Exponential Unitary Integrators for Nonseparable Quantum Hamiltonians

• URL: http://arxiv.org/abs/2211.08155v1
• Date: Tue, 15 Nov 2022 14:09:15 GMT
• Title: Exponential Unitary Integrators for Nonseparable Quantum Hamiltonians
• Authors: Maximilian Ciric, Denys I. Bondar and Ole Steuernagel
• Abstract summary: Quantum Hamiltonians containing nonseparable products of non-commuting operators are problematic for numerical studies. We extend Chin's idea to represent nonseparable terms in terms of separable ones.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum Hamiltonians containing nonseparable products of non-commuting operators, such as $\hat x^m \hat p^n$, are problematic for numerical studies using split-operator techniques since such products cannot be represented as a sum of separable terms, such as $T(\hat p) + V(\hat x)$. 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 $\hat x^2 \hat p^2 + \hat p^2 \hat x^2$. The general applicability of Chin's approach to any Hamiltonian of polynomial form is proven.

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