arXiv subjects

Piotr Kosiński

Publications and source records attributed to Piotr Kosiński.

8 recordsLinked to original sources

arXiv2026

Herglotz's formalism, Eisenhart lift and Killing vectors

The Eisenhart lift is extended to the case of dynamics described by action-dependent Lagrangians. The resulting Brinkmann metric depends on all coordinates. It is shown that the symmetries of the initial dynamics result in the existence of (conformal) Killing vectors of the Brinkmann metric. An example is given of equivalent time- and action-dependent descriptions which result in conformally equivalent metrics. It is also shown how the scaling invariance fits naturally into this scheme.

math-ph↗

arXiv2024

Fermat's Principle in General Relativity via Herglotz Variational Formalism

New form of Fermat's principle for light propagation in arbitrary (i.e. in general neither static nor stationary) gravitational field is proposed. It is based on Herglotz extension of canonical formalism and simple relation between the dynamics described by the Lagrangians homogeneous in velocities and the reduced dynamics on lower-dimensional configuration manifold. This approach is more flexible as it allows to extend immediately the Fermat principle to the case of massive particles and to eliminate any space-time coordinate, not only $x^0$.

gr-qc↗

arXiv2024

The families of Hamiltonians sharing common symmetry structure

We describe a general procedure which allows to construct, starting from a given Hamiltonian, the whole family of new ones sharing the same set of unparameterized trajectories in phase space. The symmetry structure of this family can be completely characterized provided the symmetries of initial Hamiltonian are known. Our approach covers numerous models considered in literature as well as it allows to construct novel ones.. It provides a far reaching generalization of Hietarinta et al. coupling-constant metamorphosis method and another proof of Darboux theorem.

math-ph↗

arXiv2024

Note on the Margolus-Levitin quantum speed limit for arbitrary fidelity

For vanishing fidelity between initial and final states two important quantum speed limits, the Mandelstam-Tamm limit (involving energy dispersion) and Margolus-Levitin one (involving excitation energy expectation value) have been derived. While the generalization of the former limit to the case of arbitrary fidelity is straightforward, the relevant generalization of the latter, given in the seminal paper by Giovanetti et al (Phys. Rev. A67 (2003), 052109) was based on the conjectured equality of lower and upper bounds on the right hand side of generalized Margolus-Levitin inequality, verified numerically up to seven digits. Only recently there appear two proofs of the conjecture. We provide below a very elementary new proof, based on the simplest tools from differential calculus. Thus the generalized Margolus-Levitin speed limit can be derived much in the spirit of the original one valid for vanishing fidelity.

quant-ph↗

arXiv2021

Groups, Platonic solids and Bell inequalities

The construction of Bell inequalities based on Platonic and Archimedean solids (Quantum 4 (2020), 293) is generalized to the case of orbits generated by the action of some finite groups. A number of examples with considerable violation of Bell inequalities is presented.

quant-ph↗

arXiv2019

Note on Güney-Hillery approach to Bell inequalities

We analyze certain aspects of group theoretical approach to Bell inequalities proposed by Güney and Hillery. The general procedure for constructing the relevant group orbits is described. Using Hall theorem we determine the form of Bell inequality in the single orbit case. It is shown that in this case the Bell inequality is not violated for maximally entangled state generating trivial subrepresentation if the representation under consideration is real.

quant-ph↗

arXiv2015

Note on maximally entangled Eisert-Lewenstein-Wilkens quantum games

Maximally entangled Eisert-Lewenstein-Wilkens games are analyzed. For a general class of gate operators defined in the previous papers of the first author the general conditions are derived which allow to determine the form of gate operators leading to maximally entangled games. The construction becomes particularly simple provided one does distinguish between games differing by relabelling of strategies. Some examples are presented.

quant-ph↗

arXiv2015

On Nash equilibria in Eisert-Lewenstein-Wilkens game

Landsburg method of classifying mixed Nash equilibria for maximally entangled Eisert-Lewenstein-Wilkens (ELW) game is analyzed with special emphasis on symmetries inherent to the problem. Nash equilibria for the original ELW game are determined.

quant-ph↗