Nuclear, Particle, Astroparticle and Cosmology (NUPAC) Seminars
Non-Hermitian Variations on the Quantum Mechanical Harmonic Oscillator, including Hofstadter's 'Cocoon'
Presented by Dr. Kate Brown (Physics Department, Hamilton College)
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.
2:00 pm, Tuesday, November 21, 2017
PAIS-2540, PAIS
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