Resonance and Revivals in Quantum Rotors Comparing Halfinteger

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Resonance and Revivals in Quantum Rotors --Comparing Half-integer Spin and Integer Spin Alvason Zhenhua

Resonance and Revivals in Quantum Rotors --Comparing Half-integer Spin and Integer Spin Alvason Zhenhua Li William Harter Microelectronics-Photonics Program, Physics Department University of Arkansas, Fayetteville, AR 72701 68 th Spectroscopy, June 20, 2013 1/20

Outline Motivation Integer Spin (Symmetric Rotor) Half-integer Spin (Symmetric Rotor) Summary 68 th Spectroscopy,

Outline Motivation Integer Spin (Symmetric Rotor) Half-integer Spin (Symmetric Rotor) Summary 68 th Spectroscopy, June 20, 2013 2/20

Motivation Quantum Rotor 68 th Spectroscopy, June 20, 2013 W. G. Harter, Principles of

Motivation Quantum Rotor 68 th Spectroscopy, June 20, 2013 W. G. Harter, Principles of Symmetry, Dynamics, and Spectroscopy. W iley-VCH, 1 ed. , 1993. 3 3/20

List-plot Wigner-D Matrix ---- a Rotational Matrix for Any Spin W. G. Harter, Quantum

List-plot Wigner-D Matrix ---- a Rotational Matrix for Any Spin W. G. Harter, Quantum Lecture Manual 68 th Spectroscopy, June 20, 2013 4 4/20 A. Z. Li, Quantum Resonant Beats and Revivals in the Morse Oscillators and Rotors, Ph. D. thesis, University of Arkansas (2013).

Density-plot Wigner-D Matrix ---- a Rotational Matrix for Any Spin 5 A. Z. Li,

Density-plot Wigner-D Matrix ---- a Rotational Matrix for Any Spin 5 A. Z. Li, Quantum Resonant Beats and Revivals in the Morse Oscillators and Rotors, Ph. D. thesis, University of Arkansas (2013). 68 th Spectroscopy, June 20, 2013 5/20

Density-plot Movie Wigner-D Matrix ---- a Rotational Matrix for Any Spin 6 68 th

Density-plot Movie Wigner-D Matrix ---- a Rotational Matrix for Any Spin 6 68 th Spectroscopy, June 20, 2013 6/20

J=3 Rotor Wave Functions of Integer Spin (Boson) System 68 th Spectroscopy, June 20,

J=3 Rotor Wave Functions of Integer Spin (Boson) System 68 th Spectroscopy, June 20, 2013 7/20

J=10 Dynamics of Integer Spin (Boson) System 68 th Spectroscopy, June 20, 2013 8/20

J=10 Dynamics of Integer Spin (Boson) System 68 th Spectroscopy, June 20, 2013 8/20

Space-Time-plot Rotor Wave Packet Propagation of Integer Spin (Boson) System A. Z. Li, Quantum

Space-Time-plot Rotor Wave Packet Propagation of Integer Spin (Boson) System A. Z. Li, Quantum Resonant Beats and Revivals in the Morse Oscillators and Rotors, Ph. D. thesis, University of Arkansas (2013). 68 th Spectroscopy, June 20, 2013 9/20

High Low 68 th Spectroscopy, June 20, 2013 10/20

High Low 68 th Spectroscopy, June 20, 2013 10/20

Half-integer Spinning Rotors exhibit Farey-sum Revivals 68 th Spectroscopy, June 20, 2013 11/20

Half-integer Spinning Rotors exhibit Farey-sum Revivals 68 th Spectroscopy, June 20, 2013 11/20

Outline Motivation Integer Spin (Symmetric Rotor) Half-integer Spin (Symmetric Rotor) Summary 68 th Spectroscopy,

Outline Motivation Integer Spin (Symmetric Rotor) Half-integer Spin (Symmetric Rotor) Summary 68 th Spectroscopy, June 20, 2013 12/2 0

Unique 4π Rotation Rotor Wave Functions of Half-Integer Spin (Fermion) System (a) (b) (c)

Unique 4π Rotation Rotor Wave Functions of Half-Integer Spin (Fermion) System (a) (b) (c) (d) (e) (f) 68 th Spectroscopy, June 20, 2013 13/20

J=5/2 Rotor Wave Functions of Half-Integer Spin (Fermion) System 68 th Spectroscopy, June 20,

J=5/2 Rotor Wave Functions of Half-Integer Spin (Fermion) System 68 th Spectroscopy, June 20, 2013 14/20

J=9. 5 Dynamics of Integer Spin (Fermion) System 68 th Spectroscopy, June 20, 2013

J=9. 5 Dynamics of Integer Spin (Fermion) System 68 th Spectroscopy, June 20, 2013 15/20

Space-Time-plot Rotor Wave Packet Propagation of Half-integer Spin (Fermion) System A. Z. Li, Quantum

Space-Time-plot Rotor Wave Packet Propagation of Half-integer Spin (Fermion) System A. Z. Li, Quantum Resonant Beats and Revivals in the Morse Oscillators and Rotors, Ph. D. thesis, University of Arkansas (2013). 68 th Spectroscopy, June 20, 2013 16/20

High Low 68 th Spectroscopy, June 20, 2013 17/20

High Low 68 th Spectroscopy, June 20, 2013 17/20

Half-integer Spinning Rotors exhibit Farey-sum Revivals 68 th Spectroscopy, June 20, 2013 18/20

Half-integer Spinning Rotors exhibit Farey-sum Revivals 68 th Spectroscopy, June 20, 2013 18/20

The coming next talk will address the curious connection of Farey-sum and Ford-circles A.

The coming next talk will address the curious connection of Farey-sum and Ford-circles A. Z. Li and W. G. Harter, Physical Review Letters (submitted 2013). 68 th Spectroscopy, June 20, 2013 19/20

Summary Both Integer and Half-integer Spinning Rotors exhibit Farey-sum Revivals Thanks for your time!

Summary Both Integer and Half-integer Spinning Rotors exhibit Farey-sum Revivals Thanks for your time! Pave the way for more rich dynamic behaviors in Asymmetric Rotors 68 th Spectroscopy, June 20, 2013 20/20