rj04 resonance and revivals i. quantum rotor and infinite-well dynamics william g. harter and...
TRANSCRIPT
![Page 1: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/1.jpg)
RJ04
RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS
William G. Harter and Alvason Zhenhua LiUniversity of Arkansas - Fayetteville
Physics Department and Microelectronics-Photonics Program
m=0±1±2
±3
±4
±5
±6
n=1
2
3
4
5
6
![Page 2: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/2.jpg)
RJ04
RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS
William G. Harter and Alvason Zhenhua LiUniversity of Arkansas - Fayetteville
Physics Department and Microelectronics-Photonics Program
m=0±1±2
±3
±4
±5
±6
n=1
2
3
4
5
6
Rotor revival structure includes anything ∞-well can do…. …and is easier to explain.
Won’t talk about ∞-well
![Page 3: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/3.jpg)
RJ04
RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS
William G. Harter and Alvason Zhenhua LiUniversity of Arkansas - Fayetteville
Physics Department and Microelectronics-Photonics Program
m=0±1±2
±3
±4
±5
±6
n=1
2
3
4
5
6
Rotor revival structure includes anything ∞-well can do…. …and is easier to explain.
Some Early History of Quantum RevivalsJ.H. Eberly et. al. Phys. Rev. A 23,236 (1981) Laser QuantumCavityDynamic revivalsR.S. McDowell, WGH, C.W. Patterson LosAlmos Sci. 3, 38(1982) Symmetric-top revivalsS.I. Vetchinkin, et. al. Chem. Phys. Lett. 215,11 (1993) 1D ∞-Square well revivalsAronstein, Stroud, Berry, …, Schleich,.. (1995-1998) “ “ “ “WGH, J. Mol. Spectrosc. 210, 166 (2001) Bohr-rotor revivals
So we thought we’d put this revival business to bed! Then...
Won’t talk about ∞-well
![Page 4: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/4.jpg)
More recent story of Quantum RevivalsAnne B. McCoy Chem. Phys. Lett. 501, 603(2011)...reminds me that Morse potential is integer-analytic.
Some Early History of Quantum RevivalsJ.H. Eberly et. al. Phys. Rev. A 23,236 (1981) Laser QuantumCavityDynamic revivalsR.S. McDowell, WGH, C.W. Patterson LosAlmos Sci. 3, 38(1982) Symmetric-top revivalsS.I. Vetchinkin, et. al. Chem. Phys. Lett. 215,11 (1993) 1D ∞-Square well revivalsAronstein, Stroud, Berry, …, Schleich,.. (1995-1998) “ “ “ “WGH, J. Mol. Spectrosc. 210, 166 (2001) Bohr-rotor revivals
So we thought we’d put this revival business to bed! Then this...
Leads to cool Morse revivals in: Following Talk RJ05 by Li:Resonance&Revivals II. MORSE OSCILLATOR AND DOUBLE MORSE WELL DYNAMICS.
So now we’re having a revival-revival!
...and, in words by Joannie Mitchell, I find: “I didn’t really know... revivals … at all.”
![Page 5: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/5.jpg)
What do revivals look like?(...in space-time…)
![Page 6: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/6.jpg)
![Page 7: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/7.jpg)
What do revivals look like?(...in space-time…)
OK,let’s try that again...
withquantum revivals...
![Page 8: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/8.jpg)
Time t (units of fundamental period ) τ1
Coordinate φ (units of 2π )
0/1
1/10
1/5
3/10
2/5
1/2
3/5
7/10
4/5
9/10
1/1
3/4
1/4
1/21/40-1/4-1/2
1/2
1/4
0-1/4
-1/2
(Imagine "wrap-around" φ-coordinate) +π /2
−π /2
+π−π
3/4
1/4
0/1
1/2
1/1
Time t
![Page 9: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/9.jpg)
Observable dynamics of N-level-system state Depends on Fourier spectrum of probability distribution
Ψ = e−iωnt
n=0
N
∑ ψ n
ω 0 ω1 ω 2 ω 3 ω 4
...But individual eigenfrequencies are not directly observable...
ω n
ΨΨ Ψ
![Page 10: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/10.jpg)
Ψ = e−iωnt
n=0
N
∑ ψ n
Ψ = e+iωmt
m=0
N
∑ ψ *m
ω 0 ω1 ω 2 ω 3 ω 4
ω 4
ω 3
ω 2
ω1
ω 0
...But individual eigenfrequencies are not directly observable...
Observable dynamics of N-level-system state Depends on Fourier spectrum of probability distribution
ΨΨ Ψ
![Page 11: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/11.jpg)
Ψ = e−iωnt
n=0
N
∑ ψ n
Ψ = e+iωmt
m=0
N
∑ ψ *m
Ψ Ψ = ei(ωm −ωn )t
n=0
N
∑ ψ *mψ n
= eiΔm nt
m,n=0
N
∑ ρ mnω 0 ω1 ω 2 ω 3 ω 4
ω 4
ω 3
ω 2
ω1
ω 0
...But individual eigenfrequencies are not directly observable...
