Abstract
We review some aspects of the quantization of the damped harmonic oscillator. We derive the exact action for a damped mechanical system in the frame of the path integral formulation of the quantum Brownian motion problem developed by Schwinger and by Feynman and Vernon. The doubling of the phase space degrees of freedom for dissipative systems and thermal field theories is discussed and the doubled variables are related to quantum noise effects. The ‘t Hooft proposal, according to which the loss of information due to dissipation in a classical deterministic system manifests itself in the quantum features of the system, is analyzed and the quantum spectrum of the harmonic oscillator is shown to originate from the dissipative character of the original classical deterministic system.
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© 2004 Springer-Verlag Berlin/Heidelberg
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Blasone, M., Jizba, P., Vitiello, G. (2004). Dissipation, Emergent Quantization, and Quantum Fluctuations. In: Elze, HT. (eds) Decoherence and Entropy in Complex Systems. Lecture Notes in Physics, vol 633. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40968-7_12
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DOI: https://doi.org/10.1007/978-3-540-40968-7_12
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20639-2
Online ISBN: 978-3-540-40968-7
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