1,721,339 research outputs found
Classical trajectories and quantum field theory,
No full textThe density matrix and the Wigner function formalism requires the doubling of the degrees of freedom in quantum mechanics (QM) and quantum field theory (QFT). The doubled degrees of freedom play the role of the thermal bath or environment degrees of freedom and are entangled with the system degrees of freedom. They also account for quantum noise in the fluctuating random forces in the system-environment coupling. The algebraic structure of QFT turns out to be the one of the deformed Hopf algebra. In such a frame, the trajectories in the space of the unitarily inequivalent representations of the canonical commutation relations turn out to be classical trajectories and, under convenient conditions, they may exhibit properties typical of classical chaotic trajectories in nonlinear dynamics. The quantum Brownian motion and the two-slit experiment in QM are discussed in connection with the doubling of the degrees of freedom
Fractals, coherent states and self-similarity induced noncommutative geometry
Full text linkThe self-similarity properties of fractals are studied in the framework of the theory of entire analytical
functions and the q-deformed algebra of coherent states. Self-similar structures are related to dissipation
and to noncommutative geometry in the plane. The examples of the Koch curve and logarithmic
spiral are considered in detail. It is suggested that the dynamical formation of fractals originates from
the coherent boson condensation induced by the generators of the squeezed coherent states, whose
(fractal) geometrical properties thus become manifest. The macroscopic nature of fractals appears to
emerge from microscopic coherent local deformation processes
The use of many-body physics and thermodynamics to describe the dynamics of rhythmic generators in sensory cortices engaged in memory and learning
No full textThe problem of the transition from the molecular and cellular level to the macroscopic level of observed assemblies of myriads of neurons is the subject addressed in this report. The great amount of detailed information available at molecular and cellular level seems not sufficient to account for the high effectiveness and reliability observed in the brain macroscopic functioning. It is suggested that the dissipative many-body model and thermodynamics might offer the dynamical frame underlying the rich phenomenology observed at microscopic and macroscopic level and help in the understanding on how to fill the gap between the bio-molecular and cellular level and the one of brain macroscopic functioning
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