Year: 2021
Type: preprint
Abstract: The concept of the generalized continuity equation (GCE) was recently introduced in [J. Phys. A: Math. and Theor. {\bf 52}, 1552034 (2019)], and was derived in the context of $N$ independent Schrödinger systems. The GCE is induced by a symmetry transformation which mixes the states of these systems, even though the $N$-system Lagrangian does not. As the $N$-system Schrödinger Lagrangian is not invariant under such a transformation, the GCE will involve source terms which, under certain conditions vanish and lead to conserved currents. These conditions may hold globally or locally in a finite domain, leading to globally or locally conserved currents, respectively. In this work, we extend this idea to the case of arbitrary $SU(N)$-transformations and we show that a similar GCE emerges for $N$ systems in the Dirac dynamics framework. The emerging GCEs and the conditions which lead to the attendant conservation laws provide a rich phenomenology and potential use for the preparation and control of fermionic states.
Source: arXiv (Cornell University)
Institution: National and Kapodistrian University of Athens
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3133774040