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Papers by jose f carinena

Research paper thumbnail of Locally-operating realizations of groups and superequivalence of factor systems

Physica A: Statistical Mechanics and its Applications, 1982

Research paper thumbnail of Bound states in pion-nucleus velocity-dependent potentials: Finite or infinite number

Research paper thumbnail of Sundman transformation and alternative tangent structures

Journal of Physics A, Mar 30, 2023

Research paper thumbnail of Painlevé equations, integrable systems and the stabilizer set of Virasoro orbit

Reviews in Mathematical Physics

We study a geometrical formulation of the nonlinear second-order Riccati equation (SORE) in terms... more We study a geometrical formulation of the nonlinear second-order Riccati equation (SORE) in terms of the projective vector field equation on [Formula: see text], which in turn is related to the stability algebra of Virasoro orbit. Using Darboux integrability method, we obtain the first integral of the SORE and the results are applied to the study of its Lagrangian and Hamiltonian descriptions. Using these results, we show the existence of a Lagrangian description for SORE, and the Painlevé II equation is analyzed.

Research paper thumbnail of Geodesic and Newtonian Vector Fields and Symmetries of Mechanical Systems

Research paper thumbnail of Integrability and quantization. Proceedings, 20th GIFT International Seminar, Jaca, Spain, June 5-9, 1989

Research paper thumbnail of Application of Lie Systems to Quantum Mechanics: Superposition Rules

Springer Proceedings in Physics, 2019

We prove that t-dependent Schrodinger equations on finite-dimensional Hilbert spaces determined b... more We prove that t-dependent Schrodinger 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 Kahler vector fields. This result is extended to other related Schrodinger equations, e.g. projective ones, and their properties are studied through Poisson, presymplectic, and Kahler structures. This leads to deriving nonlinear superposition rules for them depending on a lower (or equal) number of solutions than standard linear ones. As an application, we study n-qubit systems and special attention is paid to the one-qubit case.

Research paper thumbnail of Some Examples of Linear and Nonlinear Physical Systems and Their Dynamical Equations

Geometry from Dynamics, Classical and Quantum, 2014

This chapter is devoted to the discussion of a few simple examples of dynamics by using elementar... more This chapter is devoted to the discussion of a few simple examples of dynamics by using elementary means. The purpose of that is twofold, on one side after the discussion of these examples we will have a catalogue of systems to test the ideas we would be introducing later on; on the other hand this collection of simple systems will help to illustrate how geometrical ideas actually are born from dynamics.

Research paper thumbnail of Lie–Scheffers Systems

Geometry from Dynamics, Classical and Quantum, 2014

In 1893, Lie and Scheffers [Lie93] presented a result that has a deep implication regarding the n... more In 1893, Lie and Scheffers [Lie93] presented a result that has a deep implication regarding the notion of integrability that we are describing, but that has been almost unnoticed since then (for two modern general references see [Ca00, Ca07b] and [CL11]).

Research paper thumbnail of Integrable and Superintegrable Systems

Geometry from Dynamics, Classical and Quantum, 2014

There is no generally accepted definition of integrability that would include the various instanc... more There is no generally accepted definition of integrability that would include the various instances which are usually associated with the word “integrable". Occasionally the word ‘solvable’ is also used more or less as synonymous, but to emphasize the fact that the system need not be Hamiltonian.

Research paper thumbnail of The Language of Geometry and Dynamical Systems: The Linearity Paradigm

Geometry from Dynamics, Classical and Quantum, 2014

We can infer from the examples given in Chap. 1 that linear dynamical systems are interesting on ... more We can infer from the examples given in Chap. 1 that linear dynamical systems are interesting on their own.

Research paper thumbnail of Folding and Unfolding Classical and Quantum Systems

Geometry from Dynamics, Classical and Quantum, 2014

Reduction procedures, the way we understand them today (i.e. in terms of Poisson reduction) can b... more Reduction procedures, the way we understand them today (i.e. in terms of Poisson reduction) can be traced back to Sophus Lie in terms of function groups, reciprocal function groups and indicial functions [Ei61, Fo59, Lie93, Mm85].

