prof. dr hab. Piotr Garbaczewski

Zagadnienia z zakresu fizyki teoretycznej związanych:

• z podstawami fizyki kwantowej,
• nierównowagową fizyką statystyczną,
• metodami stochastycznymi w fizyce,
• dynamiką nieliniową,
• chaosem klasycznym i kwantowym,
• układami złożonymi

• J. Phys A: Math. Theor. (2020) (and arXiv:1906.06694) Brownian motion in trapping enclosures: Steep potential wells, bistable wells and false bistability of induced Feynman-Kac (well) potentials (with M. Żaba)
• Phys. Rev. E 99, 042126, (2019) (and arXiv:1810.07028) Fractional Laplacians and Levy flights in bounded domains: Killed, reflected, censored and taboo Levy flights (with V. A. Stephanovich)
• Acta Phys. Pol. B 49 (5), 921-942, (2018) (and arXiv:1802.09853) Fractional Laplacians and Levy flights in bounded domains
• Acta. Phys. Pol. B 49 (2), 145-169, (2018) (and arXiv:1611.07866) Ultrarelativistic bound states in the shallow spherical well (with M. Żaba)
• Phys. Rev. E 96, (2017), 032104 (and arXiv:1705.08402) Killing (absorption) versus survival in random motion
• J. Math. Phys. 57(7), (2016), 072302 (and arXiv:1601.07866) Ultrarelativistic bound states in the spherical well (with M. Żaba)
• Phys. Rev. E 93, (2016), 052110 (and arXiv:1604.02550) Levy flights in the infinite potential well as the hypersingular Fredholm problem (with E. Kirichenko, V. Stephanovich and M. Żaba)
• Acta Phys. Pol. B 47 (5), (2016), 1273-1290 (and arXiv:1505.01277) Ultrarelativistic (Cauchy) spectral problem in the infinite well (with E. Kirichenko, V. Stephanovich and M. Żaba)
• J. Math. Phys. 56(12), (2015), 123502 (1-21) (and arXiv:1503.07458) Nonlocally-induced (fractional) bound states: Shape analysis in the infinite Cauchy well (with M. Żaba)
• Acta Phys. Pol. B 46(2), (2015), 231-246 (and arXiv:1412.7320) Nonlocal random motions and the trapping problem (with M. Żaba)
• Acta Phys. Pol. B 46(5), (2015), 949-981 (and arXiv:1405.4724) Nonlocally-induced (quasirelativistic) bound states: Harmonic confinement and the finite well (with M. Żaba)
• J. Math. Phys. 55(9), (2014), 092103 (1-20) (and arXiv:1403.5668) Solving fractional Schrödinger-type spectral problems: Cauchy oscillator and Cauchy well (with M. Żaba)
• Cent. Eur. J. Phys. 12(3), (2014), 175-184 (and arXiv:1306.3858) Path-wise versus kinetic modeling for equilibrating non-Langevin jump-type processes (with M. Żaba and V. A. Stephanovich)
• International Journal of Statistical Mechanics, vol. 2013, (2013), 738345 (and arXiv:1303.6162) Thermalization of Levy flights: Path-wise picture in 2D (with M. Żaba)
• J. Math. Phys. 54, (2013), 072103 (1-34) (and arXiv:1302.1478) Levy flights and nonlocal quantum dynamics (with V. A. Stephanovich)
• Acta Phys. Pol. B 44, (2013), 1109-1122 (and arXiv:1303.6920) Trajectory statistics of confined Levy flights and Boltzmann-type equilibria (with M. Żaba and V. A. Stephanovich)
• Physica A 392, (2013), 3485-3496 (and arXiv:1209.5882) Levy flights in confining environments: Random paths and their statistics (with M. Żaba and V. A. Stephanovich)
• J. Phys. Conf. Ser. 361, (2012), 012012 (and arXiv:1112.5962) Probabilistic whereabouts of the „quantum potential”
• Acta Phys. Pol. B 43, (2012), 977-997 (and arXiv:1106.1530) Dynamics of confined Levy flights in terms of (Levy) semigroups(with V. A. Stephanovich)
• Phys. Rev. E 84, (2011), 011142 (and arXiv:1105.1435) Levy targeting and the principle of detailed balance(with V. A. Stephanovich)
• Physica A 390, (2011), 990-1008 (and arXiv:1004.0127) Heavy-tailed targets and (ab)normal asymptotics in diffusive motion(with V. A. Stephanovich and D. Kedzierski)
• Open Systems & Information Dynamics, 17, (2010), 287-296 (and arXiv:1004.4582)Thermalization of random motion in weakly confining potentials(with V. A. Stephanovich)
