A generalization of Fermat's principle for classical and quantum systems
The analogy between dynamics and optics had a great influence on the development of the foundations of classical and quantum mechanics. We take this analogy one step further and investigate the validity of Fermat's principle in many-dimensional spaces describing dynamical systems (i.e., the qua...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
26 September 2014
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| In: |
Physics letters
Year: 2014, Volume: 378, Issue: 44, Pages: 3205-3209 |
| ISSN: | 1873-2429 |
| DOI: | 10.1016/j.physleta.2014.09.032 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.physleta.2014.09.032 Verlag, lizenzpflichtig, Volltext: http://www.sciencedirect.com/science/article/pii/S0375960114009438 
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| Author Notes: | Tarek A. Elsayed |
| Summary: | The analogy between dynamics and optics had a great influence on the development of the foundations of classical and quantum mechanics. We take this analogy one step further and investigate the validity of Fermat's principle in many-dimensional spaces describing dynamical systems (i.e., the quantum Hilbert space and the classical phase and configuration space). We propose that if the notion of a metric distance is well defined in that space and the velocity of the representative point of the system is an invariant of motion, then a generalized version of Fermat's principle will hold. We substantiate this conjecture for time-independent quantum systems and for a classical system consisting of coupled harmonic oscillators. An exception to this principle is the configuration space of a charged particle in a constant magnetic field; in this case the principle is valid in a frame rotating by half the Larmor frequency, not the stationary lab frame. |
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| Item Description: | Gesehen am 07.08.2020 |
| Physical Description: | Online Resource |
| ISSN: | 1873-2429 |
| DOI: | 10.1016/j.physleta.2014.09.032 |