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Author  |
Aldana, M.; Lledo, M.A. |
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Title |
The Fuzzy Bit |
Type |
Journal Article |
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Year |
2023 |
Publication |
Symmetry-Basel |
Abbreviated Journal |
Symmetry-Basel |
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Volume |
15 |
Issue |
12 |
Pages |
2103 - 25pp |
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Keywords |
fuzzy sets; quantum logic; multivalued logic; Quantum Mechanics |
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Abstract |
In this paper, the formulation of Quantum Mechanics in terms of fuzzy logic and fuzzy sets is explored. A result by Pykacz, which establishes a correspondence between (quantum) logics (lattices with certain properties) and certain families of fuzzy sets, is applied to the Birkhoff-von Neumann logic, the lattice of projectors of a Hilbert space. Three cases are considered: the qubit, two qubits entangled, and a qutrit 'nested' inside the two entangled qubits. The membership functions of the fuzzy sets are explicitly computed and all the connectives of the fuzzy sets are interpreted as operations with these particular membership functions. In this way, a complete picture of the standard quantum logic in terms of fuzzy sets is obtained for the systems considered. |
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Address |
[Aldana, Milagrosa] Univ Simon Bolivar, Dept Ciencias Tierra, Valle De Sartenejas 89000, Baruta, Venezuela, Email: maldana@usb.ve; |
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Publisher |
Mdpi |
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English |
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Notes |
WOS:001131238400001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
5962 |
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Author |
Casas, F.; Oteo, J.A.; Ros, J. |
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Title |
Unitary transformations depending on a small parameter |
Type |
Journal Article |
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Year |
2012 |
Publication |
Proceedings of the Royal Society A |
Abbreviated Journal |
Proc. R. Soc. A |
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Volume |
468 |
Issue |
2139 |
Pages |
685-700 |
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Keywords |
perturbation theory; quantum mechanics; unitary transformation; Magnus expansion |
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Abstract |
We formulate a unitary perturbation theory for quantum mechanics inspired by the Lie-Deprit formulation of canonical transformations. The original Hamiltonian is converted into a solvable one by a transformation obtained through a Magnus expansion. This ensures unitarity at every order in a small parameter. A comparison with the standard perturbation theory is provided. We work out the scheme up to order ten with some simple examples. |
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Address |
[Oteo, J. A.; Ros, J.] Univ Valencia, Dept Fis Teor, E-46100 Valencia, Spain, Email: rosj@uv.es |
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Thesis |
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Publisher |
Royal Soc |
Place of Publication |
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Language |
English |
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ISSN |
1364-5021 |
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Notes |
WOS:000300185400005 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ pastor @ |
Serial |
893 |
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