Observable dynamics of N-level-system state Depends on Fourier spectrum of probability distribution
ΨΨ Ψ
![Page 12: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/12.jpg)
ω3
Ψ = e−iωnt
n=0
N
∑ ψ n
Ψ = e+iωmt
m=0
N
∑ ψ *m
ω0 ω1 ω2 ω3 ωN
ω0
ω1
ω2
ωN
Ψ Ψ = ei(ωm −ωn )t
n=0
N
∑ ψ *mψ n
= eiΔm nt
m,n=0
N
∑ ρ mn
...But individual eigenfrequencies are not directly observable...
Observable dynamics of N-level-system state Depends on Fourier spectrum of probability distribution
ΨΨ Ψ
![Page 13: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/13.jpg)
Ψ = e−iωnt
n=0
N
∑ ψ n
Ψ = e+iωmt
m=0
N
∑ ψ *m
Ψ Ψ = ei(ωm −ωn )t
n=0
N
∑ ψ *mψ n
= eiΔm nt
m,n=0
N
∑ ρ mnω 0 ω1 ω 2 ω 3 ω 4
ω 4
ω 3
ω 2
ω1
ω 0
...But individual eigenfrequencies are not directly observable… ...only differences Δmn = (ωm −ωn )
Δ04
Δ14
Δ03
Δ23
Δ13
Δ4 0 Δ41
Observable dynamics of N-level-system state Depends on Fourier spectrum of probability distribution
ΨΨ Ψ
![Page 14: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/14.jpg)
Ψ = e−iωnt
n=0
N
∑ ψ n
Ψ = e+iωmt
m=0
N
∑ ψ *m
Ψ Ψ = ei(ωm −ωn )t
n=0
N
∑ ψ *mψ n
= eiΔm nt
m,n=0
N
∑ ρ mnω 0 ω1 ω 2 ω 3 ω 4
ω 4
ω 3
ω 2
ω1
ω 0
...But individual eigenfrequencies are not directly observable… ...only differences Δmn = (ωm −ωn )
Δ04
Δ14
Δ03
Δ23
Δ13
Δ4 0 Δ41
N=5 eigenfrequenciesgives: N(N-1)/2=10 positive and : N(N-1)/2=10negative
Δm>n = ωm −ωn
Δm<n = ωm −ωn
Observable dynamics of N-level-system state Depends on Fourier spectrum of probability distribution
ΨΨ Ψ
![Page 15: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/15.jpg)
Ψ = e−iωnt
n=0
N
∑ ψ n
Ψ = e+iωmt
m=0
N
∑ ψ *m
Ψ Ψ = ei(ωm −ωn )t
n=0
N
∑ ψ *mψ n
= eiΔm nt
m,n=0
N
∑ ρ mnω 0 ω1 ω 2 ω 3 ω 4
ω 4
ω 3
ω 2
ω1
ω 0
...But individual eigenfrequencies are not directly observable… ...only differences Δmn = (ωm −ωn )
Δ04
Δ14
Δ03
Δ23
Δ13
Δ4 0 Δ41
N=5 eigenfrequenciesgives: N(N-1)/2=10 positive and : N(N-1)/2=10negative
Δm>n = ωm −ωn
Δm<n = ωm −ωn
...that is, N(N-1)/2=10 observable beats Δm<n = ωm −ωn
Observable dynamics of N-level-system state Depends on Fourier spectrum of probability distribution
ΨΨ Ψ
![Page 16: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/16.jpg)
Observable dynamics of 2-level-system state Fourier spectrum of has ONE beat frequency
Ψ = e−iωnt
n=0
N
∑ ψ n
Ψ = e+iωmt
m=0
N
∑ ψ *m
Ψ Ψ = ei(ωm −ωn )t
n=0
N
∑ ψ *mψ n
= eiΔm nt
m,n=0
N
∑ ρ mnω1 ω 2
ω 2
ω1
Δ12
Δ21
N=2 eigenfrequenciesgives: N(N-1)/2=1 positive and : N(N-1)/2=1negative
Δ2>1 = ω2 −ω1
Δ1<2 = ω1 −ω2
...that is, N(N-1)/2=1 observable beat Δm<n = ωm −ωn
ΨΨ Ψ Δ21 = −Δ12
![Page 17: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/17.jpg)
2-level-system and C2 symmetry beat dynamics
symmetric A1
vs.
antisymmetric A2
C2 Character Table describes eigenstates
1=r0 r =r1
0mod21 1
±1mod2 1 −1
![Page 18: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/18.jpg)
2-level-system and C2 symmetry beat dynamics
symmetric A1
vs.
antisymmetric A2
C2 Character Table describes eigenstates
1=r0 r =r1
0mod21 1
±1mod2 1 −1
Phasor C2 Characters describe local state beats
Initial sum
C2 Phasor-Character Table
![Page 19: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/19.jpg)
2-level-system and C2 symmetry beat dynamics
symmetric A1
vs.
