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Title:  Derivation of quantum Langevin equation from an explicit moleculemedium treatment in interaction picture 
Authors:  DATTA, SN 
Keywords:  excitationenergy condensed media electronic spectroscopy thylakoid membrane exciton processes excess electrons transport aggregate crystal chloroplast 
Issue Date:  2005 
Publisher:  AMER CHEMICAL SOC 
Citation:  JOURNAL OF PHYSICAL CHEMISTRY A, 109(50), 1141711423 
Abstract:  A quantum mechanical form of the Langevin equation is derived from an explicit consideration of the modeculemedium 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 socalled 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 zerofrequency 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 FokkerPlanck 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 socalled FokkerPlanck equation for the evolution probability is easily established. 
URI:  http://dx.doi.org/10.1021/jp053098i http://dspace.library.iitb.ac.in/xmlui/handle/10054/3788 http://hdl.handle.net/10054/3788 
ISSN:  10895639 
Appears in Collections:  Article

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