biology using a digital quantum computer: Prospects on a near-term quantum hardware emulator
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• SpiDy.jl: open-source Julia package for the study of non-Markovian stochastic dynamics
• Engineering the uncontrollable: Steering noisy spin-correlated radical-pairs with coherent and incoherent control
• Lindblad quantum dynamics from correlation functions of classical spin chains