arXiv subjects

Ricardo Gallego Torrome

Publications and source records attributed to Ricardo Gallego Torrome.

12 recordsLinked to original sources

arXiv2023

Advances in Quantum Radar and Quantum LiDAR

Quantum sensing, built upon fundamental quantum phenomena like entanglement and squeezing, is revolutionizing precision and sensitivity across diverse domains, including quantum metrology and imaging. Its impact is now stretching into radar and LiDAR applications, giving rise to the concept of quantum radar. Unlike traditional radar systems relying on classical electromagnetic, quantum radar harnesses the potential of the quantum properties of photon states like entanglement and quantum superposition to transcend established boundaries in sensitivity and accuracy. This comprehensive review embarks on an exploration of quantum radar and quantum LiDAR, guided by two primary objectives: enhancing sensitivity through quantum resources and refining accuracy in target detection and range estimation through quantum techniques. We initiate our exploration with a thorough analysis of the fundamental principles of quantum radar, which includes an evaluation of quantum illumination protocols, receiver designs, and their associated methodologies. This investigation spans across both microwave and optical domains, providing us with insights into various experimental demonstrations and the existing technological limitations. Additionally, we review the applications of quantum radar protocols for enhanced accuracy in target range determination and estimation. This section of our review involves a comprehensive analysis of quantum illumination, quantum interferometry radar, and other quantum radar protocols, providing insights into their contributions to the field. This review offers valuable insights into the current state of quantum radar, providing a deep understanding of key concepts, experiments, and the evolving landscape of this dynamic and promising field.

quant-ph↗

arXiv2023

Quantum Systems as results of Geometric Evolutions

In the framework of deterministic finslerian models, a mechanism producing dissipative dynamics at the Planck scale is discussed. It is based on a geometric evolution from Finsler to Riemann structures defined on the fiber bundle ${ TM}\to { M}$. Quantum states are equivalence classes, composed by the configurations that evolve through an internal dynamics drive by the above geometric evolution. Each equivalence class is conformed by the ontological states that evolve to the same final state. The existence of an hermitian scalar product in an associated linear space is discussed and related with the quantum pre-Hilbert space. This hermitian product emerges from geometric and statistical considerations. Our scheme recovers the main ingredients of the usual Quantum Mechanics. Several consequences are discussed and compared with the predictions of the standard Quantum Mechanics. A natural solution of the cosmological constant problems is proposed, as well as a mechanism for the absence of quantum interferences at classical scales.

math-ph↗

arXiv2015

Fiber averaged dynamics associated with the Lorentz force equation

It is shown that the Lorentz force equation is equivalent to the auto-parallel condition $\,^L\nabla_{\dot{x}}\dot{x}=0$ of a linear connection $^L\nabla$ defined on a convenient pull-back vector bundle. By using a geometric averaging method, an associated {\it averaged Lorentz connection} $\langle\,^L\nabla\rangle$ and the corresponding auto-parallel equation are obtained. After this, it is shown that in the ultra-relativistic limit and for narrow one-particle probability distribution functions, the auto-parallel curves of $\langle\,^L\nabla\rangle$ remain {\it nearby} close to the auto-parallel curves of $^L\nabla$. Applications of this result in beam dynamics and plasma physics are briefly described.

math-ph↗

arXiv2015

On the Berwald-Landsberg problem

Given a Finsler space (M,F), one can define natural average Riemannian metrics on M by averaging on the indicatrix I_x the fundamental tensor g of the Finsler function $F$. In this paper we determine explicitly the Levi-Civita connection for these average Riemannian metrics. We apply the result to the case when (M,F) is a Landsberg space. Using a particular averaging procedure, the invariance of the average metric along a homotopy in the space of Finsler structures over M is shown. As a consequence of such invariance, we prove that any C^5 regular Landsberg space is a Berwald space.

