Dr. Nick Laskin
nicklaskin.ca
Exploring the pioneering theoretical models of Dr. Nick Laskin, founder of Fractional Quantum Mechanics (FQM) and inventor of the Fractional Poisson Process (FPP).
The celebrated Black-Scholes-Merton model assumes that market prices follow continuous, continuous diffusion (Brownian motion) with **constant volatility** ($\sigma$).
Under this idealized math, option implied volatility across different strike prices should be completely flat. Yet, empirical market data reveals a pronounced "Volatility Smile"—strikes deep in-the-money or out-of-the-money trade at significantly higher implied volatilities.
This smile is proof that Black-Scholes is a mathematical fiction. In the real world, asset prices do not slide smoothly; they jump, cluster, and carry **memory**.
Dr. Laskin's **Geometric Shot Noise (GSN)** and fractional stochastic models resolve this contradiction. By replacing continuous Brownian walks with jump processes that incorporate **long-range memory**, these models naturally recover the volatility smile. Jumps are not isolated anomalies—they are correlated events with memory, reflecting how markets cluster information and price real-world risks.
Continuous, smooth paths. Volatility is assumed constant. Zero memory of past shocks.
Discontinuous jumps with fractional waiting times. Past events cluster and decay slowly over time.
Dr. Laskin's research footprints span across top-tier global institutions, bridging rigorous Ukrainian theoretical physics with advanced North American engineering labs.
Research Scientist | Ukraine
Collaborated with physics legends A.I. Akhiezer and S.V. Peletminskii. Focused on quark-gluon plasma instabilities, dense neutron matter magnetohydrodynamics, and predicted coherent Bremsstrahlung suppression in oriented crystals.
Department of Electrical & Computer Engineering | Canada
Founded Fractional Quantum Mechanics (FQM), generalizing Feynman path integrals over Brownian paths to Lévy flight trajectories. Discovered the Fractional Schrödinger Equation.
Department of Systems & Computer Engineering | Canada
Invented the Fractional Poisson Process (FPP), introducing Mittag-Leffler waiting times to resolve Markovian limits in complex network and queueing models.
Visiting Scholar | New York, USA
Applied fractional dynamics and Lévy flights to financial engineering, analyzing log-moneyness, the volatility smile, and econophysics modeling.
Director of Quantum & Financial Research | Canada
Publishing monographs, developing the Disorder Engineering Module for MOCVD semiconductor growth, and finalizing the Inverse Design Simulation API.
Four pillars of research that generalize classical equations. While the underlying mathematics are rigorous, the business application is simple: replacing flawed "smooth" assumptions with models that capture the messy, jumping reality of complex systems.
Replaces Brownian paths ($d_w = 2.0$) in Feynman path integrals with Lévy flights ($1.0 < \alpha \le 2.0$), introducing the Riesz fractional derivative operator to model quantum dynamics in fractal space.
Generalizes counting statistics by replacing the first-order time derivative in Kolmogorov-Feller equations with a fractional order $\mu$, giving rise to Mittag-Leffler waiting times.
Predicted the suppression of coherent Bremsstrahlung for relativistic particles moving through oriented crystals. Confirmed experimentally at the CERN NA-43 experiment.
Proposed the Geometric Shot Noise (GSN) model to capture market info shocks. Resolves the volatility smile as a natural by-product of shot-noise jump dynamics, defining the "New Greeks" for jump risks.
Experience the power of fractional dynamics firsthand. Adjust the sliders to see how real-world memory and jumps alter classical models in real time—from optimizing semiconductor yields to revealing the hidden geometry of financial markets.
Solve the transcendental equations for InGaN/GaN wells. Adjust the Lévy Index $\alpha$ to model impurity-induced disorder (Brownian limit is $\alpha = 2.0$).
Target a transition emission wavelength:
Simulate event counts $N(t)$ driven by Mittag-Leffler waiting times. Notice the "bursty" behavior and long flat gaps (memory trapping) as $\mu$ decreases below 1.0.
Calibrate the Geometric Shot Noise process. Increase jump frequency or magnitude to see the volatility skew/smile emerge from the underlying shot-noise shocks.
Dr. Laskin's published monographs establish FQM and FPP as recognized academic sub-disciplines, bridging theoretical physics with real-world applications. These defining works compile decades of research into comprehensive guides for academics and industry professionals alike.
World Scientific Publishing
The definitive text on FQM. Covers paths integrals over Lévy flights, fractional uncertainty relations, analytically solvable wells, fractional Bohr atoms, and time-fractional non-Markovian dynamics.
World Scientific Publishing
The first dedicated book on FPP. Systematically details the Kolmogorov-Feller fractional equations, renewal theory, inverse stable subordinators, and direct Mittag-Leffler probability design, with multi-disciplinary applications.
Commercial Semiconductor Simulation Partnerships
We propose a 12-month joint development cycle to commercialize our Fractional Schrödinger Solver kernel and deploy the **Inverse Design API** for direct MOCVD growth controller coupling. By mapping doping profiles to the Lévy Index $\alpha$, fabs can achieve real-time yield optimization for high-performance InGaN blue LEDs.