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Broken Hermiticity phase transition in Bose-Hubbard model. (arXiv:1810.05771v1 [quant-ph])
来源于:arXiv
A new version of the change of the "phase" (i.e., of the set of observable
characteristics) of a quantum system is proposed. In a general scenario the
evolution is assumed generated, before the phase transition, by some standard
Hermitian Hamiltonian $H^{(before)}$, and, after the phase transition, by one
of the recently very popular non-standard, non-Hermitian (but hiddenly
Hermitian, i.e., still unitarity-guaranteeing) Hamiltonians $H^{(after)}$. For
consistency, a smoothness of matching between the two operators as well as
between the related physical Hilbert spaces must be guaranteed. The feasibility
of the idea is illustrated via the two-mode $(N-1)-$bosonic Bose-Hubbard
Hamiltonian. In $H^{(before)}=H^{(BH)}(\varepsilon)$ we use the decreasing real
$\varepsilon^{(before)} \to 0$. In the hiddenly Hermitian continuation
$H^{(after)}=H^{(BH)}(\tilde{\varepsilon})$ the imaginary part of the purely
imaginary $\tilde{\varepsilon}^{(after)}$ grows. The smoothness of the
transition occur 查看全文>>