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Properties of the generalized master equation: Green’s functions and probability density functions in the path representation
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10.1063/1.2743969
/content/aip/journal/jcp/127/3/10.1063/1.2743969
http://aip.metastore.ingenta.com/content/aip/journal/jcp/127/3/10.1063/1.2743969
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

A part of a semi-Markovian chain with only nearest neighbor transitions and directional WT-PDFs, and . A way to simulate such a process is to first draw a random number out of a uniform density that determines the propagation direction according to the transition probabilities, and then to draw a random time out of the relevant WT-PDF.

Image of FIG. 2.
FIG. 2.

A circular three-state chain. The system is characterized by the waiting time PDFs, here denoted by , where and .

Image of FIG. 3.
FIG. 3.

A two-state semi-Markovian chain characterized by the WT-PDFs and .

Image of FIG. 4.
FIG. 4.

as a function of , for and . The exact expression in Eq. (16) (dotted curve), the Gaussian approximation (dashed curve), and the rectangular approximation are shown.

Image of FIG. 5.
FIG. 5.

The Green’s function in Eq. (18), the expression in Eq. (19) that uses the rectangular approximation, and packets of path PDFs (the size of each packet is shown at the base of the arrow pointing on the packet). Panel (a) shows, on a linear-log scale, that the approximation of a packet of path PDFs is valid only at the maximum of the packet, where panel (b) emphasizes that the packet width increases at large times (the width of the packet scales as ). Here, and with appropriate arbitrary units.

Image of FIG. 6.
FIG. 6.

A three-state chain. The system is characterized by the waiting time PDFs , , , and .

Image of FIG. 7.
FIG. 7.

A four-state chain. The system is characterized by the waiting time PDFs , , , , , and .

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/content/aip/journal/jcp/127/3/10.1063/1.2743969
2007-07-16
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Properties of the generalized master equation: Green’s functions and probability density functions in the path representation
http://aip.metastore.ingenta.com/content/aip/journal/jcp/127/3/10.1063/1.2743969
10.1063/1.2743969
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