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Abstract: In this paper we show that the evolution of a quantum state, driven by a harmonic-oscillator-type Hamiltonian, can be studied using tools exploited to characterize the evolution of a charged beam in a transport channel. The relevance of the Courrent-Snyder invariant and of Twiss-like parameters to characterize, e.g., the amount of squeezing is carefully pointed out. © 1992 Società Italiana di Fisica.
Keywords: Photon statistics and photon counting
Abstract: In this paper we discuss the modifications to the undulator brightness and central wavelength expressions due to the low-energy effects and to the inclusion of the sextupolar magnetic-field components. The corrections are calculated up to the order (K/γ)4. The mathematical details are simplified by the use of generalized Bessel functions. © 1992 Società Italiana di Fisica.
Keywords: Particle beams and particle optics | Particles in electromagnetic fields (including synchrotron radiation)
Abstract: We use the results of a recent reformulation of the theory of arbitrary-order differential equations in terms of non-Hermitian operators to show that the invariant binorm is associated to a generalized Courant-Snyder invariant. Furthermore, we indicate the existence of higher-order invariants associated to the Casimir operators of the group, utilized to treat higher-order equations. We also discuss the intrinsic supersymmetric nature of the theory developed. Finally, we show the relevance of the proposed mathematical technique to the design of fiberoptics transport systems. © 1991 Società Italiana di Fisica.
Keywords: Infinite-dimensional Lie groups | Ordinary differential equations | PACS 42.10 | Particle beams and particle optics | Propagation and transmission in homogeneous media
Abstract: In two previous papers, the authors have introduced the concept of binormal differential equations. It has been shown that invariants of the Courant-Snyder type are associated to the scalar products of the column vector associated to an ordinary differential equation and to its binormal. In this paper, we show the equivalence of the above invariant and the Lewis form. We also introduce a density matrix for a second-order differential equation and clarify the geometrical meaning of the Twiss parameters. The importance of the above results in the analysis of quantum problems such as, e.g., the evolution of squeezed states is finally stressed. © 1991 Società Italiana di Fisica.
Keywords: Infinite-dimensional Lie groups | Ordinary differential equations | Particle beams and particle optics | Propagation and transmission in homogeneous media
Abstract: We reformulate the theory of ordinary differential equations of arbitrary order with nonconstant coefficients, using the formalism of non-Hermitian operators. In particular, exploiting the technique of dissipative quantum mechanics, we show that the solution of the equations can be written in terms of a nonunitary evolution operator. Furthermore, we point out that the solution of the adjoint equations can be derived from an associated biunitary operator. We show that a number of invariants, not previously discussed, exhists. Finally, we prove that the method allows the search for approximate solutions that can be used in many physical problems. © 1991 Società Italiana di Fisica.
Keywords: Infinite-dimensional Lie groups | Ordinary differential equations | Particle beams and particle optics | Propagation and transmission in homogeneous media
Abstract: In this note we introduce a further generalization of Bessel-type functions, discussing the case of a multivariables and one-index function. This kind of function can be usefully exploited in problems in which the dipole approximation does not hold and many higher harmonics are simultaneously operating. We analyse the relevant recurrence properties, the modified forms and the generating functions. © 1991 Società Italiana di Fisica.
Keywords: PACS 02.30.Gp Special functions
Abstract: In this paper we complete the study of the evolution of multilevel systems in terms of a geometrical picture based on the so-called Cayley-Klein parameters introduced to describe rotations in classical mechanics. It is shown that these parameters and their identification in terms of Euler angles are helpful and insightful tools to clarify the dynamical features of two- and three-level atoms interacting with intense external radiation. It is finally shown that the evolution of, e.g., the three-level case depends on a rotation matrix fully equivalent to the Kobayashi-Maskawa matrix introduced in elementary-particle theory to account for generalized Cabibbo mixing angles and CP-violations in weak-decay processes. © 1989 Società Italiana di Fisica.
Keywords: PACS 03.65.Fd Algebraic methods | PACS 11.30.Jw SU and SU symmetries 2 3 | PACS 12.30 Models of weak interactions
Abstract: The eigenmodes of the longitudinal pulse propagation equation of free-electron lasers (FEL) are not in general orthogonal to each other, but rather biorthogonal to an adjoint set of eigenmodes which, we will show, represent the FEL propagation in thé reverse direction in the same resonator. We also point out the analogies of the present analysis with that relevant to the transverse-mode evolution in conventional lasers. © 1988 Società Italiana di Fisica.
Keywords: 42.60.He | Optical problems related to properties and interactions of laser beams
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