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- Nick Laskin
- Physical review. E, Statistical, nonlinear, and…
- 2002

Some properties of the fractional Schrödinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schrödinger equation we find the energy spectra of a hydrogenlike atom (fractional "Bohr atom") and of a… (More)

- Nick Laskin
- 2008

A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the Lévy 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 Lévy paths leads to fractional quantum mechanics and fractional statistical… (More)

- Nick Laskin
- 2008

A unified approach has been developed to study nonlinear dynamics of a 1D lattice of particles with long-range power-law interaction. A classical case is treated in the framework of the generalization of the well-known Frenkel-Kontorova chain model for the non-nearest interactions. Quantum dynamics is considered following Davydov’s approach for molecular… (More)

- Nick Laskin, Ioannis Lambadaris, Fotios C. Harmantzis, Michael Devetsikiotis
- Computer Networks
- 2002

We introduce a general non-Gaussian, self-similar, stochastic process called the fractional Lévy motion (fLm). We formally expand the family of traditional fractal network traffic models, by including the fLm process. The main findings are the probability density function of the fLm process, several scaling results related to a singleserver infinite buffer… (More)

- Nick Laskin
- 2008

A unified approach has been developed to study nonlinear dynamics of a 1D lattice of particles with long-range power-law interaction. Classical case is treated in the framework of the well-known FrenkelKontorova chain model. Qunatum dynamics is considered follow to Davydov’s approach to molecular excitons. In the continuum limit the problem is reduced to… (More)

- E. Ahmed, Igor Podlubny, +5 authors Reyad El-Khazali
- 2013

In this work, we study chaos control and synchronization of the commensurate fractional order Liu system. Based on the stability theory of fractional order systems, the conditions of local stability of nonlinear three-dimensional commensurate fractional order systems are discussed. The existence and uniqueness of solutions for a class of commensurate… (More)

- Nick Laskin
- 2005

An impact of integration over the paths of the Lévy flights on the quantum mechanical kernel has been studied. Analytical expression for a free particle kernel has been obtained in terms of the Fox Hfunction. A new equation for the kernel of a partical in the box has been found. New general results include the well known quantum formulae for a free particle… (More)

- Nick Laskin
- 2008

New physical and mathematical applications of recently invented fractional Poisson probability distribution have been presented. As a physical application, a new family of quantum coherent states have been introduced and studied. Mathematical applications are related to the number theory. We have developed fractional generalization of the Bell polynomials,… (More)

- Nick Laskin, I. Tomski

A path integral approach has been generalized for the non-relativistic electron charge transfer processes. The charge transfer the capture of an electron by an ion passing another atom, or more generally the problem of rearrangement collisions is formulated in terms of influence functionals. It has been shown that the electron charge transfer process can be… (More)

- Nick Laskin
- Physical review. E
- 2016

The fractional uncertainty relation is a mathematical formulation of Heisenberg's uncertainty principle in the framework of fractional quantum mechanics. Two mistaken statements presented in the Comment have been revealed. The origin of each mistaken statement has been clarified and corrected statements have been made. A map between standard quantum… (More)

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