lnu.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Born's formula from statistical mechanics of classical fields and theory of hitting times
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0002-9857-0938
2014 (English)In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 393, p. 207-221Article in journal (Refereed) Published
Abstract [en]

We consider Brownian motion in the space of fields and show that such a random field interacting with threshold type detectors produces clicks at random moments of time. The corresponding probability distribution can be approximately described by the same mathematical formalism as is used in quantum mechanics, theory of Hermitian operators in complex Hilbert space. The temporal structure of the "prequantum random field" which is the L-2-valued Wiener process plays the crucial role. Moments of detector's clicks are mathematically described as hitting times which are actively used in classical theory of stochastic processes. Born's formula appears as an approximate formula. In principle, the difference between the formula derived in this paper and the conventional Born's formula can be tested experimentally. In our model the presence of the random gain in detectors plays a crucial role. We also stress the role of the detection threshold which is not merely a technicality, but the fundamental element of the model. (C) 2013 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
2014. Vol. 393, p. 207-221
Keywords [en]
Random fields, Quantum probability of detection, Derivation of Born's formula, Threshold detectors, Asymptotics of error function, Distribution of hitting times
National Category
Physical Sciences Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-31389DOI: 10.1016/j.physa.2013.09.009ISI: 000328179200016Scopus ID: 2-s2.0-84886594744OAI: oai:DiVA.org:lnu-31389DiVA, id: diva2:685355
Available from: 2014-01-09 Created: 2014-01-09 Last updated: 2017-12-06Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Authority records BETA

Khrennikov, Andrei

Search in DiVA

By author/editor
Khrennikov, Andrei
By organisation
Department of Mathematics
In the same journal
Physica A: Statistical Mechanics and its Applications
Physical SciencesMathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 152 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf