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Derivation of quantum Langevin equation from an explicit molecule-medium treatment in interaction picture

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Title Derivation of quantum Langevin equation from an explicit molecule-medium treatment in interaction picture
 
Creator DATTA, SN
 
Subject excitation-energy
condensed media
electronic spectroscopy
thylakoid membrane
exciton processes
excess electrons
transport
aggregate
crystal
chloroplast
 
Description A quantum mechanical form of the Langevin equation is derived from an explicit consideration of the modecule-medium interaction, as advocated by Simons in 1978, and by using two identities in the interaction picture. This can be easily reduced to the classical regime, and further simplified to the macroscopic Langevin equation by considering the stochastic Langevin force autocorrelation function. One of the so-called Einstein relations appears as a byproduct. By following the methodology proposed by Simons, an exact expression for the momentum autocorrelation function is obtained. The latter can be used to calculate the zero-frequency macroscopic diffusion coefficient that is observed to satisfy the second Einstein relation. The formalism described above gives rise to the possibility of explicitly computing the transport characteristics Such as friction constant and diffusion coefficient from the corresponding quantum statistical mechanical expressions. A discussion on the Langevin equation becomes complete only when the corresponding Fokker-Planck equation is obtained. Therefore, the probability of the evolution of states with a particular absolute magnitude of linear momentum from those of another momentum eigenvalue is quantum mechanically defined. This probability appears as a special average value of a projection operator and as a special projection operator correlation function. A classical identity is introduced that is shown to be valid also for the quantum mechanically defined probability function. By using this identity, the so-called Fokker-Planck equation for the evolution probability is easily established.
 
Publisher AMER CHEMICAL SOC
 
Date 2011-07-13T22:23:36Z
2011-12-26T12:48:10Z
2011-12-27T05:45:47Z
2011-07-13T22:23:36Z
2011-12-26T12:48:10Z
2011-12-27T05:45:47Z
2005
 
Type Article
 
Identifier JOURNAL OF PHYSICAL CHEMISTRY A, 109(50), 11417-11423
1089-5639
http://dx.doi.org/10.1021/jp053098i
http://dspace.library.iitb.ac.in/xmlui/handle/10054/3788
http://hdl.handle.net/10054/3788
 
Language en