Failure of the mean-field Hartree approximation for a bosonic many-body system with non-Hermitian Hamiltonian

• URL: http://arxiv.org/abs/2601.13038v1
• Date: Mon, 19 Jan 2026 13:20:22 GMT
• Title: Failure of the mean-field Hartree approximation for a bosonic many-body system with non-Hermitian Hamiltonian
• Authors: Matias Ginzburg, Giacomo De Palma, Simone Rademacher,
• Abstract summary: We analytically solve a model of bosonic qubits with two-body interactions generated by a purely anti-Hermitian Hamiltonian.<n>We show that such a limit does not agree with the solution of the non-Hermitian Hartree evolution equation.
• Score: 2.931240348160871
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Mean-field Hartree theory is a central tool for reducing interacting many-body dynamics to an effective nonlinear one-particle evolution. This approximation has been employed also when the Hamiltonian that governs the many-body dynamics is not Hermitian. Indeed, non-Hermitian Hamiltonians model particle gain/loss or the evolution of open quantum systems between consecutive quantum jumps. Furthermore, the validity of the Hartree approximation for generic non-Hermitian Hamiltonians lies at the basis of a quantum algorithm for nonlinear differential equations. In this work, we show that this approximation can fail. We analytically solve a model of $N$ bosonic qubits with two-body interactions generated by a purely anti-Hermitian Hamiltonian, determine an analytic expression for the limit for $N\to\infty$ of the one-particle marginal state and show that such a limit does not agree with the solution of the non-Hermitian Hartree evolution equation. We further show that there exists an initial condition such that the exact one-particle marginal state undergoes a finite-time transition to a mixed state, a phenomenon that is completely absent in the case of Hermitian Hamiltonians. Our findings challenge the validity of the mean-field Hartree approximation for non-Hermitian Hamiltonians, and call for additional conditions for the validity of the mean-field regime to model the dynamics of particle gain and loss and the open-system dynamics in bosonic many-body systems.

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