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Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
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Interplay between parity-time symmetry, supersymmetry, and nonlinearity: An analytically tractable case example
Panayotis G Kevrekidis1, Jesús Cuevas-Maraver2, Avadh Saxena3
1Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA and Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 14, 2015
Summary
This study merges parity-time (PT) symmetry and supersymmetry (SUSY) to analyze complex potentials. Researchers found exact bright soliton solutions with unique oscillatory instability, advancing nonlinear physics.
Area of Science:
- Theoretical Physics
- Quantum Mechanics
- Nonlinear Dynamics
Background:
- Parity-time (PT) symmetry offers unique properties for complex potentials.
- Supersymmetry (SUSY) relates different quantum systems.
- Pöschl-Teller potential is a well-studied real potential.
Purpose of the Study:
- To combine PT symmetry and SUSY for a complex potential.
- To investigate the spectral properties and nonlinear behavior of this combined system.
- To explore the stability of exact bright soliton solutions.
Main Methods:
- Combining PT symmetry and SUSY for a complex potential derived from the Pöschl-Teller potential.
- Numerical confirmation of eigenvalues.
- Analytical identification of exact bright soliton solutions for nonlinear systems with power-law nonlinearity.
Main Results:
- Identified and numerically confirmed eigenvalues for the PT- and SUSY-combined system.
- Discovered exact bright soliton solutions for the nonlinear version of the system.
- Observed an oscillatory instability in the soliton solutions, distinct from the nonlinear Schrödinger equation.
Conclusions:
- The combination of PT symmetry and SUSY with nonlinear interactions yields novel soliton solutions.
- The identified oscillatory instability presents unique spectral and dynamical properties.
- These findings suggest a promising direction for research at the intersection of PT symmetry, SUSY, and nonlinear physics.
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