Papers › Exponential unitary integrators for nonseparable quantum Hamiltonians
Exponential unitary integrators for nonseparable quantum Hamiltonians
Maximilian Ciric, Denys I. Bondar, Ole Steuernagel
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Quantum Hamiltonians containing nonseparable products of non-commuting operators, such as x̂ᵐ p̂ⁿ, are problematic for numerical studies using split-operator techniques since such products cannot be represented as a sum of separable terms, such as T(p̂) + V(x̂). In the case of classical physics, Chin [Phys. Rev. E 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 x̂² p̂² + p̂² x̂². The general applicability of Chin's approach to any Hamiltonian of polynomial form is proven.
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