• Physica A 389, (2010), 4419-4435 (and arXiv:0907.0102) Levy flights in inhomogeneous environments (with V. A. Stephanovich)
• Cent. Eur. J. Phys. 8, (2010), 699-708 (and arXiv:0902.3536)Levy flights and Levy-Schrödinger semigroups
• Physica A 389, (2010), 936-944 (and arXiv:0907.0867)Cauchy flights in confining potentials
• Phys. Rev. E 80, (2009), 031113 (and arXiv:0904.4157)Levy flights in confining potentials(with V. A. Stephanovich)
• Acta Phys. Pol. B 40, (2009), 1353-1368 (and arXiv:0811.3856) Levy flights, dynamical duality and fractional quantum mechanics
• Phys. Rev. E 78 , (2008), 031101 (and arXiv:0805.1536)Modular Schrödinger equation and dynamical duality
• Acta Phys. Pol. B 39 , (2008), 1087-1101 (and cond-mat/0604538) Entropy and time: Thermodynamics of diffusion processes
• Cent. Eur. J. Phys. 6(1), (2008), 158-170 (and cond-mat/0703147)Information dynamics: Temporal behavior of uncertainty measures
• Acta Phys Pol. A 112, (2007), 619-634 (and arXiv:0706.2481)Information functionals and the notion of (un)certainty: Random matrix theory – inspired case
• Rep. Math. Phys. 60, (2007), 289-297 (and cond-mat/0703204)Indeterminacy relations in random dynamics
• Appl. Math. & Information Sciences, 1, (2007), 1-12 (and quant-ph/0612151)Information dynamics in quantum theory
• Phys Rev. E 74, (2006), 028101 (and cond-mat/0605505)Comment on „Connection between the Burgers equation with an elastic forcing term and a stochastic process”
• Acta Phys. Pol. B 37, (2006), 1503-1520 (and cond-mat/0510533) Entropy Methods in Random Motion
• J. Stat. Phys. 123, (2006), 315-355Differential Entropy and Dynamics of Uncertainty
• Phys. Rev. A 72, (2005), 056101 (and quant-ph/0509215)Comment on „Time-dependent entropy of simple quantum model systems”
• Phys. Lett A 341, (2005), 33-38 (and cond-mat/0504115)Shannon versus Kullback-Leibler Entropies in Nonequilibrium Random Motion
• Rep. Math. Phys. 56, (2005), 153-160 (and quant-ph/0504098)A Subtlety of the Schrödinger Picture Dynamics
• Entropy 7[4] (2005), 253-299 (and quant-ph/0408192)Differential Entropy and Time
• Acta Phys. Pol. B 36, (2005), 1561-1577 (and cond-mat/0301044) Dynamics of Uncertainty in Nonequilibrium Random Motion
• Am. J. Phys. 72 , (2004), 924-933 (and math-ph/0310023)Impenetrable Barriers and Canonical Quantization(with W. Karwowski)
• Acta Phys. Pol. B 34 , (2003), 3555-3568 (and cond-mat/0211362) Random Dynamics, Entropy Production and Fisher Information
• Physica A 317, (2003), 449-471 (and cond-mat/0202463)Frictionless Random Dynamics: Hydrodynamical Formalism(with R. Czopnik)
• Phys. Lett. A 299, (2002), 447-453 (and quant-ph/0203018)Quantum Potential and Random Phase-Space Dynamics(with R. Czopnik)
• Phys. Lett. A 293, (2002), 23-28 (and quant-ph/0106011)Parametric Dynamics of Level Spacings in Quantum Chaos
• Acta Phys. Pol. B 33, (2002), 1001-1024 (and cond-mat/0103246) Signatures of Randomness in Quantum Spectra
• Acta Phys. Pol. B 32, (2001), 1421-1436 (and cond-mat/0011106) Local Characteristics of Random Motion
• Acta Phys. Pol. B 32, (2001), 1437- 1450 (and cond-mat/0011105) Charged Brownian Particle in a Magnetic Field(with R. Czopnik)
• Phys. Rev. E 63, (2001), 021105 (and cond-mat/0005353)Brownian Motion in a Magnetic Field(with R. Czopnik)
• Physica A 285, (2000), 187-198 (and cond-mat/0002437)Stochastic Models of Exotic Transport
• J. Math. Phys. 41 (2000), 6843-6860 (and chao-dyn/9910028)Ornstein-Uhlenbeck-Cauchy Process(with R. Olkiewicz)
• Phys. Lett. A 257, (1999), 31-36 (and quant-ph/9904080)Noise perturbations in the Brownian motion and quantum dynamics
• Phys. Rev. E 59, (1999), 1498–1511 (and cond-mat/9809288)Perturbations of Noise: Origins of Isothermal Flows
