dorsal/arxiv
View SchemaApproach to Quantum Kramers' Equation and Barrier Crossing Dynamics
| Authors | Dhruba Banerjee, Bidhan Chandra Bag, Suman Kumar Banik, Deb Shankar Ray |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0111005 |
| URL | https://arxiv.org/abs/quant-ph/0111005 |
| DOI | 10.1103/PhysRevE.65.021109 |
| Journal | Phys. Rev. E 65 (2002) 021109 |
Abstract
We have presented a simple approach to quantum theory of Brownian motion and barrier crossing dynamics. Based on an initial coherent state representation of bath oscillators and an equilibrium canonical distribution of quantum mechanical mean values of their co-ordinates and momenta we have derived a $c$-number generalized quantum Langevin equation. The approach allows us to implement the method of classical non-Markovian Brownian motion to realize an exact generalized non-Markovian quantum Kramers' equation. The equation is valid for arbitrary temperature and friction. We have solved this equation in the spatial diffusion-limited regime to derive quantum Kramers' rate of barrier crossing and analyze its variation as a function of temperature and friction. While almost all the earlier theories rest on quasi-probability distribution functions (like Wigner function) and path integral methods, the present work is based on {\it true probability distribution functions} and is independent of path integral techniques. The theory is a natural extension of the classical theory to quantum domain and provides a unified description of thermal activated processes and tunneling.
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"abstract": "We have presented a simple approach to quantum theory of Brownian motion and\nbarrier crossing dynamics. Based on an initial coherent state representation of\nbath oscillators and an equilibrium canonical distribution of quantum\nmechanical mean values of their co-ordinates and momenta we have derived a\n$c$-number generalized quantum Langevin equation. The approach allows us to\nimplement the method of classical non-Markovian Brownian motion to realize an\nexact generalized non-Markovian quantum Kramers\u0027 equation. The equation is\nvalid for arbitrary temperature and friction. We have solved this equation in\nthe spatial diffusion-limited regime to derive quantum Kramers\u0027 rate of barrier\ncrossing and analyze its variation as a function of temperature and friction.\nWhile almost all the earlier theories rest on quasi-probability distribution\nfunctions (like Wigner function) and path integral methods, the present work is\nbased on {\\it true probability distribution functions} and is independent of\npath integral techniques. The theory is a natural extension of the classical\ntheory to quantum domain and provides a unified description of thermal\nactivated processes and tunneling.",
"arxiv_id": "quant-ph/0111005",
"authors": [
"Dhruba Banerjee",
"Bidhan Chandra Bag",
"Suman Kumar Banik",
"Deb Shankar Ray"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"physics.chem-ph"
],
"doi": "10.1103/PhysRevE.65.021109",
"journal_ref": "Phys. Rev. E 65 (2002) 021109",
"title": "Approach to Quantum Kramers\u0027 Equation and Barrier Crossing Dynamics",
"url": "https://arxiv.org/abs/quant-ph/0111005"
},
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