Seminar Event Detail

Colloquium Series

Date:  Tuesday, January 16, 2018
Location:  1360 East Hall (4:10 PM to 5:00 PM)

Title:  Parity-Time (PT) Symmetric systems: An analysis of dimer and trimer models

Abstract:   In the late 1990s, a novel idea came to fruition concerning the study of the fundamentals
of quantum mechanics. In the works of Bender and Boettcher [1] and Bender et. al [1, 2],
it was proposed that Hamiltonians that respect the physical symmetries of the dynamics,
namely parity (P) and time-reversal (T), could have real eigenvalues even if said Hamiltonian
were non-Hermitian.

In this talk, we will discuss the cases of two-site (dimer) and three-site (trimer) PTsymmetric
models respecting the parity-time (PT) symmetry with linear and nonlinear
gain/loss profiles. We also examine solutions arising from these dimer and trimer models
and their regions of stability. We will present both analytical and numerical results
concerning this work. In addition, we will examine both dimer and trimer models with a
rapidly-varying gain/loss profile. In this part of the work, we discuss the derivation a set of
averaged equations and examine its solutions and stability regions. We also compare these
results with those obtained by direct simulation of the full set of nonlinear equations.

[1] C.M. Bender and S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998)
[2] C.M. Bender, S. Boettcher and P.N. Meisinger, J. Math. Phys. 40, 2201 (1999).


Speaker:  Rudy Horne
Institution:  Morehouse College

Event Organizer:     


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