Quantum theory of nonconservative systems

Caldirola, P.

doi:10.1007/bf02721487

Cited by 87 publications

(22 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The linear dissipative processes in quantum optical systems can be also studied with SU(1, 1) Lie algebra in the framework of the Liouville space formulation [46,47]. Furthermore, beam splitters [48][49][50] interferometers [51], and linear directional couplers [52,53] are successfully described by SU (2) Lie algebra. In these studies the Baker-Campbell-Hausdorff formulas are useful, where in many cases the quantities to be calculated are exponential functions of the generators of the Lie algebras.…”

Section: Application Of Su(1 1) Casimir Operatormentioning

confidence: 99%

See 1 more Smart Citation

An Alternative Model of the Damped Harmonic Oscillator Under the Influence of External Force

Abdalla

Al-Ismael

2009

Int J Theor Phys

View full text Add to dashboard Cite

In this paper we introduce the modified time-dependent damped harmonic oscillator. An exact solution of the wave function for both Schrödinger picture and coherent state representation are given. The linear and quadratic invariants are also discussed and the corresponding eigenvalues and eigenfunctions are calculated. The Hamiltonian is transformed to SU(1, 1) Lie algebra and an application to the generalized coherent state is discussed. It has been shown that when the system is under critical damping case the maximum squeezing is observed in the first quadrature F x . However, for the overcritical damping case the maximum squeezing occurs in the second quadrature F y . Also it has been shown that the system for both cases is sensitive to the variation in the coherent state phase.

show abstract

Section: Application Of Su(1 1) Casimir Operatormentioning

confidence: 99%

“…In the present communication we reconsider the problem of time-dependent harmonic oscillator which has been extensively studied in the mid of the last century, see for example [1][2][3][4][5][6][7][8][9][10][11][12]. The question which may arise why one comes back to study one of the old problem and try to resurrect it.…”

Section: Introductionmentioning

confidence: 96%

An Alternative Model of the Damped Harmonic Oscillator Under the Influence of External Force

Abdalla

Al-Ismael

2009

Int J Theor Phys

View full text Add to dashboard Cite

show abstract

“…If so, one could have underestimated lessons coming from one elementary example, namely, the exponentially damped mass or KanaiCaldirola systems 25,26 .…”

Section: Advances In Mathematical Physicsmentioning

confidence: 99%

On the Existence and Robustness of Steady Position-Momentum Correlations for Time-Dependent Quadratic Systems

Gianfreda

Landolfi

2012

Advances in Mathematical Physics

View full text Add to dashboard Cite

We discuss conditions giving rise to stationary position-momentum correlations among quantum states in the Fock and coherent basis associated with the natural invariant for the one-dimensional time-dependent quadratic Hamiltonian operators such as the Kanai-Caldirola Hamiltonian. We also discuss some basic features such as quantum decoherence of the wave functions resulting from the corresponding quantum dynamics of these systems that exhibit no timedependence in their quantum correlations. In particular, steady statistical momentum averages are seen over welldefined time intervals in the evolution of a linear superposition of the basis states of modified exponentially damped mass systems.

show abstract

“…The fundamental commutation relations of this model are time independent; however, the time-dependent uncertainty products, obtained in this way, vanish as time tends to infinity [6]. The Caldirola-Kanai theory with an explicit time-dependent Hamiltonian is another kind of variation theory [7,8,9]. In the quantum version of this theory, both the canonical commutation rules and the uncertainty products tend to zero as time tends to infinity.…”

Section: Introductionmentioning

confidence: 99%