1/20 resonance and revivals in quantum rotors --- comparing half-integer spin and integer spin...
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![Page 1: 1/20 Resonance and Revivals in Quantum Rotors --- Comparing Half-integer Spin and Integer Spin Alvason Zhenhua Li William Harter Microelectronics-Photonics](https://reader038.vdocuments.mx/reader038/viewer/2022103122/56649cb95503460f94980098/html5/thumbnails/1.jpg)
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Resonance and Revivals in Quantum Rotors --- Comparing Half-integer Spin and Integer Spin
Alvason Zhenhua LiWilliam Harter
Microelectronics-Photonics Program, Physics Department University of Arkansas, Fayetteville, AR 72701
68th Spectroscopy, June 20, 2013
![Page 2: 1/20 Resonance and Revivals in Quantum Rotors --- Comparing Half-integer Spin and Integer Spin Alvason Zhenhua Li William Harter Microelectronics-Photonics](https://reader038.vdocuments.mx/reader038/viewer/2022103122/56649cb95503460f94980098/html5/thumbnails/2.jpg)
68th Spectroscopy, June 20, 2013
Outline
SummarySummary
MotivationMotivation
Integer Spin(Symmetric Rotor)
Half-integer Spin(Symmetric Rotor)
2/20
![Page 3: 1/20 Resonance and Revivals in Quantum Rotors --- Comparing Half-integer Spin and Integer Spin Alvason Zhenhua Li William Harter Microelectronics-Photonics](https://reader038.vdocuments.mx/reader038/viewer/2022103122/56649cb95503460f94980098/html5/thumbnails/3.jpg)
68th Spectroscopy, June 20, 2013
Quantum RotorMotivationMotivation
33/20W. G. Harter, Principles of Symmetry, Dynamics, and Spectroscopy.W iley-VCH,1ed.,1993.
![Page 4: 1/20 Resonance and Revivals in Quantum Rotors --- Comparing Half-integer Spin and Integer Spin Alvason Zhenhua Li William Harter Microelectronics-Photonics](https://reader038.vdocuments.mx/reader038/viewer/2022103122/56649cb95503460f94980098/html5/thumbnails/4.jpg)
68th Spectroscopy, June 20, 2013
Wigner-D Matrix ---- a Rotational Matrix for Any SpinList-plotList-plot
44/20
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).
![Page 5: 1/20 Resonance and Revivals in Quantum Rotors --- Comparing Half-integer Spin and Integer Spin Alvason Zhenhua Li William Harter Microelectronics-Photonics](https://reader038.vdocuments.mx/reader038/viewer/2022103122/56649cb95503460f94980098/html5/thumbnails/5.jpg)
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68th Spectroscopy, June 20, 2013
Wigner-D Matrix ---- a Rotational Matrix for Any SpinDensity-plotDensity-plot
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A. Z. Li, Quantum Resonant Beats and Revivals in the Morse Oscillators and Rotors, Ph.D. thesis, University of Arkansas (2013).
![Page 6: 1/20 Resonance and Revivals in Quantum Rotors --- Comparing Half-integer Spin and Integer Spin Alvason Zhenhua Li William Harter Microelectronics-Photonics](https://reader038.vdocuments.mx/reader038/viewer/2022103122/56649cb95503460f94980098/html5/thumbnails/6.jpg)
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68th Spectroscopy, June 20, 2013
Wigner-D Matrix ---- a Rotational Matrix for Any SpinDensity-plot MovieDensity-plot Movie
6/20
![Page 7: 1/20 Resonance and Revivals in Quantum Rotors --- Comparing Half-integer Spin and Integer Spin Alvason Zhenhua Li William Harter Microelectronics-Photonics](https://reader038.vdocuments.mx/reader038/viewer/2022103122/56649cb95503460f94980098/html5/thumbnails/7.jpg)
68th Spectroscopy, June 20, 2013
Rotor Wave Functions of Integer Spin (Boson) System
7/20
J=3J=3
![Page 8: 1/20 Resonance and Revivals in Quantum Rotors --- Comparing Half-integer Spin and Integer Spin Alvason Zhenhua Li William Harter Microelectronics-Photonics](https://reader038.vdocuments.mx/reader038/viewer/2022103122/56649cb95503460f94980098/html5/thumbnails/8.jpg)
68th Spectroscopy, June 20, 2013
Dynamics of Integer Spin (Boson) System
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J=10J=10
![Page 9: 1/20 Resonance and Revivals in Quantum Rotors --- Comparing Half-integer Spin and Integer Spin Alvason Zhenhua Li William Harter Microelectronics-Photonics](https://reader038.vdocuments.mx/reader038/viewer/2022103122/56649cb95503460f94980098/html5/thumbnails/9.jpg)
68th Spectroscopy, June 20, 2013
Rotor Wave Packet Propagation of Integer Spin (Boson) System Space-Time-plotSpace-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).
