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Author |
Sels, D.; Brosens, F.; Magnus, W. |
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Title |
Wigner distribution functions for complex dynamical systems : a path integral approach |
Type |
A1 Journal article |
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Year  |
2013 |
Publication |
Physica: A : theoretical and statistical physics |
Abbreviated Journal |
Physica A |
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Volume |
392 |
Issue |
2 |
Pages |
326-335 |
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Keywords |
A1 Journal article; Theory of quantum systems and complex systems; Condensed Matter Theory (CMT) |
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Abstract |
Starting from Feynmans Lagrangian description of quantum mechanics, we propose a method to construct explicitly the propagator for the Wigner distribution function of a single system. For general quadratic Lagrangians, only the classical phase space trajectory is found to contribute to the propagator. Inspired by Feynmans and Vernons influence functional theory we extend the method to calculate the propagator for the reduced Wigner function of a system of interest coupled to an external system. Explicit expressions are obtained when the external system consists of a set of independent harmonic oscillators. As an example we calculate the propagator for the reduced Wigner function associated with the CaldeiraLegett model. |
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Publisher |
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Place of Publication |
Amsterdam |
Editor |
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Wos |
000311135200004 |
Publication Date |
2012-09-14 |
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Series Editor |
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Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
0378-4371; |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
2.243 |
Times cited |
9 |
Open Access |
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Notes |
; ; |
Approved |
Most recent IF: 2.243; 2013 IF: 1.722 |
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Call Number |
UA @ lucian @ c:irua:101414 |
Serial |
3921 |
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Author |
Sels, D.; Brosens, F.; Magnus, W. |
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Title |
Classical trajectories : a powerful tool for solving tunneling problems |
Type |
A1 Journal article |
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Year |
2012 |
Publication |
Physica: A : theoretical and statistical physics |
Abbreviated Journal |
Physica A |
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Volume |
391 |
Issue |
1/2 |
Pages |
78-81 |
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Keywords |
A1 Journal article; Theory of quantum systems and complex systems; Condensed Matter Theory (CMT) |
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Abstract |
In the realm of Ehrenfests theorem, classical trajectories obeying Newtons laws have been proven useful to construct explicit solutions to the time-dependent WignerLiouville equation. Whereas previous works have particularly focused on the initial distribution function as a vehicle found to carry the signatures of quantum statistics into the time-dependent solution, the present paper shows that the LagrangeCharpit method based on classical trajectories can be successfully invoked as well to tackle quantum mechanical features with no classical counterpart, such as tunneling. |
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Corporate Author |
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Publisher |
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Place of Publication |
Amsterdam |
Editor |
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Language |
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Wos |
000297230700010 |
Publication Date |
2011-08-25 |
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Series Editor |
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Series Title |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
0378-4371; |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
2.243 |
Times cited |
7 |
Open Access |
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Notes |
; ; |
Approved |
Most recent IF: 2.243; 2012 IF: 1.676 |
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Call Number |
UA @ lucian @ c:irua:92359 |
Serial |
370 |
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Author |
Sels, D.; Brosens, F.; Magnus, W. |
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Title |
On the path integral representation of the Wigner function and the BarkerMurray ansatz |
Type |
A1 Journal article |
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Year |
2012 |
Publication |
Physics letters : A |
Abbreviated Journal |
Phys Lett A |
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Volume |
376 |
Issue |
6/7 |
Pages |
809-812 |
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Keywords |
A1 Journal article; Theory of quantum systems and complex systems; Condensed Matter Theory (CMT) |
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Abstract |
The propagator of the Wigner function is constructed from the WignerLiouville equation as a phase space path integral over a new effective Lagrangian. In contrast to a paper by Barker and Murray (1983) [1], we show that the path integral can in general not be written as a linear superposition of classical phase space trajectories over a family of non-local forces. Instead, we adopt a saddle point expansion to show that the semiclassical Wigner function is a linear superposition of classical solutions for a different set of non-local time dependent forces. As shown by a simple example the specific form of the path integral makes the formulation ideal for Monte Carlo simulation. |
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Publisher |
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Place of Publication |
Amsterdam |
Editor |
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Language |
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Wos |
000301167300005 |
Publication Date |
2012-01-17 |
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Series Editor |
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Series Title |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
0375-9601; |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
1.772 |
Times cited |
7 |
Open Access |
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Notes |
; ; |
Approved |
Most recent IF: 1.772; 2012 IF: 1.766 |
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Call Number |
UA @ lucian @ c:irua:94006 |
Serial |
2445 |
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