Research paper thumbnail of Relativistic quantum kinematics in the Moyal representation

Journal of Physics A: Mathematical and General, 1990

Research paper thumbnail of A geometric characterisation of Lagrangian second-order differential equations

Research paper thumbnail of Invariant Structures for Dynamical Systems: Poisson Dynamics

Geometry from Dynamics, Classical and Quantum, 2014

In this chapter we will start developing systematically one of the inspiring principles of this b... more In this chapter we will start developing systematically one of the inspiring principles of this book: all geometrical structures should be dynamically determined. In other words, given a dynamical system \(\Gamma \) we try to determine the geometrical structures determined by \(\Gamma \). The exact nature of the geometrical structure determined by \(\Gamma \) that we will be interested in will depend on the problem we are facing, however the simplest ones will always be of interest: symmetries and constants of motion as it was discussed in the previous chapter. Higher order objects like contravariant o covariant tensors of order 2 tensorial will be discussed now. This problem will lead us in particular to the study of Poisson and symplectic structures compatible with our given dynamical system \(\Gamma \).

Research paper thumbnail of Tensorial dynamics on the space of quantum states

Journal of Physics A, Aug 9, 2017

Research paper thumbnail of Tangent bundle geometry from dynamics: Application to the Kepler problem

International Journal of Geometric Methods in Modern Physics, Feb 14, 2017

Research paper thumbnail of XVIII International Fall Workshop on Geometry and Physics

Research paper thumbnail of Connes' Tangent Groupoid and Deformation Quantization

arXiv (Cornell University), Feb 20, 1998

Research paper thumbnail of Lie systems and Schr\"odinger equations

arXiv: Mathematical Physics, 2016

We prove that ttt-dependent Schr\"odinger equations on finite-dimensional Hilbert spaces det... more We prove that ttt-dependent Schr\"odinger equations on finite-dimensional Hilbert spaces determined by ttt-dependent Hermitian Hamiltonian operators can be described through Lie systems admitting a Vessiot--Guldberg Lie algebra of K\"ahler vector fields. This result is extended to other related Schr\"odinger equations, e.g. projective ones, and their properties are studied through Poisson, presymplectic and K\"ahler structures. This leads to derive nonlinear superposition rules for them depending in a lower (or equal) number of solutions than standard linear ones. Special attention is paid to applications in nnn-qubit systems.

Research paper thumbnail of Locally-operating realizations of groups and superequivalence of factor systems

Physica A: Statistical Mechanics and its Applications, 1982

Research paper thumbnail of Bound states in pion-nucleus velocity-dependent potentials: Finite or infinite number

Research paper thumbnail of Sundman transformation and alternative tangent structures

Journal of Physics A, Mar 30, 2023

Research paper thumbnail of Painlevé equations, integrable systems and the stabilizer set of Virasoro orbit

Reviews in Mathematical Physics

We study a geometrical formulation of the nonlinear second-order Riccati equation (SORE) in terms... more We study a geometrical formulation of the nonlinear second-order Riccati equation (SORE) in terms of the projective vector field equation on [Formula: see text], which in turn is related to the stability algebra of Virasoro orbit. Using Darboux integrability method, we obtain the first integral of the SORE and the results are applied to the study of its Lagrangian and Hamiltonian descriptions. Using these results, we show the existence of a Lagrangian description for SORE, and the Painlevé II equation is analyzed.

Research paper thumbnail of Geodesic and Newtonian Vector Fields and Symmetries of Mechanical Systems

Research paper thumbnail of Integrability and quantization. Proceedings, 20th GIFT International Seminar, Jaca, Spain, June 5-9, 1989

Research paper thumbnail of Application of Lie Systems to Quantum Mechanics: Superposition Rules

Springer Proceedings in Physics, 2019

We prove that t-dependent Schrodinger equations on finite-dimensional Hilbert spaces determined b... more We prove that t-dependent Schrodinger 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 Kahler vector fields. This result is extended to other related Schrodinger equations, e.g. projective ones, and their properties are studied through Poisson, presymplectic, and Kahler structures. This leads to deriving nonlinear superposition rules for them depending on a lower (or equal) number of solutions than standard linear ones. As an application, we study n-qubit systems and special attention is paid to the one-qubit case.

