Time-dependent variational Monte Carlo

The time-dependent variational Monte Carlo (t-VMC) method is a quantum Monte Carlo approach to study the dynamics of closed, non-relativistic quantum systems in the context of the quantum many-body problem. It is an extension of the variational Monte Carlo method, in which a time-dependent pure quantum state is encoded by some variational wave function, generally parametrized as Ψ ( X , t ) = exp ⁡ ( ∑ k a k ( t ) O k ( X ) ) {\displaystyle \Psi (X,t)=\exp \left(\sum _{k}a_{k}(t)O_{k}(X)\right)} where the complex-valued a k ( t ) {\displaystyle a_{k}(t)} are time-dependent variational parameters, X {\displaystyle X} denotes a many-body configuration and O k ( X ) {\displaystyle O_{k}(X)} are time-independent operators that define the specific ansatz.

Source: Wikipedia — Time-dependent variational Monte Carlo (CC BY-SA 4.0)

Time-dependent variational Monte Carlo

The time-dependent variational Monte Carlo (t-VMC) method is a quantum Monte Carlo approach to study the dynamics of closed, non-relativistic quantum systems in the context of the quantum many-body problem. It is an extension of the variational Monte Carlo method, in which a time-dependent pure quantum state is encoded by some variational wave function, generally parametrized as Ψ ( X , t ) = exp ⁡ ( ∑ k a k ( t ) O k ( X ) ) {\displaystyle \Psi (X,t)=\exp \left(\sum _{k}a_{k}(t)O_{k}(X)\right)} where the complex-valued a k ( t ) {\displaystyle a_{k}(t)} are time-dependent variational parameters, X {\displaystyle X} denotes a many-body configuration and O k ( X ) {\displaystyle O_{k}(X)} are time-independent operators that define the specific ansatz.

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Source: Wikipedia "Time-dependent variational Monte Carlo" · CC BY-SA 4.0

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