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Papers by jose f carinena

Physica A: Statistical Mechanics and its Applications, 1982

Physical Review C, 1984

The possibility of bound states in a velocity-dependent potential of the Kisslinger type, such as... more The possibility of bound states in a velocity-dependent potential of the Kisslinger type, such as that used to describe the low-energy pion-nucleus interaction, is discussed. It is shown in a specific example that, for a real potential, the number of bound states is finite and their binding energies are real, in contradiction with general results claimed by other authors.~N UCLEAR REACTIONS Pion-nucleus optical potential; nuclear bound states of pions in nuclei; velocity-dependent potential.

Journal of Physics A, Mar 30, 2023

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.

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.

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.

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]).

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.

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.

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].

Journal of Physics A: Mathematical and General, 1990

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 \(\Gamma \).

Journal of Physics A, Aug 9, 2017

A geometric description of the space of states of a finite-dimensional quantum system and of the ... more 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 of observables defined by a pair of contravariant tensor fields. The first one is a Poisson tensor field that encodes the commutator product and allows us to develop a Hamiltonian mechanics. The other tensor field is symmetric, encodes the Jordan product and provides the variances and covariances of measures associated with the observables. This tensorial formulation of quantum systems is able to describe, in a natural way, the Markovian dynamical evolution as a vector field on the space of states. Therefore, it is possible to consider dynamical effects on non-linear physical quantities, such as entropies, purity and concurrence. In particular, in this work the tensorial formulation is used to consider the dynamical evolution of the symmetric and skewsymmetric tensors and to read off the corresponding limits as giving rise to a contraction of the initial Jordan and Lie products.

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

In this paper we consider a manifold with a dynamical vector field and inquire about the possible... more 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 diffeomorphic with affine spaces. In particular, we consider the problem in connection with conformal vector fields of second order and apply the procedure to vector fields conformally related with the harmonic oscillator (f-oscillators). We select one which covers the vector field describing the Kepler problem.

arXiv (Cornell University), Feb 20, 1998

We address one of the open problems in quantization theory recently listed by Rieffel. By develop... more We address one of the open problems in quantization theory recently listed by Rieffel. By developing in detail Connes' tangent groupoid principle and using previous work by Landsman, we show how to construct a strict flabby quantization, which is moreover an asymptotic morphism and satisfies the reality and traciality constraints, on any oriented Riemannian manifold. That construction generalizes the standard Moyal rule. The paper can be considered as an introduction to quantization theory from Connes' point of view.

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.

Physica A: Statistical Mechanics and its Applications, 1982

Physical Review C, 1984

The possibility of bound states in a velocity-dependent potential of the Kisslinger type, such as... more The possibility of bound states in a velocity-dependent potential of the Kisslinger type, such as that used to describe the low-energy pion-nucleus interaction, is discussed. It is shown in a specific example that, for a real potential, the number of bound states is finite and their binding energies are real, in contradiction with general results claimed by other authors.~N UCLEAR REACTIONS Pion-nucleus optical potential; nuclear bound states of pions in nuclei; velocity-dependent potential.

Journal of Physics A, Mar 30, 2023

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.

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.

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.

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]).

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.

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.

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].

Journal of Physics A: Mathematical and General, 1990

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 \(\Gamma \).

Journal of Physics A, Aug 9, 2017

A geometric description of the space of states of a finite-dimensional quantum system and of the ... more 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 of observables defined by a pair of contravariant tensor fields. The first one is a Poisson tensor field that encodes the commutator product and allows us to develop a Hamiltonian mechanics. The other tensor field is symmetric, encodes the Jordan product and provides the variances and covariances of measures associated with the observables. This tensorial formulation of quantum systems is able to describe, in a natural way, the Markovian dynamical evolution as a vector field on the space of states. Therefore, it is possible to consider dynamical effects on non-linear physical quantities, such as entropies, purity and concurrence. In particular, in this work the tensorial formulation is used to consider the dynamical evolution of the symmetric and skewsymmetric tensors and to read off the corresponding limits as giving rise to a contraction of the initial Jordan and Lie products.

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

In this paper we consider a manifold with a dynamical vector field and inquire about the possible... more 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 diffeomorphic with affine spaces. In particular, we consider the problem in connection with conformal vector fields of second order and apply the procedure to vector fields conformally related with the harmonic oscillator (f-oscillators). We select one which covers the vector field describing the Kepler problem.

arXiv (Cornell University), Feb 20, 1998

We address one of the open problems in quantization theory recently listed by Rieffel. By develop... more We address one of the open problems in quantization theory recently listed by Rieffel. By developing in detail Connes' tangent groupoid principle and using previous work by Landsman, we show how to construct a strict flabby quantization, which is moreover an asymptotic morphism and satisfies the reality and traciality constraints, on any oriented Riemannian manifold. That construction generalizes the standard Moyal rule. The paper can be considered as an introduction to quantization theory from Connes' point of view.

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.