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О некоторых свойствах операторов обобщенного углового момента
No full text[Jannussis A.; Янусис А.]; [Кtenas P.; Ктенас П.]English. Bulgarian, Russian summar
LIE-ADMISSIBLE PERTURBATION-METHODS FOR OPEN QUANTUM-SYSTEMS
No full textWe consider open quantum systems described by a Hamiltonian of the type H0 + lambdaV, where lambda is a small parameter. For such systems, we develop perturbative methods of solution of the corresponding Liouville-von Neumann and Schrodinger equations, by introducing "dissipation" operators which connect conservative to dissipative systems. In the case of the density matrix, the corresponding operator LAMBDA is nothing but the non-unitary LAMBDA-transformation of Misra, Prigogine and Courbage. Our perturbative approach possesses a Lie-admissible structure, since the "dissipation" operators obey time-evolution equations whose brackets are the product of a Lie-admissible algebra. Explicit solutions for such operators are found in the form of series expansions in lambda. The matrix formulation of the above results is also given
LANDAU-ZENER-LIKE TRANSITIONS OF A DRIVEN CALDIROLA-KANAI OSCILLATOR
No full textWe discuss the generalized tunneling through a dynamical barrier for a damped and forced oscillator of the Caldirola-Kanai type. The Landau-Zener-like probability transition from the oscillator ground state to the nth energy level is exactly evaluated by using the Wei-Norman algebraic form of the time evolution operator. Considering a specific example, we show that an increase of the friction parameter gamma implies a decrease of the occupation probability
DISSIPATIVE TUNNELING OF THE INVERTED CALDIROLA-KANAI OSCILLATOR
No full textWe discuss, in the phase time approach, quantum tunnelling in the presence of dissipation for an inverted oscillator with Caldirola-Kanai damping. The exact expressions of time delay, traversal time and effective tunnelling velocity are derived. Some paradoxical aspects of tunnelling related to the particle speed in crossing the barrier-such as the Hartmann-Fletcher effect-are briefly considered
TIME EVOLUTION OF CALDIROLA-KANAI OSCILLATORS
No full textWe discuss, in the Schrodinger picture, the time evolution of open quantum systems driven by Hamiltonians of the Caldirola-Kanai (CK) type, i.e. the usual CK Hamiltonian, the inverted one (obtained by letting omega --> iomega) and the CK Hamiltonian with complex friction coefficient. The approach we use is essentially based on the Lie-admissible treatment of non-Hermitian Hamiltonians and on the Wei-Horman expression of the time-development operator. The explicit expressions of the CK propagators are derived. By passing to Bloch statistics (letting t --> - iHBARbeta), we find also the density matrix and the main thermodynamical quantities of the imaginary friction CK oscillator
QUANTUM GROUPS AND LIE-ADMISSIBLE TIME EVOLUTION
No full textThe time evolution of operators for q-oscillators is derived for the first time by exploiting the connection between q-deformation algebras and Lie-admissible algebras
BOSE REALIZATION OF A NONCANONICAL HEISENBERG ALGEBRA
No full textWe find out the Bose realization of a generalized Heisenberg algebra, in which the bracket of the annihilation and creation operators is proportional to a polynomial function of the number operator. The eigenvalues of the corresponding oscillator are derived in a special case. We stress also the connection between non-canonical commutation relations and q-algebras
QUANTUM TUNNELING OF A DAMPED AND DRIVEN, INVERTED HARMONIC-OSCILLATOR
No full textUsing the evolution operator method, we derive the exact propagator of the generalized parametric oscillator in its more general form. This result is exploited to obtain the exact wavefunction of a damped and driven, inverted harmonic oscillator of the Caldirola-Kanai type, taking a Gaussian wavepacket as the initial state. We discuss the tunnelling process of such a system. The probability density and the persistence probability are evaluated. The expression for the sojourn time is derived for a small external force, and is the sum of two terms, whose explicit forms are obtained in the case of an extended wavepacket. The first term is an increasing function of the dissipation parameter gamma, whereas the second one is strictly due to the presence of the driving force
STUDY OF THE GENERALIZED PARAMETRIC OSCILLATOR
No full textWe find the exact solution of the time evolution for the generalized parametric oscillator, both in the Schrodinger and in the Heisenberg representation, by exploiting the SLJ (1, 1) structure of the Hamiltonian, the isomorphism between the SU(1, 1) and SL(2, R) groups and the Wei-Norman expression of the evolution operator. Coherent states and Berry's phase are briefly considered
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