• J. Math. Phys. 40, (1999), 1057–1073 (and math-ph/9804014)Cauchy Noise and Affiliated Stochastic Processes(with R. Olkiewicz)
• Chaos, Solitons and Fractals 9 , (1998) 29-41(and quant-ph/9710015)Schrödinger`s interpolating dynamics and Burgers’ flows,(with G. Kondrat, R. Olkiewicz)
• Phys. Rev. E 57, (1998), 569-572(and chao-dyn/9706002)Diffusion Process in a Flow,
• Acta Phys. Pol. B 28, (1997), 1731-1746 (and chao-dyn/9603018), Burgers velocity fields and electromagnetic forcing in diffusive (Markovian) matter transport (with G. Kondrat, R. Olkiewicz)
• J. Tech. Phys., 38, (1997), 205-209 (and quant-ph/9802003), Schrödinger`s interpolation problem and its probabilistic solutions
• Phys. Rev. E 55, (1997), 1401-1412 (and cond-mat/9802013), Burgers’ flows as Markovian diffusion processes (with G. Kondrat, R. Olkiewicz)
• J. Math. Phys., 38, (1997), 1-15 (and quant-ph/9507002), Non-negative Feynman-Kac Kernels in Schrödinger`s interpolation problem, (with Ph. Blanchard, R. Olkiewicz)
• Phys. Rev. Lett. 77, (1996), 2608-11 (and cond-mat/9802060), Burgers velocity fields and dynamical transport processes, (with G. Kondrat)
• Phys. Rev. A 54, (1996), 1733-6 (and quant-ph/9601016), Comment on „Why quantum mechanics cannot be represented as a Markov process”, (with R. Olkiewicz)
• Acta Phys. Polon. B 27, (1996), 617-642 (and quant-ph/9802004), Schrödinger`s Interpolation Problem Through Feynman-Kac Kernels
• J. Math. Phys. 37, (1996), 732-751 (and quant-ph/9505012), Feynman-Kac kernels in Markovian representations of the Schrödinger interpolating dynamics, (with R.Olkiewicz)
• Phys. Rev. E 51, (1995), 4114-4131 (and quant-ph/9505003), Schrödinger problem, Levy processes and noise in relativistic quantum mechanics (with J.R.Klauder, R.Olkiewicz)
• Phys. Rev. A 51, (1995), 3445-3453, Why quantum dynamics can be formulated as a Markov process, (with R.Olkiewicz)
• Phys. Rev. E 49, (1994), 3815-3824 (and /quant-ph/9802005), Natural boundaries for the Smoluchowski equation and affiliated diffusion processes (with Ph. Blanchard)
• Phys. Lett. A 185, (1994), 149-154, Drifts versus forces: The Ehrenfest theorem for Markovian diffusions
• Phys. Lett. A 178, (1993), 7-10, On the statistical origins of the de Broglie-Bohm quantum potential: Brownian motion in a field of force as the Bernstein process
• Phys. Lett. A 172, (1993), 208-214, Physical significance of the Nelson-Newton laws
• J. Math. Phys. 33, (1992), 3393-3401, Rotational diffusions as seen by relativistic observers
• Phys. Rev. A 46, (1992), 4634-4638, Quantum dynamics from the Brownian recoil principle (with J.P. Vigier)
• Phys. Lett. A 167, (1992), 445-451, Brownian motion and its descendants according to Schrödinger (with J.P. Vigier)
• Phys. Lett. A 164, (1992), 6-16, Relativistic problem of random flights and Nelson’s stochastic mechanics
• Phys. Lett. A 162, (1992), 129-136, Derivation of the quantum potential from realistic Brownian particle motions
• Fortschr. Phys. 38, (1990), 447-475, Randomness in the quantum description of the neutral spin 1/2 particles
• Phys. Lett. A 147, (1990), 168-174, Accelerated stochastic diffusion processes
• Phys. Lett. A 143, (1990), 85-90, Random versus deterministic paths in stochastic mechanics
• Fortschr. Phys. 35, (1987), 771-792, Stochastic mechanics and the Kepler problem: scattering states (with D. Prorok)
• Int. J. Mod. Phys. A 2, (1987), 223-248, Canonical action-angle formalism for quantized nonlinear fields
• J. Phys. A 20, (1987), 4789-4798, Stochastic quantisation of the Fermi oscillator: Non-Z₂ route
• J. Phys. A 20, (1987), 3381-3392, Bosons, fermions, and spins 1/2 :the interplay on lattices of arbitrary dimension
• J. Phys. A 20, (1987), 1277-1283, Some aspects of the boson-fermion (in)equivalence: A remark on the paper by Hudson and Parthasarathy
