General validity of reciprocity in quantum mechanics

Abstract

The concept of reciprocity symmetry for matter-wave propagation is established for nonrelativistic quantum mechanics with previous results in the literature extended to include nonlocal interactions. Examples are given for cases with both local and nonlocal potentials, where we show in particular that reciprocity can be violated for the motion of a charged particle in an external electromagnetic field. In addition, this symmetry is applied to interpret a recent analysis ͓Phys. Rev. A 64, 042716 ͑2001͔͒ on the symmetry of transmission through one-dimensional complex potentials, with the emphasis that the validity of reciprocity can go beyond that of time-reversal symmetry, such as in the presence of absorption in which the latter symmetry breaks down.

Reciprocity in quantum, electromagnetic and other wave scattering

“…Reciprocity for nonlocal potentials has been considered in [24][25][26]. The second remark is that a larger family of possible reciprocity operators is also allowed: Those when U of (77) is a Hilbert space operator acting on wave functions as…”

“…Reciprocity was considered for nonlocal electrodynamical [24,25] and nonlocal quantum mechanical systems [26]. In a recent publication of Leung and Young [27], the aspect of gauge invariance was discussed from the point of view of quantum mechanical interpretation of reciprocity, and new gauge invariant formulations of reciprocity were suggested and analyzed.…”

Constraints on the reciprocal propagation of a quantum particle through a one-dimensional localized complex potential

“…It is known that the transmission and reflection coefficients are identical whether the particle is incident from the left or from the right side in the case of real (nonabsorptive) potentials. In the case of a complex potential with absorption, one still has the same transmission for both left-and right-incidence, but the reflection coefficients will be different in general for particles incident from different sides of the potential [5,6]. (Note that there is a sign error in (9a) of ref.…”

Switching Reciprocity On and Off in a Magneto-Optical X-Ray Scattering Experiment Using Nuclear Resonance ofα−Fe57Foils

“…The conventionally used condition of reciprocity in linear systems [2] is the self-transpose (also called complex symmetric) property of the matrix of the scattering potential, of the index of refraction, of the dielectric/magnetic permeability tensors, or of the Green's function [2,10,15]. This matrix must be considered in the polarization basis distinguished by the scattering processes in question [23].…”

“…The term 'reciprocity' has been introduced by Stokes [1], and the numerous subsequent related publications cover the whole 20 th century, as it is summarized in the review paper of Potton [2]. Reciprocity theorems were derived for various scattering problems, telling under which conditions and limitations the reciprocity principle is valid [3][4][5][6][7], and situations in the field of local and nonlocal electromagnetism [8][9][10][11], sound waves [12], electric circuits [13], radio communication [14], and local and nonlocal quantum mechanical scattering problems [5,15,16] were considered. Nonreciprocal devices (circulators and isolators) with on-chip integration possibility were also suggested [17].…”