antisymmetric A2
C2 Character Table describes eigenstates
1=r0 r =r1
0mod21 1
±1mod2 1 −1
Phasor C2 Characters describe local state beats
Initial sum
1/4-beat
C2 Phasor-Character Table
![Page 20: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/20.jpg)
2-level-system and C2 symmetry beat dynamics
symmetric A1
vs.
antisymmetric A2
C2 Character Table describes eigenstates
1=r0 r =r1
0mod21 1
±1mod2 1 −1
Phasor C2 Characters describe local state beats
Initial sum
1/4-beat
1/2-beat
C2 Phasor-Character Table
![Page 21: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/21.jpg)
2-level-system and C2 symmetry beat dynamics
symmetric A1
vs.
antisymmetric A2
C2 Character Table describes eigenstates
1=r0 r =r1
0mod21 1
±1mod2 1 −1
Phasor C2 Characters describe local state beats
Initial sum
1/4-beat
1/2-beat
3/4-beat
C2 Phasor-Character Table
![Page 22: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/22.jpg)
2-level-system and C2 symmetry beat dynamics
m=+1, 0, -1
C2 Phasor-Character Table
![Page 23: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/23.jpg)
What do revivals look like?...in per-space-time…
(… that is:frequency radian/sec.
vs
k-vector km radian/cm)
ωm
![Page 24: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/24.jpg)
N-level-system and revival-beat wave dynamics Bm2=B42
Bm2=B32
Bm2=B22
Bm2=B
![Page 25: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/25.jpg)
N-level-system and revival-beat wave dynamics
![Page 26: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/26.jpg)
N-level-system and revival-beat wave dynamics
![Page 27: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/27.jpg)
0123456789
1011121314151617
Harmonic Oscillator level spectrum contains the Rotor Levels as a subset
N-level-system and revival-beat wave dynamics
![Page 28: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/28.jpg)
N-level-system and revival-beat wave dynamics (Just 2-levels (0, ±1) (and some ±2) excited)
![Page 29: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/29.jpg)
N-level-system and revival-beat wave dynamics (Just 2-levels (0, ±1) (and some ±2) excited) (4-levels (0, ±1,±2,±3) (and some ±4) excited)
![Page 30: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/30.jpg)
N-level-system and revival-beat wave dynamics (9 or10-levels (0, ±1, ±2, ±3, ±4,..., ±9, ±10, ±11...) excited)
Zeros (clearly) and “particle-packets” (faintly) have paths labeled by fraction sequences like: 0
7,1
7,2
7,3
7,4
7,5
7,6
7,1
1
1
7
2
7
3
7
4
7
5
7
6
7
4
7
5
7
6
7
1
1
0
1
![Page 31: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/31.jpg)
Farey Sum algebra of revival-beat wave dynamicsLabel by numerators N and denominators D of rational fractions N/D
![Page 32: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/32.jpg)
Farey Sum algebra of revival-beat wave dynamicsLabel by numerators N and denominators D of rational fractions N/D
![Page 33: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/33.jpg)
A Lesson in Rational Fractions N/D (...that you can take home for your kids!)
![Page 34: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/34.jpg)
Farey Sum related to vector sum
andFord Circles1/1-circle has
diameter 1
![Page 35: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/35.jpg)
Farey Sum related to vector sum
andFord Circles
1/2-circle hasdiameter 1/22=1/4
1/1-circle hasdiameter 1
![Page 36: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/36.jpg)
Farey Sum related to vector sum
andFord Circles
1/2-circle hasdiameter 1/22=1/4
1/3-circles havediameter 1/32=1/9
![Page 37: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/37.jpg)
Farey Sum related to vector sum
andFord Circles
1/2-circle hasdiameter 1/22=1/4
1/3-circles havediameter 1/32=1/9
n/d-circles havediameter 1/d2
![Page 38: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/38.jpg)
Farey Sum related to vector sum
andFord Circles
1/2-circle hasdiameter 1/22=1/4
1/3-circles havediameter 1/32=1/9
n/d-circles havediameter 1/d2
![Page 39: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/39.jpg)
Cm algebra of revival-phase dynamics
![Page 40: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/40.jpg)
Cm algebra of revival-phase dynamics
![Page 41: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/41.jpg)
Summary
Quantum rotor revivals obey wonderfully simplegeometry, number, and group theoretical analysis
andas the next talk will show...
![Page 42: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/42.jpg)
Summary
Quantum rotor revivals obey wonderfully simplegeometry, number, and group theoretical analysis
andas the next talk will show…
“I still don’t really know... revivals … at all.”
![Page 43: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/43.jpg)
QuickTime™ and aH.264 decompressor
are needed to see this picture.
Simulation of revival-intensity dynamics
![Page 44: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/44.jpg)
QuickTime™ and aH.264 decompressor
are needed to see this picture.
![Page 45: RJ04 RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS William G. Harter and Alvason Zhenhua Li University of Arkansas - Fayetteville](https://reader030.vdocuments.net/reader030/viewer/2022032804/56649e575503460f94b5058e/html5/thumbnails/45.jpg)