Super-Lagrangian and variational principle for generalized continuity equations
@article{Diakonos2019SuperLagrangianAV, title={Super-Lagrangian and variational principle for generalized continuity equations}, author={Fotis K. Diakonos and Peter Schmelcher}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2019} }
We present a variational approach which shows that the wave functions belonging to quantum systems in different potential landscapes, are pairwise linked to each other through a generalized continuity equation. This equation contains a source term proportional to the potential difference. In case the potential landscapes are related by a linear symmetry transformation in a finite domain of the embedding space, the derived continuity equation leads to generalized currents which are divergence…
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References
SHOWING 1-10 OF 16 REFERENCES
Generalized continuity equations from two-field Schrödinger Lagrangians
- Physics, Mathematics
- 2016
A variational scheme for the derivation of generalized, symmetry-induced continuity equations for Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a Lagrangian which…
Invariant current approach to wave propagation in locally symmetric structures
- Mathematics
- 2015
A theory for wave mechanical systems with local inversion and translation symmetries is developed employing the two-dimensional solution space of the stationary Schr\"odinger equation. The local…
Invariants of broken discrete symmetries.
- MathematicsPhysical review letters
- 2014
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize…
Local symmetry dynamics in one-dimensional aperiodic lattices: a numerical study
- Physics, Mathematics
- 2013
A unifying description of lattice potentials generated by aperiodic one-dimensional sequences is proposed in terms of their local reflection or parity symmetry properties. We demonstrate that the…
Emmy Noether's Wonderful Theorem
- Physics
- 2010
A beautiful piece of mathematics, Noether's Theorem touches on every aspect of physics. Emmy Noether proved her theorem in 1915 and published it in 1918. This profound concept demonstrates the…
Local symmetries and perfect transmission in aperiodic photonic multilayers
- Physics
- 2013
We develop a classification of perfectly transmitting resonances occuring in effectively onedimensional optical media which are decomposable into locally reflection symmetric parts. The local…
Invariant currents in lossy acoustic waveguides with complete local symmetry
- Physics, Mathematics
- 2015
The Noether Theorems: Invariance and Conservation Laws in the Twentieth Century
- Mathematics
- 2010
Preface.-Acknowledgements.- I. "Invariant Variational Problems". II.- Invariance and Conservation Laws in the Twentieth Century. The Inception and Reception of the Noether Theorems. - 1. The…
Local symmetries in one-dimensional quantum scattering
- Physics
- 2013
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