Wyszukiwarka
dr Maciej Kuna
Zatrudnienie
- Adiunkt w Instytut Fizyki i Informatyki Stosowanej
Publikacje
Filtry
wszystkich: 8
Katalog Publikacji
Rok 2019
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Systems, Environments, and Soliton Rate Equations: Toward Realistic Modeling
PublikacjaIn order to solve a system of nonlinear rate equations one can try to use some soliton methods. The procedure involves three steps: (1) find a ‘Lax representation’ where all the kinetic variables are combined into a single matrix ρ, all the kinetic constants are encoded in a matrix H; (2) find a Darboux–Bäcklund dressing transformation for the Lax representation iρ˙=[H,f(ρ)], where f models a time-dependent environment; (3) find...
Rok 2016
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Crystallization of space: Space-time fractals from fractal arithmetic
PublikacjaFractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetics allows one to define calculus and algebra intrinsic to the fractal in question, and one can formulate classical and quantum physics within the fractal set. In particular, fractals in space-time can be generated by means of homogeneous spaces associated...
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Fourier transforms on Cantor sets: A study in non-Diophantine arithmetic and calculus
PublikacjaFractals equipped with intrinsic arithmetic lead to a natural definition of differentiation, integration, and complex structure. Applying the formalism to the problem of a Fourier transform on fractals we show that the resulting transform has all the required basic properties. As an example we discuss a sawtooth signal on the ternary middle-third Cantor set. The formalism works also for fractals that are not self-similar.
Rok 2014
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Quantum structure in competing lizard communities
PublikacjaAlmost two decades of research on applications of the mathematical formalism of quantum theory as a modeling tool in domains different from the micro-world has given rise to many successful applications in situations related to human behavior and thought, more specifically in cognitive processes of decision-making and the ways concepts are combined into sentences. In this article, we extend this approach to animal behavior, showing...
Rok 2013
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Systems, environments, and soliton rate equations: A non-Kolmogorovian framework for population dynamics
PublikacjaSoliton rate equations are based on non-Kolmogorovian models of probability and naturally include autocatalytic processes. The formalism is not widely known but has great unexplored potential for applications to systems interacting with environments. Beginning with links of contextuality to non- Kolmogorovity we introduce the general formalism of soliton rate equations and work out explicit examples of subsystems interacting with...
Rok 2010
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General solution of quantum mechanical equations of motion with time-dependent Hamiltonians: A Lie algebraic approach
PublikacjaThe unitary operators U(t), describing the quantum time evolution of systems with a time-dependent Hamiltonian, can be constructed in an explicit manner using the method of time-dependent invariants. We clarify the role of Lie-algebraic techniques in this context and elaborate the theory for SU(2) and SU(1,1). In these cases we give explicit formulae for obtaining general solutions from special ones. We show that the constructions...
Rok 2003
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Quantum morphogenesis: A variation on Thom`s catastrophe theory.
PublikacjaZaproponowano nowy opis morfogenezy na poziomie kwantowym w oparciu o rozwiązania samo przełączające nieliniowego równania von Neumanna.
Rok 2002
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Covariance approach to the free photon field
PublikacjaWprowadziliśmy teorię fotonu poprzez tą samą zasadę, co dla pojedynczej czą-stki w kwantowej mechanice używając C*-algebraicznego podejścia kowariantychukładów.
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