| 1. |
- Kurasov, Pavel, et al.
(author)
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AHARONOV-BOHM RING TOUCHING A QUANTUM WIRE : HOW TO MODEL IT AND TO SOLVE THE INVERSE PROBLEM
- 2011
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In: Reports on mathematical physics. - 0034-4877 .- 1879-0674. ; 68:3, s. 271-287
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Journal article (peer-reviewed)abstract
- An explicitly solvable model of the gated Aharonov-Bohm ring touching a quantum wire is constructed and investigated. The inverse spectral and scattering problems are discussed. It is shown that the Titchmarsh-Weyl matrix function associated with the boundary vertices determines a unique electric potential on the graph even though the graph contains a loop. This system gives another family of isospectral quantum graphs.
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| 2. |
- Bock, Wolfgang
(author)
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Hamiltonian path integrals in momentum space representation via white noise techniques
- 2014
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In: Reports on mathematical physics. - : Elsevier. - 0034-4877 .- 1879-0674. ; 73:1, s. 91-107
-
Journal article (peer-reviewed)abstract
- The concepts of Feynman integrals in white noise analysis are used to construct the Feynman integrand for the harmonic oscillator in momentum space representation as a Hida distribution. Moreover it is shown that in a limit sense, the potential free case fulfills the conservation of momentum.
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| 3. |
- Khrennikov, Andrei, 1958-
(author)
-
Quantum correlations as correlations of classical Gaussian signals : "entanglement'' at the subquantum level
- 2012
-
In: Reports on mathematical physics. - 0034-4877 .- 1879-0674. ; 69:2, s. 213-228
-
Journal article (peer-reviewed)abstract
- We show that correlations between observables on composite quantum systems can be mathematically represented as correlations of quadratic forms of classical Gaussian signals. The formalism covers correlations for entangled quantum systems; for example, measurements of spin projections for two electrons in the singlet state. In this paper we show that at the subquantum level all quantum systems are correlated including systems in factorizable states. However, in the latter case quadratic forms of the prequantum fields (at the subquantum level these forms represent quantum observables) are uncorrelated. Thus “subquantum entanglement” for prequantum fields representing quantum systems in factorizable states cannot be found by using quantum observables. We have to go beyond quantum mechanics. Coupling with generalized quantum models of Mielnik and Zyczkowski are discussed.
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