1,720,991 research outputs found
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
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
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
CALDIROLA-KANAI HAMILTONIAN WITH COMPLEX FRICTION COEFFICIENT
No full textIn the present note we find the exact solution of the time-dependent Schrodinger equation for the Caldirola-Kanai Hamiltonian with complex friction coefficient by applying the biorthogonal method. The eigenfunction normalization takes place in the extended Hilbert space L(2){R X [0, T]}, where T is the time. From the biorthonormal solutions we calculate the eigenvalues which are complex and discrete, the matrix elements of the current density and the occupation probability
NON-HERMITIAN TUNNELING OF OPEN QUANTUM-SYSTEMS
No full textWe discuss some aspects of the time picture of tunneling for open quantum systems described by non-Hermitian (NH) Hamiltonians. The concept of sojourn time for such systems is introduced in the framework of the biorthonormal formalism. Due to the various definitions of probability density in the non-Hermitian case, we get three different sojourn times, two real and one complex. We consider as model of a dissipative NH system the complex, generalized parametric oscillator, for which we derive the exact expressions of the three sojourn times in terms of the Wei-Norman characteristic functions entering the non-unitary evolution operators. The special case of the inverted Caldirola-Kanai oscillator with complex friction parameter is investigated for an initial extended wavepacket. We also discuss the Landau-Zener-like transitions of the NH parametric oscillator, i.e. the dissipative tunneling through a dynamical barrier due to the perturbative effect of the damping
TUNNELING PROCESS FOR NON-HERMITIAN SYSTEMS - THE COMPLEX-FREQUENCY INVERTED OSCILLATOR
No full textWe study the tunnel effect for an inverted oscillator with complex frequency. The solution of the corresponding non-Hermitian (NH) Schrodinger equation is found by the evolution operator method, based on the SU(1, 1) structure of the Hamiltonian and the Wei-Norman theorem. We put forward a generalization of dwell time for NH systems built up from their biorthonormal states. The resulting tunnelling time turns out to be complex
REAL PLANCK DISTRIBUTION FOR A COMPLEX Q-BOSON GAS
No full textWe discuss the energy-density distribution for a gas of q-bosons with complex deformation parameter by exploiting a new q-complex oscillator algebra in which both the number operator and the energy eigenvalues are real. The corresponding Planck distribution generalizes the results obtained for a real q-boson gas, including Wien's and Stephan's laws, and the role of an effective Planck constant depending on the parameter modulus
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