scholarly journals Path algebras, wave-particle duality, and quantization of phase space

2016 ◽  
Vol 107 (3) ◽  
pp. 409-426
Author(s):  
Murray Gerstenhaber
Keyword(s):  
Phase Space ◽  
Path Algebras ◽  
Wave Particle Duality

scholarly journals Evidence of wave particle duality in human brain dynamics

2020 ◽  
Author(s):  
Mayukha Pal ◽  
Neeraj . ◽  
Prasanta Panigrahi
Keyword(s):  
Phase Space ◽  
Low Frequency ◽  
Brain Dynamics ◽  
Epileptogenic Zone ◽  
Unstable Periodic Orbits ◽  
Wave Dynamics ◽  
Coherent Wave ◽  
Wave Particle Duality ◽  
Epileptic Patients ◽  
Frequency Components

Abstract Clear evidence of wave-particle duality in the brain dynamics is demonstrated for the first time, from the EEG signals of healthy individuals and epileptic patients. The low frequency components exhibit particle type behaviour in a phase-space description, with the potentials as coordinates and their instantaneous changes as the corresponding velocities. The closed paths reveal periodic motion, well described by one linear oscillator or possibly coupled ones with limit cycle dynamics and synchronization at the macroscopic level. The epileptic patients reveal dynamical features of bi-stability, originating from non-linearity, a prominent feature in the signals from the epileptogenic zone and much enhanced during the periods of seizure. Analogy from the phase-space of oscillator dynamics reveals dominance of potential energy in the signals from the epileptogenic zone, as also in the patients during occurrence of seizure. The acceleration, arising from the change of velocity, is found to be particularly strong in epileptic patients, when the phase space shows bi-stability and bursty behaviour. Wave behaviour with characteristics of superposition emerges in the frequency range corresponding to the observed unstable periodic orbits, that appear at the boundary of alpha and beta waves of 8-14Hz, centred at 10Hz. A modulated carrier wave is observed for all subjects at 18Hz, higher in width for patients. Coherent wave dynamics, with interference playing a key role in the wave packet collapse and revival, is observed starting from 18Hz, with the coherence getting significantly enhanced around 40-45Hz. Mechanism of intra frequency energy transfer is shown to be neutral turbulence.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

PHASE-SPACE CONSIDERATIONS IN THE TRANSVERSE MOMENTUM ANALYSIS

1987 ◽  
Vol 48 (C2) ◽  
pp. C2-233-C2-239
Author(s):  
P. DANIELEWICZ
Keyword(s):  
Phase Space ◽  
Transverse Momentum

The Black Swan: Yeats and the Science of the Unknown

2017 ◽  
Vol 47 (2) ◽  
pp. 350-359
Author(s):  
Aoife Lynch
Keyword(s):  
Twentieth Century ◽  
Scientific Theory ◽  
Black Swan ◽  
Max Planck ◽  
Universal History ◽  
New Concepts ◽  
Wave Particle Duality ◽  
Paradigmatic Change

This essay views science as a creative mask for the poetry and philosophy of W.B. Yeats. It explores the changing worldview which occurred at the beginning of the twentieth century with the discovery of wave-particle duality by Max Planck in 1900. It considers the new concepts of reality which arose at this time in relation to modernism and Yeats's response to the paradigmatic change of era he was a part of. Accordingly, the poet's understanding of universal history in A Vision (1925, 1937) is used alongside close readings of his poetry to evince an argument which unites that poetry with philosophy, scientific theory, and modernism as aspects of one universe of knowledge which refracts different aspects of itself through the prism of time.

Phase space of mechanical systems with a gauge group

1991 ◽  
Vol 161 (2) ◽  
pp. 13-75 ◽  
Author(s):  
Lev V. Prokhorov ◽  
Sergei V. Shabanov
Keyword(s):  
Phase Space ◽  
Gauge Group ◽  
Mechanical Systems

Numerical Study on Particle Distribution in Longitudinal Phase Space and Beam Current Profile using Compact Electron Beam Simulator for Heavy Ion Inertial Fusion

2017 ◽  
Vol 137 (5) ◽  
pp. 344-348
Author(s):  
Takashi Kikuchi ◽  
Yasuo Sakai ◽  
Jun Hasegawa ◽  
Kazuhiko Horioka ◽  
Kazumasa Takahashi ◽  
...  
Keyword(s):  
Electron Beam ◽  
Phase Space ◽  
Particle Distribution ◽  
Numerical Study ◽  
Heavy Ion ◽  
Beam Current ◽  
Inertial Fusion ◽  
Current Profile ◽  
Longitudinal Phase
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