1D hopping transport with nearest-neighbor interactions

1
1D hopping transport with nearest-neighbor
interactions
?? 2011.12
2
(No Transcript)
3
(No Transcript)
4
Equilibrium system
Gibbs-Boltzmann distribution
Heat, particle, or volume exchanges are reversible
In the P-V plane
reversible transformation
the external conditions are varied slowly enough
5
Equilibrium VS nonequilibrium system
Master equation
6
stationary state
Master equation
Detailed balance
7
stationary state
If
and
Metropolis rate
8
KatzLebowitzSpohn (KLS) model
Y
E
X
along, transverse, agaist the field
9
Zero rang process
Periodic boundary condition
10
Zero rang process
11
simple exclusion process (SEP)
asymmetric simple exclusion process (ASEP)
symmetric simple exclusion process (SSEP)
totally asymmetric simple exclusion process
(TASEP)
12
Physical quantity in TASEP
13
Physical quantity in TASEP
14
Physical quantity in TASEP
15
Physical quantity in TASEP
16
Mean field theory
density profile
17
Mean field theory
maximal-current phase
18
Mean field theory
(HD)
19
(No Transcript)
20
Detailed balance
21
Unidirectional hopping transport
four-site dependent rate
22
Unidirectional hopping transport
Mean field
23
Mean field
24
Time dependent density functional theory
Solved by Maple
25
Unidirectional hopping transport
26
Unidirectional hopping transport
27
Unidirectional hopping transport
correlator
28
Unidirectional hopping transport
29
Unidirectional hopping transport
30
Time dependent density functional theory
31
Equilibrium density correlator
32
Equilibrium density correlator
33
(No Transcript)
34
Equilibrium density correlator
35
Kinetic monte carlo method
36
Kinetic monte carlo method
tglobaltglobaltmin
37
Results of classical DFT calculations
38
Results of classical DFT calculations
39
(No Transcript)
40
Coupling mechanism II
41
Bulk-adapted couplings
42
Bulk-adapted couplings
43
outlook
Long range Coulomb interactions?
44
outlook

• Quantum transport processes for particle-particle
  interactions
• photoelectric devicesclassical TDFT
• Controlling transport on the nanoscale

45
reference
Exact density functionals in one dimension 2000
J. Phys. A Math. Gen. 33 L41
Kinetics in one-dimensional lattice gas and Ising
models from time-dependent density-functional
theory Phys. Rev. E 65, 066112 (2002)
46

• Thank you !