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 to the modeling 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 while still being computationally tractable.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 to the modeling 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 while still being computationally tractable.

arXiv:2406.05030The Journal of Chemical PhysicsAug 21, 20247 citations

Tutorial on the stochastic simulation of dissipative quantum oscillators

CR Hogg (21966221), J Glatthard (21965201), F Cerisola (21945560) +1 more

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.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.

Aug 2, 20254 citations

Semiclassical asymptotics of quantum stochastic equations

V. P. Belavkin, Vassili Nikitich Kolokoltsov

Theoretical and Mathematical PhysicsNov 1, 199110 citations

Coupling Classical and Quantum Variables using Continuous Quantum Measurement Theory

Lajos Diósi, J. J. Halliwell

Continuous quantum measurement theory is used to construct a phenomenological description of the interaction of a quasiclassical variable $X$ with a quantum variable $x$ , where the quasiclassical nature of $X$ is assumed to have come about as a result of decoherence. The state of the quantum subsystem evolves according to the stochastic nonlinear Schr\"odinger equation of a continuously measured system, and the classical system couples to a stochastic $c$ number $\overline{x}(t)$ representing the imprecisely measured value of $x$ . The theory gives intuitively sensible results even when the quantum system starts out in a superposition of well-separated localized states.Continuous quantum measurement theory is used to construct a phenomenological description of the interaction of a quasiclassical variable $X$ with a quantum variable $x$, where the quasiclassical nature of $X$ is assumed to have come about as a result of decoherence. The state of the quantum subsystem evolves according to the stochastic nonlinear Schr\"odinger equation of a continuously measured system, and the classical system couples to a stochastic $c$ number $\overline{x}(t)$ representing the imprecisely measured value of $x$. The theory gives intuitively sensible results even when the quantum system starts out in a superposition of well-separated localized states.

arXiv:quant-ph/9705008Physical Review LettersOct 5, 199884 citations

Stochastic Processes in Quantum Systems

C. V. Heer

Elsevier eBooksJan 1, 19721 citation

Continuous quantum measurement theory is used to construct a phenomenological description of the interaction of a quasiclassical variable

X

with a quantum variable

x

, where the quasiclassical nature of

X

is assumed to have come about as a result of decoherence. The state of the quantum subsystem evolves according to the stochastic nonlinear Schr\"odinger equation of a continuously measured system, and the classical system couples to a stochastic

c

number

\overline{x}(t)

representing the imprecisely measured value of

x

. The theory gives intuitively sensible results even when the quantum system starts out in a superposition of well-separated localized states.