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1/20 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 th Spectroscopy, June 20, 2013

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Outline Summary Motivation Integer Spin (Symmetric Rotor) Integer Spin (Symmetric Rotor) Half-integer Spin (Symmetric Rotor) Half-integer Spin (Symmetric Rotor) 2/20

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

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

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

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

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

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

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

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High Low 68th Spectroscopy, June 20, /20

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

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

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

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

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68th Spectroscopy, June 20, 2013 Dynamics of Integer Spin (Fermion) System 15/20 J=9.5

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

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High Low 68th Spectroscopy, June 20, /20

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

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68th Spectroscopy, June 20, /20 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).

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

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