Research paper thumbnail of Some Examples of Linear and Nonlinear Physical Systems and Their Dynamical Equations

Geometry from Dynamics, Classical and Quantum, 2014

This chapter is devoted to the discussion of a few simple examples of dynamics by using elementar... more This chapter is devoted to the discussion of a few simple examples of dynamics by using elementary means. The purpose of that is twofold, on one side after the discussion of these examples we will have a catalogue of systems to test the ideas we would be introducing later on; on the other hand this collection of simple systems will help to illustrate how geometrical ideas actually are born from dynamics.

Research paper thumbnail of Lie–Scheffers Systems

Geometry from Dynamics, Classical and Quantum, 2014

In 1893, Lie and Scheffers [Lie93] presented a result that has a deep implication regarding the n... more In 1893, Lie and Scheffers [Lie93] presented a result that has a deep implication regarding the notion of integrability that we are describing, but that has been almost unnoticed since then (for two modern general references see [Ca00, Ca07b] and [CL11]).

Research paper thumbnail of Integrable and Superintegrable Systems

Geometry from Dynamics, Classical and Quantum, 2014

There is no generally accepted definition of integrability that would include the various instanc... more There is no generally accepted definition of integrability that would include the various instances which are usually associated with the word “integrable". Occasionally the word ‘solvable’ is also used more or less as synonymous, but to emphasize the fact that the system need not be Hamiltonian.

Research paper thumbnail of The Language of Geometry and Dynamical Systems: The Linearity Paradigm

Geometry from Dynamics, Classical and Quantum, 2014

We can infer from the examples given in Chap. 1 that linear dynamical systems are interesting on ... more We can infer from the examples given in Chap. 1 that linear dynamical systems are interesting on their own.

Research paper thumbnail of Folding and Unfolding Classical and Quantum Systems

Geometry from Dynamics, Classical and Quantum, 2014

Reduction procedures, the way we understand them today (i.e. in terms of Poisson reduction) can b... more Reduction procedures, the way we understand them today (i.e. in terms of Poisson reduction) can be traced back to Sophus Lie in terms of function groups, reciprocal function groups and indicial functions [Ei61, Fo59, Lie93, Mm85].

Research paper thumbnail of Relativistic quantum kinematics in the Moyal representation

Journal of Physics A: Mathematical and General, 1990

Research paper thumbnail of A geometric characterisation of Lagrangian second-order differential equations

Research paper thumbnail of Invariant Structures for Dynamical Systems: Poisson Dynamics

Geometry from Dynamics, Classical and Quantum, 2014

In this chapter we will start developing systematically one of the inspiring principles of this b... more In this chapter we will start developing systematically one of the inspiring principles of this book: all geometrical structures should be dynamically determined. In other words, given a dynamical system \(\Gamma \) we try to determine the geometrical structures determined by \(\Gamma \). The exact nature of the geometrical structure determined by \(\Gamma \) that we will be interested in will depend on the problem we are facing, however the simplest ones will always be of interest: symmetries and constants of motion as it was discussed in the previous chapter. Higher order objects like contravariant o covariant tensors of order 2 tensorial will be discussed now. This problem will lead us in particular to the study of Poisson and symplectic structures compatible with our given dynamical system \(\Gamma \).

Research paper thumbnail of Tensorial dynamics on the space of quantum states

Journal of Physics A, Aug 9, 2017

Research paper thumbnail of Tangent bundle geometry from dynamics: Application to the Kepler problem

International Journal of Geometric Methods in Modern Physics, Feb 14, 2017

Research paper thumbnail of XVIII International Fall Workshop on Geometry and Physics

Research paper thumbnail of Connes' Tangent Groupoid and Deformation Quantization

arXiv (Cornell University), Feb 20, 1998

Research paper thumbnail of Lie systems and Schr\"odinger equations

arXiv: Mathematical Physics, 2016

We prove that ttt-dependent Schr\"odinger equations on finite-dimensional Hilbert spaces det... more We prove that ttt-dependent Schr\"odinger equations on finite-dimensional Hilbert spaces determined by ttt-dependent Hermitian Hamiltonian operators can be described through Lie systems admitting a Vessiot--Guldberg Lie algebra of K\"ahler vector fields. This result is extended to other related Schr\"odinger equations, e.g. projective ones, and their properties are studied through Poisson, presymplectic and K\"ahler structures. This leads to derive nonlinear superposition rules for them depending in a lower (or equal) number of solutions than standard linear ones. Special attention is paid to applications in nnn-qubit systems.