Events Calendar
Non-Hermitian Variations on the Quantum Mechanical Harmonic Oscillator, including Hofstadter's 'Cocoon'
Tuesday November 21, 2017
| 2:00 pm
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Presenter: | Dr. Kate Brown (Physics Department, Hamilton College) |
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| 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: | PAIS-2540, PAIS | |
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