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Non-Hermitian Variations on the Quantum Mechanical Harmonic Oscillator, including Hofstadter's 'Cocoon'

Tuesday November 21, 2017
2:00 pm

 Presenter:  Dr. Kate Brown (Physics Department, Hamilton College)
 Series:  Nuclear, Particle, Astroparticle and Cosmology (NUPAC) Seminars
 Abstract:  In recent decades it has been shown that the Hamiltonian and other operators do not need to be represented by Hermitian matrices in order to obtain a valid quantum mechanical theory.  In Parity-Time symmetric quantum mechanics, the P and T operators take on the role of the Hermitian conjugate, and it is possible to describe quantum mechanical systems that are fundamentally non-Hermitian, yet have real energy spectra, unitary time evolution, etc.  In this talk we will introduce the basic machinery of  PT quantum mechanics, and explore a few simple examples: the simplest two-level systems for even and odd time-reversal; a class of Hamiltonians that represent a complex extension of the harmonic oscillator; and a non-Hermitian extension of the Hamiltonian that gives rise to the famous Hofstadter butterfly plot. The Hofstadter butterfly plot shows energy eigenvalues as a function of magnetic flux; this butterfly can be thought of as emerging from a corresponding 'cocoon' plot in the complex realm.
 Host:  Dinesh Loomba
 Location:  Room 190, Physics & Astronomy

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