104,203 research outputs found
Quantization of the dynamics of a particle on a double cone by preserving Noether symmetries
No full textThe classical quantization of the motion of a free particle and that of an harmonic oscillator on a double cone are achieved by a quantization scheme [M. C. Nucci, Theor. Math. Phys. 168 (2011) 994], that preserves the Noether point symmetries of the underlying Lagrangian in order to construct the Schrödinger equation. The result is different from that given in [K. Kowalski, J. Rembielński, Ann. Phys. 329 (2013) 146]. A comparison of the different outcomes is provided
Reduction of the classical MICZ-Kepler problem to a two-dimensional linear isotropic harmonic oscillator
No full textThe classical MICZ-Kepler problem is shown to be reducible to an isotropic two-dimensional system of linear harmonic oscillators and a conservation law in terms of new variables related to the Ermanno-Bernoulli constants and the components of the Poincare vector. An algorithmic route to linearization is shown based on Lie symmetry analysis and the reduction method [Nucci, J. Math. Phys. 37, 1772 (1996) ]. First integrals are also obtained by symmetry analysis and the reduction method [Marcelli and Nucci,J. Math. Phys. 44, 2111 (2002) ]
Quantization of quadratic Liénard-type equations by preserving Noether symmetries
No full textThe classical quantization of a family of a quadratic Liénard-type equation (Liénard II equation) is achieved by a quantization scheme (Nucci 2011) [28] that preserves the Noether point symmetries of the underlying Lagrangian in order to construct the Schrödinger equation. This method straightforwardly yields the Schrödinger equation as given in Choudhury and Guha (2013) [6]
Jacobi's last multiplier and the complete symmetry group of the Ermakov-Pinney equation
No full textThe Ermakov-Pinney equation possesses three Lie point symmetries with the algebra sl(2, R). This algebra does not provide a representation of the complete symmetry group of the Ermakov-Pinney equation. We show how the representation of the group can be obtained with the use of the method described in Nucci, J. Nonlin. Math. Phys. 12 ( 2005) ( this issue), which is based on the properties of Jacobi's last multiplier (Bianchi L, Lezioni sulla teoria dei gruppi continui finiti di trasformazioni, Enrico Spoerri, Pisa, 1918), the method of reduction of order ( Nucci, J. Math. Phys 37 ( 1996), 1772 - 1775) and an interactive code for calculating symmetries ( Nucci, Interactive REDUCE programs for calcuating classical, non-classical and Lie-Backlund symmetries for differential equations (preprint: Georgia Institute of Technology, Math 062090-051, 1990, and CRC Handbook of Lie Group Analysis of Differential Equations. Vol. 3: New Trends in Theoretical Developments and Computational Methods, Editor: Ibragimov N H, CRC Press, Boca Raton, 1996, 415 - 481)
Noether symmetries and the quantization of a Liénard-type nonlinear oscillator
No full textThe classical quantization of a Liénard-type nonlinear oscillator is achieved by a quantization scheme (M. C. Nucci. Theor. Math. Phys., 168:994–1001, 2011) that preserves the Noether point symmetries of the underlying Lagrangian in order to construct the Schrödinger equation. This method straightforwardly yields the Schrödinger equation in the momentum space as given in (V. Chithiika Ruby, M. Senthilvelan, and M. Lakshmanan. J. Phys. A: Math. Gen., 45:382002, 2012), and sheds light on the apparently remarkable connection with the linear harmonic oscillator
The harmony in the Kepler and related problems
No full textThe technique of reduction of order developed by Nucci [J. Math. Phys. 37, 1772-1775 (1996)] is used to produce nonlocal symmetries in addition to those reported by Krause [J. Math. Phys. 35, 5734-5748 (1994)] in his study of the complete symmetry group of the Kepler problem. The technique is shown to be applicable to related problems containing a drag term which have been used to model the motion of low altitude satellites in the Earth's atmosphere and further generalizations. A consequence of the application of this technique is the demonstration of the group theoretical relationship between the simple harmonic oscillator and the Kepler and related problems
An algebraic approach to laying a ghost to rest
No full textIn the recent literature there has been a resurgence of interest in the fourth-order field-theoretic model of Pais-Uhlenbeck (1950 Phys. Rev. 79 145-65) which has not had a good reception over the past half a century due to the existence of ghosts in the properties of the quantum mechanical solution. Bender and Mannheim (2008 J. Phys. A: Math. Theor. 41 304018) were successful in persuading the corresponding quantum operator to 'give up the ghost'. Their success had the advantage of making the model of Pais-Uhlenbeck acceptable to the physics community and in the process added further credit to the cause of advancement of the use of PT symmetry. We present a case for the acceptance of the Pais-Uhlenbeck model in the context of Dirac's theory by providing an Hamiltonian that is not quantum mechanically haunted. The essential point is the manner in which a fourth-order equation is rendered into a system of second-order equations. We show by means of the method of reduction of order (Nucci M C 1996 J. Math. Phys. 37 1772-5) that it is possible to construct a Hamiltonian that gives rise to a satisfactory quantal description without having to abandon Dirac
Are all classical superintegrable systems in two-dimensional space linearizable?
No full textSeveral examples of classical superintegrable systems in a two-dimensional space are shown to possess hidden symmetries leading to their linearization. They include those determined fifty years ago in the work of Friš et al. [Phys. Lett. 13, 354-356 (1965)], their generalizations, and the more recent Tremblay-Turbiner-Winternitz system [F. Tremblay et al., J. Phys. A: Math. Theor. 42, 242001 (2009)]. We conjecture that all classical superintegrable systems in the two-dimensional space have hidden symmetries that make them linearizable
Superintegrable systems in non-Euclidean plane: Hidden symmetries leading to linearity
No full textNineteen classical superintegrable systems in two-dimensional non-Euclidean spaces are shown to possess hidden symmetries leading to their linearization. They are the two Perlick systems [Ballesteros et al., Classical Quantum Gravity 25, 165005 (2008)], the Taub-NUT system [Ballesteros et al., SIGMA 7, 048 (2011)], and all the 17 superintegrable systems for the four types of Darboux spaces as determined by Kalnins et al. [J. Math. Phys. 44, 5811-5848 (2003)]
An automatic system to locate phase-to-ground faults in medium voltage cable networks based on the wavelet analysis of high-frequency signals
No full textThe paper presents a microcontroller-based automatic system that applies the continuous wavelet analysis to the measured fault-originated electromagnetic transients in order to locate phase-to-ground faults in power distribution networks composed by coaxial cables. The paper describes the numerical procedure conceived to: (i) detect the presence of fault-originated transients superimposed to steady-state voltage waveforms, (ii) identify the faulted phase-conductor and (iii) identify the part of the fault transient that can be used to build a specific mother wavelet so to improve the fault location accuracy. The paper also describes the implementation of the procedure into an embedded microcontroller as well as its experimental validation carried out by means of analog real-time generated fault waveforms obtained from EMTP simulations. © 2011 IEEE.DESLDepartment of Electrical Engineering, University of Bologna, Bologna, Italy, Conference code: 86744, Export Date: 25 April 2012, Source: Scopus, Art. No.: 6019280, doi: 10.1109/PTC.2011.6019280, Language of Original Document: English, Correspondence Address: Paolone, M.; Department of Electrical Engineering, University of Bologna, Bologna, Italy; email: [email protected], References: Radial distribution test feeders (1991) IEEE Trans. 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