In physics, fractional quantum mechanics is a generalization of standard quantum mechanics, which naturally comes out when the Brownian-like quantum paths substitute with the Lévy-like ones in the Feynman path integral.It has been discovered by Nick Laskin who coined the term fractional quantum mechanics. In this paper we study the quantum transport on networks with a temporal evolution governed by the fractional Schr\"odinger equation. Space-time fractional Schrödinger equation. Learn more about the change. Phys. The density matrix of a free particle has been expressed in terms of the Fox's H function. Since the relativistic kinetic energy can be viewed as an approximate realization of the fractional kinetic energy, the particle teleportation should be an observable relativistic effect in quantum mechanics. Fractional path integrals over the paths of the Levy flights are defined. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractality of the L\'evy paths leads to fractional quantum mechanics and fractional statistical mechanics. continuity equation in fractional quantum mechanics has a missing source term, which leads to particle teleportation, i.e., a particle can teleport from a place to another. Read "Fractional Quantum Mechanics" by Nick Laskin available from Rakuten Kobo. )-dimensional models, or flux tubes in three-dimensional models, can have any (fractional) angular momentum. The book covers related topics on time fractional quantum mechanics, fractional classical mechanics and the [alpha]-stable Lévy random process. COVID-19: Updates on library services and operations. Introduction. Regarding quantum physics, it has been only in the previous decade or so that the corresponding literature resulted in a set of defying papers. [Fract. A new extension of a fractality concept in quantum physics has been developed. The different boundary conditions are naturally implemented using sets of functions with the appropriate behavior. Fractional calculus is a couple of centuries old, but its development has been less embraced and it was only within the last century that a program of applications for physics started. The fractional quantum Hall effect is a very counter-intuitive physical phenomenon. The results given earlier by Saxena et al. Fractional time (non-unitary) quantum mechanics is discussed for both Schrödinger and Heisenberg representations of quantum mechanics. A Math. In recent years it has emerged that these so-called anyons have rather unexpected applications, such as the fractional Hall effect, anyonic excitations in films of liquid helium, and high-temrperature superconductivity. The path integrals over the Lévy paths are defined and fractional quantum and statistical mechanics have been developed via new fractional path integrals approach. Fractional quantum mechanics is a recently emerged and rapidly developing field of quantum physics. Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. A path integral approach to quantum physics has been developed. In recent years the application of fractional calculus in quantum theory became a rapidly growing area. This is the first monograph on fundamentals and physical applications of fractional quantum mechanics, written by its founder. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractality of the Levy paths leads to fractional quantum mechanics and fractional statistical mechanics. Europ. Mécanique quantique fractionnelle - Fractional quantum mechanics Un article de Wikipédia, l'encyclopédie libre . Fractional path integrals over the paths of the Lévy flights are defined. Fractional quantum mechanics is a recently emerged and rapidly developing field of quantum … Several special cases as solutions of one dimensional non-homogeneous fractional equations occurring in the quantum mechanics are presented. It implies that many electrons, acting in concert, can create new particles having a charge smaller than the charge of any indi-vidual electron. Rev. Buy this book eBook 67,40 € price for Spain (gross) Buy eBook ISBN … Particles with fractional statistics interpolating between bosons and fermions have attracted considerable interest from mathematical physicists. Fractional statistical mechanics has been developed via the path integral approach. Using the momentum-space approach, we obtain bound states for multiple Dirac-δ wells in the framework of space-fractional quantum mechanics. We generalize the dynamics based on continuous-time quantum walks, with transitions to nearest neighbors on the network, to the fractional case that allows long-range displacements. I read about Fractional Quantum Mechanics and it seemed interesting. E 62, 3135–3145 (2000) ADS MATH Google Scholar 54. The fractional Schrödinger equation and the fractional path integral are new fundamental physical concepts introduced and elaborated in the book. The fractional quantum mechanics has been developed via the new fractional path integrals approach. Phys. Quantum Mechanics of Fractional-Spin Particles Frank Wilczek Institute for Theoretical Physics, University of California, Santa Barbara, California 93106 (Received 22 June 1982) Composites formed from charged particles and vortices in. This is the first monograph on fundamentals and physical applications of fractional quantum mechanics, written by its founder. Anal., 13(2) (2010), pp. Its application provides a convenient technique for solving certain classes of ordinary and partial differential equations which arise in quantum mechanics from classical quadratic hamiltonians. This is not the way things are supposed to be. : 1.1 It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.

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