1. 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 72701 68th Spectroscopy, June 20, 2013

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

3. 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.

4. 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).

5. 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).

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

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

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

9. 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).

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

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

12. 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

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

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

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

16. 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).

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

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

19. 68th Spectroscopy, June 20, 2013 19/20 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).

20. 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 !