1) again: dephasing and energy relaxation with redfield theory
DESCRIPTION
1) Again: Dephasing and Energy Relaxation with Redfield Theory. 1965+. 2) Compare with: Kubo Lineshape Theory. 1957. Bloch Model :. Redfield Model :. 2. Pollard, Friesner JCP 100 (1994) 5054, Oxtoby, Rice, CPL 42 (1976) 1. 2. Spatial Coherence. IR-Spectrum. - PowerPoint PPT PresentationTRANSCRIPT
1) Again: Dephasing and Energy Relaxation with Redfield Theory
2) Compare with: Kubo Lineshape Theory
h Q0 (1- ) ( - )H Q0
2
Q = F0
0
o
1965+
1957
d dt/ = - i -
n
n
m
m mm
nn
mm
nm
(t+dt)
mm
nn
mm
nm
(t)
n
n
m
m mm
nn
mm
nm
(t+dt)
mm
nn
mm
nm
(t)Rn m n m
=1/ T2
mm mmR =1/ T1
Bloch Model:
n
n
m
m mm
nn
mm
nm
(t+dt)
mm
nn
mm
nm
(t)
Redfield Model:
Rn m n m
mm mmR
Rn mk l
Rm mnn
Rn m n m
mm mmR
Rn mk l
Rm mnn
Q = F0
Q F (t) Q F (0)
o
Q H (t) Q H (0)2
Rn m n m
mm mmR
Rn mk l
Rm mnn
2
Pollard, Friesner JCP 100 (1994) 5054,Oxtoby, Rice, CPL 42 (1976) 1
0 2 4 6 8 10 12-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
25 50 75 100 125 150 175 200
0
0.1
0.2
0.3
0.4
25 50 75 100 125 150 175 200
0
0.5
1
1.5
2
2.5
3
IR-Spectrum
0 2 4 6 8 10 12-1
-0.5
0
0.5
1
Spatial Coherence
0 2 4 6 8 10 12
0
0.1
0.2
0.3
0.4
0.5
0 2 4 6 8 10 12
0
0.5
1
1.5
2
2.5
3
0 2 4 6 8 10 12
0
0.2
0.4
0.6
0.8
0 2 4 6 8 10 12
0
0.5
1
1.5
2
2.5
3
Level Populations
Energy above zero-level
H H(t) (o)2 2 2Q.Q
JG( )
F F2 Q.Q (t) (0)
JF( )
m
m+1
m-1
m-2
m+2
1h
2 (m+1) e JF( )0
- h 0
1h
2 m JF( )0
12h
2
- h 2012h
2 (m+1)(m+2) e JG( )2 0
12h
212h
2 m(m-2) JG( )2 0
Rm mnn
m
14h
2
{
Rn mnm
n
1h
2 { (m+n) + (n+m+2) e }
JF( )0
- h 0
11h
2 (m-n) J2 G( )0
JG( )20
[(n+1)(n+2) +(m+1)(m+2)] e + + n (n-1) m (m-1)
- h 20 {
Pure dephasing:
Population-induced:
JG( )
S Dpectral ensity
10 fs time
c
modulation strength
modulation speed
2) Compare with Kubo Lineshape Theory - totally classical !
h Q0 (1- ) ( - )H Q0
2
0 o
H H(t) (o)2 2 2Q.Q (t) (o) A C Futo orrelation unction
Q
(t)
10 fs time
c
modulation strength
modulation speed
d dt (t) (t)Q/ = i Q
Q = Q exp{i } exp{i d } (t) t0 0
tintegrate:
Q Q = Q exp{i } exp{i d } (t) (0) t02
0
tautocorrelate:
(t) (o)
exp{ d (t )
M( ) }0
t
cumulant expansion:
=M ( )t
(t) (o)
exp{ d (t )
M( ) }0
t
=M ( )t
Q
(t)
10 fs time
c
modulation strength
modulation speed
e xp { i M ( ) + d d
M ( ) }
0
t
0
t
0
general:
Kubo
=0,fast M(t)