Spectral properties of a time-periodic Fokker-Planck equation

Alpatov, P.; Reichl, L. E.

doi:10.1103/physreve.49.2630

Cited by 9 publications

(5 citation statements)

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“…Here, E, T and V represent the total energy, kinetic energy and potential energy, respectively; q is the generalized coordinate and p is the generalized momentum; m and ω are the mass and frequency of the oscillator. If one maps the energy distribution in the phase space, one will find that the contour of a constant energy is an ellipse (Figure 1a), since equation (2) can be reduced into 22 22 1…”

Section: The Original Concept Of H According To Planckmentioning

confidence: 99%

“…Since the Planck's constant is a fundamental physical constant, it is involved in many areas of studies, including the foundation of quantum mechanics [18,19], quantum field theory [20,21], the study of chaos [22] and tunneling [23], etc. There have been many previous attempts to explain the physical basis of the Planck's constant [24][25][26][27][28].…”

Section: Implications On the Physical Meaning Of Heisenberg's Uncertamentioning

confidence: 99%

“…If one maps the energy distribution in the phase space, one will find that the contour of a constant energy is an ellipse (Figure 1a), since equation ( 2) can be reduced into 22 22 1…”

Section: The Original Concept Of H According To Planckmentioning

confidence: 99%

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Physical interpretation of Planck’s constant based on the Maxwell theory

Chang

2017

Chinese Phys. B

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The discovery of the Planck's relation is generally regarded as the starting point of quantum physics. The Planck's constant h is now regarded as one of the most important universal constants. The physical nature of h, however, has not been well understood. It was originally suggested as a fitting constant to explain the black-body radiation. Although Planck had proposed a theoretical justification of h, he was never satisfied with that. To solve this outstanding problem, we used the Maxwell theory to directly calculate the energy and momentum of a radiation wave packet. We found the energy of the wave packet is indeed proportional to its oscillation frequency. This allows us to derive the value of the Planck's constant. Furthermore, we showed that the emission and transmission of a photon follows the principle of all-or-none. The "strength" of the wave packet can be characterized by  , which represents the integrated strength of the vector potential along a transverse axis. We reasoned that  should have a fixed cut-off value for all photons. Our results suggest that a wave packet can behave like a particle. This offers a simple explanation to the recent satellite observations that the cosmic microwave background follows closely the black-body radiation as predicted by the Planck's law. PACS: 03.50.De; 03.65.-w; 03.65.TaInvestigating the physical origin of the Planck's constant is not only important for advancing our understanding on the foundation of quantum physics, it is also relevant to the current study of cosmology. According to the Big Bang theory [5], in the early day of the universe, it is filled with energetic photons. After the universe cooled down, these primordial photons became the Cosmic Microwave Background (CMB) that we can detect today [6]. From the recent satellite measurements, the microwave detected in the CMB follows

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Section: The Original Concept Of H According To Planckmentioning

confidence: 99%

Section: Implications On the Physical Meaning Of Heisenberg's Uncertamentioning

confidence: 99%

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Physical interpretation of Planck’s constant based on the Maxwell theory

Chang

2017

Chinese Phys. B

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“…Nonautonomous Fokker-Planck equations arise for instance in the study of a periodically driven Brownian rotor [6] and in this case λ(t) and θ(t) are periodic functions of time. In statistical mechanics, Eq.…”

Section: Introductionmentioning

confidence: 99%

“…Non-autonomous Fokker-Planck equations arise for instance in the study of a periodically driven Brownian rotor [1] and in this case λ(t) and θ(t) are periodic functions of time. In statistical mechanics, equation (1.2) arises as a natural generalization of equation (1.1) in the context of non-equilibrium thermodynamics [17].…”

Section: Introductionmentioning

confidence: 99%