arXiv: Disordered Systems and Neural Networks, 2020
Networks that have power-law connectivity, commonly referred to as the scale-free networks, are a... more Networks that have power-law connectivity, commonly referred to as the scale-free networks, are an important class of complex networks. A heterogeneous mean-field approximation has been previously proposed for the Ising model of the Barabasi-Albert model of scale-free networks with classical spins on the nodes wherein it was shown that the critical temperature for such a system scales logarithmically with network size. For finite sizes, there is no criticality for such a system and hence no true phase transition in terms of singular behavior. Further, in the thermodynamic limit, the mean-field prediction of an infinite critical temperature for the system may exclude any true phase transition even then. Nevertheless, with an eye on potential applications of the model on biological systems that are generally finite, one may still try to find approximations that describe the relevant observables quantitatively. Here we present an alternative, approximate formulation for the description...
We study the polarization transport of transverse phonons by adopting a new approach based on the... more We study the polarization transport of transverse phonons by adopting a new approach based on the quantum mechanics of spin-orbit interactions. This approach has the advantage of being apt for incorporating fluctuations in the system. The formalism gives rise to Berry effect terms manifested as the Rytov polarization rotation law and the polarization-dependent Hall effect. We derive the distribution of the Rytov rotation angle in the presence of thermal noise and show that the rotation angle is robust against fluctuations.
We derive the semiclassical equations of motion of a transverse acoustical wave packet propagatin... more We derive the semiclassical equations of motion of a transverse acoustical wave packet propagating in a phononic crystal subject to slowly varying perturbations. The formalism gives rise to Berry effect terms in the equations of motion, manifested as the Rytov polarization rotation law and the polarization-dependent Hall effect. We show that the formalism is also applicable to the case of non-periodic inhomogeneous media, yielding explicit expressions for the Berry effect terms.
The propagation of electromagnetic waves in an unmagnetized weakly inhomogeneous cold plasma is e... more The propagation of electromagnetic waves in an unmagnetized weakly inhomogeneous cold plasma is examined. We show that the inhomogeneity induces a gauge connection term in wave equation, which gives rise to Berry effects in the dynamics of polarized rays in the post geometric optics approximation. The polarization plane of a plane polarized ray rotates as a result of the geometric Berry phase, which is the Rytov rotation. Also, the Berry curvature causes the optical Hall effect, according to which, rays of left/right circular polarization deflect oppositely to produce a spin current directed across the direction of propagation.
The data of velocity rotation curve in spiral galaxies, almost for galaxies which have close cent... more The data of velocity rotation curve in spiral galaxies, almost for galaxies which have close central surface brightness, collapse onto a universal scaling function. Since scaling functions are the signature of emergence in complex systems we are led to the idea that explanation of constant velocity in spiral galaxies needs considering cooperative behavior instead of interpretation based on reductionism approach.
arXiv: Disordered Systems and Neural Networks, 2020
Networks that have power-law connectivity, commonly referred to as the scale-free networks, are a... more Networks that have power-law connectivity, commonly referred to as the scale-free networks, are an important class of complex networks. A heterogeneous mean-field approximation has been previously proposed for the Ising model of the Barabasi-Albert model of scale-free networks with classical spins on the nodes wherein it was shown that the critical temperature for such a system scales logarithmically with network size. For finite sizes, there is no criticality for such a system and hence no true phase transition in terms of singular behavior. Further, in the thermodynamic limit, the mean-field prediction of an infinite critical temperature for the system may exclude any true phase transition even then. Nevertheless, with an eye on potential applications of the model on biological systems that are generally finite, one may still try to find approximations that describe the relevant observables quantitatively. Here we present an alternative, approximate formulation for the description...
We study the polarization transport of transverse phonons by adopting a new approach based on the... more We study the polarization transport of transverse phonons by adopting a new approach based on the quantum mechanics of spin-orbit interactions. This approach has the advantage of being apt for incorporating fluctuations in the system. The formalism gives rise to Berry effect terms manifested as the Rytov polarization rotation law and the polarization-dependent Hall effect. We derive the distribution of the Rytov rotation angle in the presence of thermal noise and show that the rotation angle is robust against fluctuations.
We derive the semiclassical equations of motion of a transverse acoustical wave packet propagatin... more We derive the semiclassical equations of motion of a transverse acoustical wave packet propagating in a phononic crystal subject to slowly varying perturbations. The formalism gives rise to Berry effect terms in the equations of motion, manifested as the Rytov polarization rotation law and the polarization-dependent Hall effect. We show that the formalism is also applicable to the case of non-periodic inhomogeneous media, yielding explicit expressions for the Berry effect terms.
The propagation of electromagnetic waves in an unmagnetized weakly inhomogeneous cold plasma is e... more The propagation of electromagnetic waves in an unmagnetized weakly inhomogeneous cold plasma is examined. We show that the inhomogeneity induces a gauge connection term in wave equation, which gives rise to Berry effects in the dynamics of polarized rays in the post geometric optics approximation. The polarization plane of a plane polarized ray rotates as a result of the geometric Berry phase, which is the Rytov rotation. Also, the Berry curvature causes the optical Hall effect, according to which, rays of left/right circular polarization deflect oppositely to produce a spin current directed across the direction of propagation.
The data of velocity rotation curve in spiral galaxies, almost for galaxies which have close cent... more The data of velocity rotation curve in spiral galaxies, almost for galaxies which have close central surface brightness, collapse onto a universal scaling function. Since scaling functions are the signature of emergence in complex systems we are led to the idea that explanation of constant velocity in spiral galaxies needs considering cooperative behavior instead of interpretation based on reductionism approach.
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Papers by reza torabi