Noncyclic and nonadiabatic geometric phase for counting statistics

2010/04/30 by Jun Ohkubo, Thomas Eggel
Neuroscience · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Geometric distribution #Geometric phase #Interpretation (philosophy) #Neural dynamics and brain function #Phase (matter) #Photon counting #Probability and statistics #Probability distribution #Statistical Mechanics and Entropy #cond-mat.stat-mech #physics.chem-ph

paper · pdf · doi:10.1088/1751-8113/43/42/425001

12 pages, 1 figure

arxiv created 2010/09/16 · openalex publication_date 2010/09/30 · arxiv updated 2015/05/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We propose a general framework of the geometric-phase interpretation for counting statistics. Counting statistics is a scheme to count the number of specific transitions in a stochastic process. The cumulant generating function for the counting statistics can be interpreted as a `phase', and it is generally divided into two parts: the dynamical phase and a remaining one. It has already been shown that for cyclic evolution the remaining phase corresponds to a geometric phase, such as the Berry phase or Aharonov-Anandan phase. We here show that the remaining phase also has an interpretation as a geometric phase even in noncyclic and nonadiabatic evolution.

Citations

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