1. Fractional Quantum Mechanics (Foundational Papers)
Fractional Quantum Mechanics
Physical Review E, Vol. 62, No. 3, pp. 3135–3145.
The foundational paper introducing Fractional Quantum Mechanics. Replaces the path integral over Brownian trajectories with a path integral over Lévy flights, deriving the Fractional Schrödinger Equation with Riesz spatial derivatives.
Fractional Schrödinger Equation
Physical Review E, Vol. 66, No. 5, 056108.
Establishes the Hermiticity of the fractional Hamilton operator, parity conservation, and the probability current density for fractional quantum states.
Time-Fractional Quantum Mechanics
Chaos, Solitons & Fractals, Vol. 102, pp. 16–28.
Generalizes time evolution using Caputo fractional derivatives, exploring non-Markovian memory effects in open quantum systems.
2. Fractional Stochastic Processes & Router Buffering
Fractional Poisson Process
Communications in Nonlinear Science and Numerical Simulation, Vol. 8, No. 3-4, pp. 201–213.
Introduces the Fractional Poisson Process using fractional Kolmogorov-Feller equations, establishing exact probability distributions for long-memory waiting times.
Generalized Router Buffer Model & Alternative Fractional Processes
Carleton University Research Report & Applied Physics Letters
Formulates an alternative approach to the Kolmogorov-Mandelbrot method for fractional Brownian motion, developing a generalized buffer queue model for self-similar internet data packet bursts.
3. Financial Physics & Econophysics
Jumps and Volatility Smiles in Financial Markets
Physica A: Statistical Mechanics and its Applications, Vol. 287, No. 3-4, pp. 482–492.
Applies fractional Lévy processes to financial options pricing, deriving the implied volatility smile from heavy-tailed price dynamics.
4. Books & Reference Monographs
Fractional Quantum Mechanics (Monograph)
World Scientific Publishing, ISBN: 978-981-3220-93-5.
The definitive research monograph unifying 18 years of fractional quantum theory, Riesz derivatives, fractional spin, gravity, and quantum statistical mechanics.
5. Commercial Consulting & Technology Integration
Dr. Laskin provides direct advisory services through TopQuark Inc., assisting corporate research labs, financial engineering desks, and semiconductor fabs in deploying fractional stochastic kernels into production software.