Fractals, dissipation and coherent states

Abstract

Self-similarity properties of fractal structures, including the logarithmic spiral, are related to quantum dissipative dynamics, generalized squeezed coherent states and noncommutative geometry in the plane. The rôle played by the fractal Hamiltonian which actually turns out to be the fractal free energy is discussed. Time evolution characterized by the breakdown of time-reversal symmetry is controlled by the entropy. Coherent boson condensation induced by the generators of the coherent states is shown to control the formation of fractals. Vice-versa, coherent generalized states are recognized to possess self-similar fractal structure. The global nature of fractals appears to emerge from irreversible coherent local deformation processes. © 2012 Springer-Verlag.