![Page 10: 1/20 Resonance and Revivals in Quantum Rotors --- Comparing Half-integer Spin and Integer Spin Alvason Zhenhua Li William Harter Microelectronics-Photonics](https://reader038.vdocuments.mx/reader038/viewer/2022103122/56649cb95503460f94980098/html5/thumbnails/10.jpg)
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68th Spectroscopy, June 20, 201310/20
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68th Spectroscopy, June 20, 201311/20
Half-integer Spinning Rotors exhibit Farey-sum Revivals
Farey−sum−Rule:aA⊕bB=a+bA+B
0
1⊕
12=0 +11+2
=13
0
1⊕13=0 +11+ 3
=14
1
3⊕
12=1+13+2
=25
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3⊕
25=1+23+5
=38
0
1⊕
14=0 +11+ 4
=15
![Page 12: 1/20 Resonance and Revivals in Quantum Rotors --- Comparing Half-integer Spin and Integer Spin Alvason Zhenhua Li William Harter Microelectronics-Photonics](https://reader038.vdocuments.mx/reader038/viewer/2022103122/56649cb95503460f94980098/html5/thumbnails/12.jpg)
68th Spectroscopy, June 20, 2013
Outline
SummarySummary
MotivationMotivation
Integer Spin(Symmetric Rotor)
Half-integer Spin(Symmetric Rotor)
12/20
![Page 13: 1/20 Resonance and Revivals in Quantum Rotors --- Comparing Half-integer Spin and Integer Spin Alvason Zhenhua Li William Harter Microelectronics-Photonics](https://reader038.vdocuments.mx/reader038/viewer/2022103122/56649cb95503460f94980098/html5/thumbnails/13.jpg)
(a)
(d)
(c)(b)
(e) (f)
Rotor Wave Functions of Half-Integer Spin (Fermion) SystemUnique 4π RotationUnique 4π Rotation
68th Spectroscopy, June 20, 201313/20
![Page 14: 1/20 Resonance and Revivals in Quantum Rotors --- Comparing Half-integer Spin and Integer Spin Alvason Zhenhua Li William Harter Microelectronics-Photonics](https://reader038.vdocuments.mx/reader038/viewer/2022103122/56649cb95503460f94980098/html5/thumbnails/14.jpg)
68th Spectroscopy, June 20, 2013
Rotor Wave Functions of Half-Integer Spin (Fermion) System
14/20
J=5/2J=5/2
![Page 15: 1/20 Resonance and Revivals in Quantum Rotors --- Comparing Half-integer Spin and Integer Spin Alvason Zhenhua Li William Harter Microelectronics-Photonics](https://reader038.vdocuments.mx/reader038/viewer/2022103122/56649cb95503460f94980098/html5/thumbnails/15.jpg)
68th Spectroscopy, June 20, 2013
Dynamics of Integer Spin (Fermion) System
15/20
J=9.5J=9.5
![Page 16: 1/20 Resonance and Revivals in Quantum Rotors --- Comparing Half-integer Spin and Integer Spin Alvason Zhenhua Li William Harter Microelectronics-Photonics](https://reader038.vdocuments.mx/reader038/viewer/2022103122/56649cb95503460f94980098/html5/thumbnails/16.jpg)
68th Spectroscopy, June 20, 2013
Rotor Wave Packet Propagation of Half-integer Spin (Fermion) System Space-Time-plotSpace-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).
![Page 17: 1/20 Resonance and Revivals in Quantum Rotors --- Comparing Half-integer Spin and Integer Spin Alvason Zhenhua Li William Harter Microelectronics-Photonics](https://reader038.vdocuments.mx/reader038/viewer/2022103122/56649cb95503460f94980098/html5/thumbnails/17.jpg)
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68th Spectroscopy, June 20, 201317/20
![Page 18: 1/20 Resonance and Revivals in Quantum Rotors --- Comparing Half-integer Spin and Integer Spin Alvason Zhenhua Li William Harter Microelectronics-Photonics](https://reader038.vdocuments.mx/reader038/viewer/2022103122/56649cb95503460f94980098/html5/thumbnails/18.jpg)
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68th Spectroscopy, June 20, 201318/20
Half-integer Spinning Rotors exhibit Farey-sum Revivals
Farey−sum−Rule:aA⊕bB=a+bA+B
0
1⊕
12=0 +11+2
=13
0
1⊕13=0 +11+ 3
=14
1
3⊕
12=1+13+2
=25
![Page 19: 1/20 Resonance and Revivals in Quantum Rotors --- Comparing Half-integer Spin and Integer Spin Alvason Zhenhua Li William Harter Microelectronics-Photonics](https://reader038.vdocuments.mx/reader038/viewer/2022103122/56649cb95503460f94980098/html5/thumbnails/19.jpg)
68th Spectroscopy, June 20, 201319/20
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!