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arXiv · 2211.08155

Exponential unitary integrators for nonseparable quantum Hamiltonians

Maximilian Ciric·Denys I. Bondar·Ole Steuernagel
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Abstract

Quantum Hamiltonians containing nonseparable products of non-commuting operators, such as $\hat{\bf x}^m \hat{\bf p}^n$, are problematic for numerical studies using split-operator techniques since such products cannot be represented as a sum of separable terms, such as $T(\hat{\bf p}) + V(\hat{\bf x})$. In the case of classical physics, Chin [Phys. Rev. E $\bf 80$, 037701 (2009)] developed a procedure to approximately represent nonseparable terms in terms of separable ones. We extend Chin's idea to quantum systems. We demonstrate our findings by numerically evolving the Wigner distribution of a Kerr-type oscillator whose Hamiltonian contains the nonseparable term $\hat{\bf x}^2 \hat{\bf p}^2 + \hat{\bf p}^2 \hat{\bf x}^2$. The general applicability of Chin's approach to any Hamiltonian of polynomial form is proven.

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Maximilian Ciric, Denys I. Bondar, Ole Steuernagel. 2022-11-15. Exponential unitary integrators for nonseparable quantum Hamiltonians. https://doi.org/10.1140/epjp/s13360-023-03819-3

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