Zobrazeno 1 - 10
of 58
pro vyhledávání: '"Żaba, Mariusz"'
Autor:
Garbaczewski, Piotr, Żaba, Mariusz
Publikováno v:
J. Phys A: Math. Theor. 55 (30), 3005005,(2022)
We discuss an impact of various (path-wise) reflection-from-the barrier scenarios upon confining properties of a paradigmatic family of symmetric $\alpha $-stable L\'{e}vy processes, whose permanent residence in a finite interval on a line is secured
Externí odkaz:
http://arxiv.org/abs/2201.09582
Autor:
Garbaczewski, Piotr, Zaba, Mariusz
Publikováno v:
J. Phys. A: Math. Theor. 53 (2020) 315001 (39pp)
We investigate signatures of convergence for a sequence of diffusion processes on a line, in conservative force fields stemming from superharmonic potentials $U(x)\sim x^m$, $m=2n \geq 2$. This is paralleled by a transformation of each $m$-th diffusi
Externí odkaz:
http://arxiv.org/abs/1906.06694
Akademický článek
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Akademický článek
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Autor:
Zaba, Mariusz, Garbaczewski, Piotr
Publikováno v:
Acta Phys. Pol. B 49 (2), 145-169, (2018)
We determine approximate eigenvalues and eigenfunctions shapes for bound states in the $3D$ shallow spherical ultrarelativistic well. Existence thresholds for the ground state and first excited states are identified, both in the purely radial and orb
Externí odkaz:
http://arxiv.org/abs/1611.01745
Publikováno v:
Phys. Rev. E 93, 052110 (2016)
We study L\'evy flights {{with arbitrary index $0< \mu \leq 2$}} inside a potential well of infinite depth. Such problem appears in many physical systems ranging from stochastic interfaces to fracture dynamics and multifractality in disordered quantu
Externí odkaz:
http://arxiv.org/abs/1604.02550
Autor:
Żaba, Mariusz, Garbaczewski, Piotr
Publikováno v:
J. Math. Phys. 57 (7), 072302, (2016)
We address an eigenvalue problem for the ultrarelativistic (Cauchy) operator $(-\Delta )^{1/2}$, whose action is restricted to functions that vanish beyond the interior of a unit sphere in three spatial dimensions. We provide high accuracy spectral d
Externí odkaz:
http://arxiv.org/abs/1601.07866
Publikováno v:
Acta Phys. Pol. B 47 (5), 1273-1291, (2016)
We analyze spectral properties of the ultrarelativistic (Cauchy) operator $|\Delta |^{1/2}$, provided its action is constrained exclusively to the interior of the interval $[-1,1] \subset R$. To this end both analytic and numerical methods are employ
Externí odkaz:
http://arxiv.org/abs/1505.01277
Autor:
Żaba, Mariusz, Garbaczewski, Piotr
Publikováno v:
J. Math. Phys. 56 (12), 123502, (2015)
Fractional (L\'{e}vy-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 properties of the prototype example of the Cauchy operator $(-\De
Externí odkaz:
http://arxiv.org/abs/1503.07458
Autor:
Garbaczewski, Piotr, Żaba, Mariusz
Publikováno v:
Acta Phys. Pol. B 46 (2), 231-246, (2015)
L\'evy 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 particular L\'evy process may be subject to physically implementable
Externí odkaz:
http://arxiv.org/abs/1412.7320