## Action-at-a-distance in a solvable quantum model

Miloslav Znojil

Among quantum systems with finite Hilbert space a specific role is played by systems controlled by non-Hermitian Hamiltonian matrices $$H\neq H^\dagger$$ for which one has to upgrade the Hilbert-space metric by replacing the conventional form $$\Theta^{(Dirac)}=I$$ of this metric by a suitable upgrade $$\Theta^{(non−Dirac)}\neq I$$ such that the same Hamiltonian becomes self-adjoint in the new, upgraded Hilbert space, $$H=H\ddagger=\Theta^{−1}H^\dagger\Theta$$. The problems only emerge in the context of scattering where the requirement of the unitarity was found to imply the necessity of a non-locality in the interaction, compensated by important technical benefits in the short-range-nonlocality cases. In the present paper we show that an why these technical benefits (i.e., basically, the recurrent-construction availability of closed-form Hermitizing metrics $$\Theta^{(non−Dirac)}$$ can survive also in certain specific long-range-interaction models.

http://arxiv.org/abs/1410.3583
Quantum Physics (quant-ph)