Summary
We calculate in exact closed form the commutator and the anticommutator of the collective operators which describe pair transfer in a Josephson junction. We determine the conditions under which the exact commutation rules reduce to the approximate ones used in the pseudospin-angular-momentum and in the number-phase-angle formulation of the junction dynamics. The exact commutation relations are applied to the description of superradiance in Josephson junctions.
Riassunto
In questo lavoro si calcolano esattamente ed in forma chiusa il commutatore e l'anti-commutatore degli operatori collettivi che descrivono il trasferimento di coppie in una giunzione Josephson. Si discute inoltre in quali condizioni le regole di commutazione esatte possono essere approssimate con quelle di momento angolare o di numero-angolo di fase introdotte in alcune formulazioni della dinamica di una giunzione. Infine le regole di commutazione esatte sono usate per studiare il fenomeno della superradianza nelle giunzioni Josephson.
Резюме
Мы вычисляем в явной замкнутой форме коммутатор и антикоммутатор коллективных операторов, которые описывают перенос пары в соединении Джозефсона. Мы определяем условия, когда точное правило коммутации сводится к приближенному, которое используется в формулировках динамики соединения. Точные коммутационные соотношения применяются для описания сврхсветимости в соединениях Джозефсона.
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Lugiato, L.A., Milani, M. On the quantum-mechanical description of Josephson junctions. Nuov Cim B 55, 417–434 (1980). https://doi.org/10.1007/BF02739171
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DOI: https://doi.org/10.1007/BF02739171