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Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics)
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Physics of Fractal Operators (Paperback, Softcover reprint of the original 1st ed. 2003)
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Physics of Fractal Operators (Paperback, Softcover reprint of the original 1st ed. 2003)
Series: Institute for Nonlinear Science
Expected to ship within 10 - 15 working days
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In Chapter One we review the foundations of statistieal physies and
frac tal functions. Our purpose is to demonstrate the limitations
of Hamilton's equations of motion for providing a dynamical basis
for the statistics of complex phenomena. The fractal functions are
intended as possible models of certain complex phenomena;
physical.systems that have long-time mem ory and/or long-range
spatial interactions. Since fractal functions are non
differentiable, those phenomena described by such functions do not
have dif ferential equations of motion, but may have
fractional-differential equations of motion. We argue that the
traditional justification of statistieal mechan ics relies on
aseparation between microscopic and macroscopie time scales. When
this separation exists traditional statistieal physics results.
When the microscopic time scales diverge and overlap with the
macroscopie time scales, classieal statistieal mechanics is not
applicable to the phenomenon described. In fact, it is shown that
rather than the stochastic differential equations of Langevin
describing such things as Brownian motion, we ob tain fractional
differential equations driven by stochastic processes."
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