• Int. J. Theor. Phys. 25, (1986), 1193-1208, Boson-fermion duality in four dimensions: Comments on the paper by Luther and Schotte
• Phys. Rev. D 33, (1986), 2916-2921, Stochastic mechanics and the Kepler problem
• J. Math. Phys. 27, (1986), 612-614, Fermion excitations of the nonlinear Schrödinger field in the attractive case
• J. Math. Phys. 26, (1985), 2684-2692, Fermi states of Bose systems in three space dimensions. II. The solvable version of the Hubbard model
• J. Math. Phys. 26, (1985), 2039-2044, Boson approximants for lattice Fermi systems
• J. Math. Phys. 26, (1985), 490-494, Fermi states of Bose systems in three space dimensions
• J. Math. Phys. 25, (1984), 969-981, On quantum solitons and their classical relatives: Reducible quantum fields and infinite constituent „elementary” systems
• J. Math. Phys. 25, (1984), 862-871, Quantization of spinor fields. IV. Joint Bose- Fermi spectral problems
• Ann. Phys. (NY), 150, (1983), 22-47, Chiral invariant Gross-Neveu model: classical versus quantum
• Nucl. Phys. B 218, (1983), 321-332, Quantum meaning of classical (field) theory for Fermi systems
• J. Math. Phys. 24, (1983), 1806-1809, Non-Grassmann quantization of the massive Thirring model
• J. Math. Phys. 24, (1983), 651-658, Mechanisms of the fermion-boson reciprocity
• J. Math. Phys. 24, (1983), 341-346, Quantization of spinor fields. III. Fermions on coherent (Bose) domains
• Ann. Phys. (NY) 139, (1982), 293-313, On quantum solitons and their classical relatives: Bethe ansatz states in soliton sectors of the sine-Gordon systems
• J. Math. Phys. 23, (1982), 442-450, Quantization of spinor fields. II. Meaning of bosonization in 1+1 and 1+3 dimensions
• J. Math. Phys. 22, (1981), 1272-1279, On quantum solitons and their classical relatives. II. Fermion-boson reciprocity and classical vs quantum problem for the sine-Gordon system
• J. Math. Phys. 22, (1981), 574-580, On quantum solitons and their classical relatives: Spin 1/2 approximation of the sine-Gordon system
• J. Math. Phys. 21, (1980), 2670-2675, A concept of spin 1/2 approximation in the quantum theory of lattice Bose systems
• Phys. Lett. 73 A, (1979), 280-282, NonGrassmann quantization of the Dirac system
• Phys. Lett. 71 A, (1979), 9-12, The quantum pendulum as spin 1/2
• Phys. Lett. 68 A, (1978), 191-193, Almost Fermi, Bose distributions or spin 1/2 approximation of Bose modes in quantum theory
• Nuovo Cim. 44 A, (1978), 108-120, A canonical description of the solitary quantum decay (with G. Vitiello)
• J. Math. Phys. 19, (1978), 642-652, Quantization of spinor fields
• Bull. Acad . Pol. Sci. 26, (1978), 361-369, Introduction to the lattice quantization of the sine-Gordon system (with Z. Popowicz)
• Physics Reports 36 C, (1978), 65-135, The method of boson expansions in quantum theory
• Bull. Acad. Pol. Sci. 25, (1977), 711-713, Boson expansions of the Jordan-Wigner representation
• Rep. Math. Phys. 11, (1977), 73-80, Representations of the CAR generated by the representations of the CCR III. Non-Fock extension (with Z. Popowicz)
• Int. J. Theor. Phys. 15, (1976), 809-814, Remark on Kalnay theory of fermions constructed from bosons
• Bull. Acad. Pol. Sci. 24, (1976), 201-205, Representations of the CAR generated by representations of the CCR. II
• Bull. Acad. Pol. Sci. 23, (1975), 1113-1117, Spin-1 vector boson structure of free spin-1/2 quantum field
• Commun. Math. Phys. 43, (1975), 131-136, Representations of the CAR generated by representations of the CCR. Fock case
• Rep. Math. Phys. 7, (1975), 321-335, Functional representations of the canonical anticommutation relations and their application in quantum field theory
• Rep. Math. Phys. 6, (1974), 431-444, On generating functionals for antisymmetric functions and their application in quantum field theory (with J. Rzewuski)