math.DG↗

arXiv2012

Jacobi equations and particle accelerator beam dynamics

A geometric formulation of the linear beam dynamics in accelerator physics is presented. In particular, it is proved that the linear transverse and longitudinal dynamics can be interpret geometrically as an approximation to the Jacobi equation of an affine averaged Lorentz connection. We introduce a specific notion reference trajectory as integral curves of the main velocity vector field. A perturbation caused by the statistical nature of the bunch of particles is considered.

math-ph↗

arXiv2010

There are no $\mathcal{C}^5$-Regular Pure $y$-Global Landsberg Surfaces

We show that there are not pure $\mathcal{C}^5$ regular y-global Landsberg surfaced. The proof is based on the averaged connection associated with the linear Chern's connection and the classification of irreducibles holonomies of torsion-free affine connections. The structure consists on exausting all the possible cases and showing that in dimension 2 Landsberg condition implies Berwald condition.

math.DG↗

arXiv2010

On the generalization of theorems from Riemannian to Finsler Geometry I: Metric Theorems

A method to generalize results from Riemannian Geometry to Finsler geometry is presented. We use the method to generalize several results that involve only metric conditions. Between them we show that the topology induced by the Finsler structure is equivalent to the manifold topology, we provide a new proof of the Hopf-Rinow theorem in Finsler geometry and we prove the existence of the center of mass of a convex body when the non-symmetric distance function comes from a non-reversible Finsler function.

math.DG↗

arXiv2010

On the two dimensional Berwald-Landsberg problem

The Berwald-Landsberg problem is considered for two dimensional manifolds. We sketch the proof that there are not $\mathcal{C}^5$-regular $y$-global pure Landsberg surfaces. The method used consists on considerer the holonomy representation of the averaged Chern connection and then exhausting all the possible cases, showing that in dimension 2 Landsberg condition implies Berwald condition.

math.DG↗

arXiv2010

Fluid Models from Kinetic Models using a Geometric Averaging Procedure

We interpret the Lorentz force equation as a geodesic equation associated with a non-linear connection. Using a geometric averaging procedure, we prove that for narrow and smooth one-particle distribution functions whose supports are invariant under the flow of the Lorentz equation, a bunch of charged point particles can be described by a charged cold fluid model in the ultra-relativistic regime. The method used to prove this result does not require additional hypotheses on the higher moments of the distribution. This is accomplished by estimating the expressions that include the differential operators appearing in the charged cold fluid model equation. Under the specified conditions of narrowness and ultra-relativistic dynamics, it turns out that these differential expressions are close to zero, justifying the use of the charged cold fluid model. The method presented in the work can also be applied to justify the use of warm plasmas and other models.

math-ph↗

arXiv2009

Averaged Lorentz Dynamics and an application in Plasma Dynamics

Using a geometric averaging procedure applied to a non-affine linear connection, we prove that for a narrow one particle distribution function and in the ultra-relativistic limit, a bunch of point charged particles can be described by a Charged Cold Fluid Model, without additional hypothesis on the moments.

math-ph↗

arXiv2009

On a rigidity condition for Berwald Spaces

We show that which that for a Berwald structure, any Riemannian structure that is preserved by the Berwald connection leaves the indicatrix invariant under horizontal parallel transport. We also obtain the converse result: if $({\bf M},F)$ is a Finsler structure such that there exists a Riemannian structure that leaves invariant the indicatrix under parallel transport of the associated Levi-Civita connection, then the structure $({\bf M},F)$ is Berwald. As application, a necessary condition for pure Landsberg spaces is formulated. Using this criterion we provide an strategy to solve the existence or not of pure Landsberg surfaces

math.DG↗

arXiv2007

On a covariant version of Caianiello's Model

Caianiello's derivation of Quantum Geometry through an isometric embedding of the spacetime ({\bf M},\tilde{g}) in the pseudo-Riemannian structure ({\bf T^*M},g^*_{AB}) is reconsidered. In the new derivation, a non-linear connection and the bundle %%@ formalism induce a Lorentzian-type structure in the 4-dimensional manifold {\bf M} that is covariant %%@ under arbitrary local coordinate transformations in {\bf M}. If models with maximal acceleration are required to be non-trivial, gravity should be supplied with other interactions in a unification framework.

gr-qc↗