Zobrazeno 1 - 10
of 39
pro vyhledávání: '"Maciej Blaszak"'
Autor:
Maciej Blaszak, Krzysztof Marciniak
Publikováno v:
Open Communications in Nonlinear Mathematical Physics, Vol Proceedings: OCNMP... (2024)
In this paper we systematically consider various ways of generating integrable and separable Hamiltonian systems in canonical and in non-canonical representations from algebraic curves on the plane. In particular, we consider St\"ackel transform betw
Externí odkaz:
https://doaj.org/article/1438eaef500146d3b63e479d631c8bce
Autor:
Maciej Blaszak, Ziemowit Domański
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications.
In this paper we construct Lax pairs for St\"ackel systems with separation curves from so-called Benenti class. For each system of considered family we present an infinite family of Lax representations, parameterized by smooth functions of spectral p
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d5a2bf91d48ae078e46cb6eb70f2b17d
https://doi.org/10.3842/sigma.2019.045
https://doi.org/10.3842/sigma.2019.045
Autor:
Maciej Błaszak
This accessible monograph introduces physicists to the general relation between classical and quantum mechanics based on the mathematical idea of deformation quantization and describes an original approach to the theory of quantum integrable systems
Publikováno v:
Annals of Physics. 371:460-477
In this article we prove that many Hamiltonian systems that can not be separably quantized in the classical approach of Robertson and Eisenhardt can be separably quantized if we extend the class of admissible quantizations through a suitable choice o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::949e6561d455c09289894ab46490848f
https://doi.org/10.1016/j.aop.2016.06.007
https://doi.org/10.1016/j.aop.2016.06.007
Publikováno v:
Annals of Physics. 351:152-165
In this paper, we consider the problem of quantization of classical St\"ackel systems and the problem of separability of related quantum Hamiltonians. First, using the concept of St\"ackel transform, all considered systems are expressed by flat coord
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::504dd88949cfe5f791189d1c1e73030a
https://doi.org/10.1016/j.aop.2014.08.015
https://doi.org/10.1016/j.aop.2014.08.015
Autor:
Ziemowit Domański, Maciej Blaszak
Publikováno v:
Annals of Physics. 344:29-42
In this paper is considered a problem of defining natural star-products on symplectic manifolds, admissible for quantization of classical Hamiltonian systems. First, a construction of a star-product on a cotangent bundle to an Euclidean configuration
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b62f137411a316dcae813b27ea1b4603
https://doi.org/10.1016/j.aop.2014.02.013
https://doi.org/10.1016/j.aop.2014.02.013
Autor:
Maciej Blaszak, Ziemowit Domański
We perform a detailed analysis of the behavior of coherent and squeezed states undergoing time evolution. We calculate time dependence of expectation values of position and momentum in coherent and squeezed states (which can be interpreted as quantum
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::be649b81c81cb754e6a66f3cbee79717
http://arxiv.org/abs/1601.02114
http://arxiv.org/abs/1601.02114
Autor:
Krzysztof Marciniak, Maciej Blaszak
Publikováno v:
Reports on Mathematical Physics. 55:325-339
Given a foliation S of a manifold M, a distribution Z in M transveral to S and a Poisson bivector \Pi on M we present a geometric method of reducing this operator on the foliation S along the distribution Z. It encompasses the classical ideas of Dira
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fbbaf5ad06d05b86fb44d8925015a45f
https://doi.org/10.1016/s0034-4877(05)80049-7
https://doi.org/10.1016/s0034-4877(05)80049-7
Autor:
Maciej Blaszak
A modern Hamiltonian theory offering a unified treatment of all types of systems (i.e. finite, lattice, and field) is presented. Particular attention is paid to nonlinear systems that have more than one Hamiltonian formulation in a single coordinate
Autor:
Maciej Blaszak, Krzysztof Marciniak
Publikováno v:
Studies in Applied Mathematics.
In this paper, we discuss the conditions under which the coupled KdV and coupled Harry Dym hierarchies possess inverse (negative) parts. We further investigate the structure of nonlocal parts of tensor invariants of these hierarchies, in particular,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0c7bc3bde7211196ee7d26604e9a0efb
https://doi.org/10.1111/sapm.12008
https://doi.org/10.1111/sapm.12008