Local-time representation of path integrals
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F15%3A00236012" target="_blank" >RIV/68407700:21340/15:00236012 - isvavai.cz</a>
Result on the web
<a href="https://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.062137" target="_blank" >https://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.062137</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1103/PhysRevE.92.062137" target="_blank" >10.1103/PhysRevE.92.062137</a>
Alternative languages
Result language
angličtina
Original language name
Local-time representation of path integrals
Original language description
We derive a local-time path-integral representation for a generic one-dimensional time-independent system. In particular, we show how to rephrase the matrix elements of the Bloch density matrix as a path integral over x-dependent local-time profiles. Thelatter quantify the time that the sample paths x(t) in the Feynman path integral spend in the vicinity of an arbitrary point x. Generalization of the local-time representation that includes arbitrary functionals of the local time is also provided. We argue that the results obtained represent a powerful alternative to the traditional Feynman-Kac formula, particularly in the high- and low-temperature regimes. To illustrate this point, we apply our local-time representation to analyze the asymptotic behavior of the Bloch density matrix at low temperatures. Further salient issues, such as connections with the Sturm-Liouville theory and the Rayleigh-Ritz variational principle, are also discussed.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA14-07983S" target="_blank" >GA14-07983S: Vacuum structure in Quantum Field Theories</a><br>
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Physical Review E
ISSN
1539-3755
e-ISSN
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Volume of the periodical
92
Issue of the periodical within the volume
6
Country of publishing house
US - UNITED STATES
Number of pages
13
Pages from-to
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UT code for WoS article
000367081600001
EID of the result in the Scopus database
2-s2.0-84954548252