Scattering theory using smeared non-Hermitian potentials

0333961 - ÚJF 2010 RIV US eng J - Journal Article
Znojil, Miloslav
Scattering theory using smeared non-Hermitian potentials.
Physical Review D: Particles, Fields, Gravitation and Cosmology. Roč. 80, č. 4 (2009), 045009/1-045009/12. ISSN 1550-7998
R&D Projects: GA MŠMT LC06002; GA ČR GA202/07/1307
Institutional research plan: CEZ:AV0Z10480505
Keywords : symmetric quantum-mechanics * pseudo-hermiticity * real spectrum
Subject RIV: BE - Theoretical Physics
Impact factor: 4.922, year: 2009

Local non-Hermitian potentials V(x)not equal V-*(x) can, sometimes, generate stable bound states Sigma(x) at real energies. Unfortunately, the idea [based on the use of a non-Dirac ad hoc metric Theta(x,x('))not equal delta(x-x(')) in Hilbert space] cannot directly be transferred to scattering due to the related loss of the asymptotic observability of x [cf. H. F. Jones, Phys. Rev. D 78, 065032 (2008)]. We argue that for smeared (typically, nonlocal or momentum-dependent) potentials V not equal V-dagger this difficulty may be circumvented. A return to the usual (i.e., causal and unitary) quantum scattering scenario is then illustrated via an exactly solvable multiple-scattering example. In it, the anomalous loss of observability of the coordinate remains restricted to a small vicinity of the scattering centers.
Permanent Link: http://hdl.handle.net/11104/0178813