Zobrazeno 1 - 10
of 99
pro vyhledávání: '"Carinena, J. F."'
Publikováno v:
Eur. Phys. J. Plus 138, 339 (2023)
A Lie system is a non-autonomous system of ordinary differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional Lie algebra of vector fields. Lie systems have been generalised in the lit
Externí odkaz:
http://arxiv.org/abs/2204.00954
Publikováno v:
J. Phys. A 55, 385206 (2022)
A stratified Lie system is a nonautonomous system of first-order ordinary differential equations on a manifold $M$ described by a $t$-dependent vector field $X=\sum_{\alpha=1}^rg_\alpha X_\alpha$, where $X_1,\ldots,X_r$ are vector fields on $M$ spann
Externí odkaz:
http://arxiv.org/abs/1905.13102
Publikováno v:
J. Phys. A: Math. Theor., 50, 365301, 2017
A geometric description of the space of states of a finite-dimensional quantum system and of the Markovian evolution associated with the Kossakowski-Lindblad operator is presented. This geometric setting is based on two composition laws on the space
Externí odkaz:
http://arxiv.org/abs/1705.05186
Publikováno v:
International Journal of Geometric Methods in Modern Physics Vol. 14 (2017) 1750047
In this paper we consider a manifold with a dynamical vector field and inquire about the possible tangent bundle structures which would turn the starting vector field into a second order one. The analysis is restricted to manifolds which are diffeomo
Externí odkaz:
http://arxiv.org/abs/1612.07484
We prove that $t$-dependent Schr\"odinger equations on finite-dimensional Hilbert spaces determined by $t$-dependent Hermitian Hamiltonian operators can be described through Lie systems admitting a Vessiot--Guldberg Lie algebra of K\"ahler vector fie
Externí odkaz:
http://arxiv.org/abs/1611.05630
Publikováno v:
J. Phys. A: Math. Theor. 49 (2016) 425202 (13pp)
We present a substantial generalisation of a classical result by Lie on integrability by quadratures. Namely, we prove that all vector fields in a finite-dimensional transitive and solvable Lie algebra of vector fields on a manifold can be integrated
Externí odkaz:
http://arxiv.org/abs/1606.02472
Publikováno v:
J. Math. Phys. 56, 063505 (2015)
Constants of motion, Lagrangians and Hamiltonians admitted by a family of relevant nonlinear oscillators are derived using a geometric formalism. The theory of the Jacobi last multiplier allows us to find Lagrangian descriptions and constants of the
Externí odkaz:
http://arxiv.org/abs/1506.02235
Autor:
Cariñena, J. F., de Lucas, J.
Publikováno v:
J. Math. Anal. App. 430, 648--671 (2015)
This work analyses types of group actions on families of $t$-dependent vector fields of a particular class, the hereby called quasi-Lie families. We devise methods to obtain the defined here quasi-Lie invariants, namely a kind of functions constant a
Externí odkaz:
http://arxiv.org/abs/1505.07241
Publikováno v:
Journal of Physics A. Mathematical and Theoretical 48(21), 2014
In this paper we extend the Lie theory of integration in two different ways. First we consider a finite dimensional Lie algebra of vector fields and discuss the most general conditions under which the integral curves of one of the fields can be obtai
Externí odkaz:
http://arxiv.org/abs/1409.7549
Publikováno v:
J. of Phys. A (Math. Theor.) 46, no. 43, Art. no. 435202 (2013)
In a recent paper, Post and Winternitz studied the properties of two-dimensional Euclidean potentials that are linear in one of the two Cartesian variables. In particular, they proved the existence of a potential endowed with an integral of third-ord
Externí odkaz:
http://arxiv.org/abs/1309.7245