24 citations · 92 across the 19 of their papers we have counts for
19 papers
Tamed Feynman-Kac diffusion processes: Killing-branching intertwine
Piotr Garbaczewski, Mariusz Żaba
Relaxation to equilibrium of a drifted Brownian motion is quantified by a transition probability density function, whose main (multiplicative) entry is an inferred Feynman-Kac kern…
Killing versus branching: Unexplored facets of diffusive relaxation
P. Garbaczewski, M. Zaba
We analyze the relaxation dynamics of Feynman-Kac path integral kernel functions in terms of branching diffusion processes with killing. This sheds new light on the admissible path…
(Nonequilibrium) dynamics of diffusion processes with non-conservative drifts
P. Garbaczewski, M. Żaba
The nonequilibrium Fokker-Planck dynamics with a non-conservative drift field, in dimension , can be related with the non-Hermitian quantum mechanics in a real scalar pote…
Levy processes in bounded domains: Path-wise reflection scenarios and signatures of confinement
Piotr Garbaczewski, Mariusz Żaba
We discuss an impact of various (path-wise) reflection-from-the barrier scenarios upon confining properties of a paradigmatic family of symmetric -stable Lévy processes, whose p…
Levy flights in steep potential wells: Langevin modeling versus direct response to energy landscapes
P. Garbaczewski, M. Zaba
We investigate the non-Langevin relative of the Lévy-driven Langevin random system, under an assumption that both systems share a common (asymptotic, stationary, steady-state) targ…
Brownian motion in trapping enclosures: Steep potential wells, bistable wells and false bistability of induced Feynman-Kac (well) potentials
Piotr Garbaczewski, Mariusz Zaba
We investigate signatures of convergence for a sequence of diffusion processes on a line, in conservative force fields stemming from superharmonic potentials , $m=2n…
Ultrarelativistic bound states in the shallow spherical well
Mariusz Zaba, Piotr Garbaczewski
We determine approximate eigenvalues and eigenfunctions shapes for bound states in the shallow spherical ultrarelativistic well. Existence thresholds for the ground state and…
Lévy flights in the infinite potential well as the hypersingular Fredholm problem
Elena V. Kirichenko, Piotr Garbaczewski, Vladimir Stephanovich +1
We study Lévy flights {with arbitrary index } inside a potential well of infinite depth. Such problem appears in many physical systems ranging from stochastic interface…
Ultrarelativistic bound states in the spherical well
Mariusz Żaba, Piotr Garbaczewski
We address an eigenvalue problem for the ultrarelativistic (Cauchy) operator , whose action is restricted to functions that vanish beyond the interior of a unit sphere…
Ultrarelativistic (Cauchy) spectral problem in the infinite well
Elena V. Kirichenko, Piotr Garbaczewski, Vladimir Stephanovich +1
We analyze spectral properties of the ultrarelativistic (Cauchy) operator , provided its action is constrained exclusively to the interior of the interval $[-1,1] \subse…
Nonlocally-induced (fractional) bound states: Shape analysis in the infinite Cauchy well
Mariusz Żaba, Piotr Garbaczewski
Fractional (Lévy-type) operators are known to be spatially nonlocal. This becomes an issue if confronted with a priori imposed exterior Dirichlet boundary data. We address spectral…
Nonlocal random motions: The trapping problem
Piotr Garbaczewski, Mariusz Żaba
Lévy stable (jump-type) processes are examples of intrinsically nonlocal random motions. This property becomes a serious obstacle if one attempts to model conditions under which a…
Nonlocally-induced (quasirelativistic) bound states: Harmonic confinement and the finite well
Piotr Garbaczewski, Mariusz Żaba
Nonlocal Hamiltonian-type operators, like e.g. fractional and quasirelativistic, seem to be instrumental for a conceptual broadening of current quantum paradigms. However physicall…
Solving fractional Schroedinger-type spectral problems: Cauchy oscillator and Cauchy well
Mariusz Zaba, Piotr Garbaczewski
This paper is a direct offspring of Ref. [J. Math. Phys. 54, 072103, (2013)] where basic tenets of the nonlocally induced random and quantum dynamics were analyzed. A number of men…
Path-wise versus kinetic modeling for equilibrating non-Langevin jump-type processes
Mariusz Żaba, Piotr Garbaczewski, Vladimir Stephanovich
We discuss two independent methods of solution of a master equation whose biased jump transition rates account for long jumps of Lévy-stable type and nonetheless admit a Boltzmanni…
Trajectory statistics of confined Lévy flights and Boltzmann-type equilibria
Mariusz Zaba, Piotr Garbaczewski, Vladimir Stephanovich
We analyze a specific class of random systems that are driven by a symmetric Lévy stable noise, where Langevin representation is absent. In view of the Lévy noise sensitivity to en…
Thermalization of Levy flights: Path-wise picture in 2D
Mariusz Zaba, Piotr Garbaczewski
We analyze two-dimensional (2D) random systems driven by a symmetric Lévy stable noise which, under the sole influence of external (force) potentials , asymptotically set do…
Levy flights in confining environments: Random paths and their statistics
M. Zaba, P. Garbaczewski, V. Stephanovich
We analyze a specific class of random systems that are driven by a symmetric Lévy stable noise. In view of the Lévy noise sensitivity to the confining "potential landscape" where j…
Asymptotic entanglement of two atoms in squeezed light field
L. Jakobczyk, R. Olkiewicz, M. Zaba
The dynamics of entanglement between two - level atoms interacting with a common squeezed reservoir is investigated. It is shown that for spatially separated atoms there is a uniqu…