testing formulas for decay rates
DESCRIPTION
Equations for decay rates. Testing formulas for decay rates. N atoms inside a sphere: t heoretical prediction. Large wavelength. Wavelength 4 times larger than size of sphere. Wavelength equal to radius of sphere. Small wavelength. Dependence on shape. - PowerPoint PPT PresentationTRANSCRIPT
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Testing formulas for decay ratesEquations for decay rates
)s(eigenvalue/ ,...,2,1)( F Ni
Ni
ji
rrk
rrkji
F
ji
jiij ,sin
,1
0
0
)(1:1 NN
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)1(),1(:2 12)(
212)(
1 FFN NN
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N atoms inside a sphere:theoretical prediction
1 where
,)()()(2
3
2/1
010102)(
in
rkjrkjrkjN
nnnNi
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Large wavelength
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Wavelength 4 times larger than size of sphere
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Wavelength equal to radius of sphere
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Small wavelength
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Dependence on shape
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Dependence on shape, large wavelength
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Dependence on shape, wavelength larger than size
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Dependence on shape, wavelength comparable with size
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Dependence on shape, short wavelength
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Superradiant state vector, large wavelength
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Superradiant state vector,wavelength 4 times larger than size of sphere
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Superradiant state vector, wavelength equal to radius of sphere
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Superradiant state vector,small wavelength
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Decay rates for different wavelength
0n
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Decay rates for different wavelength
0n
3,2,1n
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Decay rates for different wavelength
0n
3,2,1n
8,7,6,5,4n
15,...,10,9n
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Calculating the decay rate of “superradiance” 0
Rk
Rk
Rk
NN
0
02
0
)(0 2
)2sin(1
)(2
3
max/,,...,3,2,1/,0, ,),()(nnmnNiiimninmn Yrkj
βΒβ
Tmax
Tmax )(,)( ΒΒSΒFΒF nn
.)()( polynomial of zerolargest :)( maxmaxmax0 nnn SF
. of instead )1( :matrix theof Size 2max Nn
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Numerical results for 0
63.4
30.4)10(
......
28.3)2(
21.3)1(
48.2)0(
52.14/1/,1000
)(0
0
0
0
0
)(0
N
N
RN
55.46
39.46)4(
96.45)3(
19.44)2(
05.44)1(
90.39)0(
00.381/,1000
)(0
0
0
0
0
0
)(0
N
N
RN