Upon the horizon’s verge: Thermal particle creation between and approaching horizons

Quantum particle creation from spacetime horizons, or accelerating boundaries in the dynamical Casimir effect, can have an equilibrium, or thermal, distribution. Using an accelerating boundary in flat spacetime (moving mirror), in this paper (arXiv:2208.01992) we investigate the production of thermal energy flux despite non-equilibrium accelerations, the evolution between equilibrium states, and the “interference” between horizons. In particular, this allows us to give a complete solution to the particle spectrum of the accelerated boundary correspondence with Schwarzschild-de Sitter spacetime.

Time delays, choice of energy-momentum variables and relative locality in doubly special relativity

Doubly Special Relativity (DSR) theories consider (quantum-gravity motivated) deformations of the symmetries of special relativity compatible with a relativity principle. The existence of time delays for massless particles, one of their proposed phenomenological consequences, is a delicate question, since, contrary to what happens with Lorentz Invariance Violation (LIV) scenarios, they are not simply determined by the modification in the particle dispersion relation. While some studies of DSR assert the existence of photon time delays, in this paper (arXiv:2207.03799) we generalize a recently proposed model for time delay studies in DSR and show that the existence of photon time delays does not necessarily follow from a DSR scenario, determining in which cases this is so. Moreover, we clarify long-standing questions about the arbitrariness in the choice of the energy-momentum labels and the independence of the time delay on this choice, as well as on the consistency of its calculation with the relative locality paradigm of DSR theories. Finally, we show that the result for time delays is reproduced in models that consider propagation in a noncommutative spacetime.

Unimodularity and invariant volume forms for Hamiltonian dynamics on Poisson-Lie groups

In this paper (arXiv:2207.05511), we discuss several relations between the existence of invariant volume forms for Hamiltonian systems on Poisson-Lie groups and the unimodularity of the Poisson-Lie structure. In particular, we prove that Hamiltonian vector fields on a Lie group endowed with a unimodular Poisson-Lie structure preserve a multiple of any left-invariant volume on the group. Conversely, we also prove that if there exists a Hamiltonian function such that the identity element of the Lie group is a nondegenerate singularity and the associated Hamiltonian vector field preserves a volume form, then the Poisson-Lie structure is necessarily unimodular. Furthermore, we illustrate our theory with different interesting examples, both on semisimple and unimodular Poisson-Lie groups.

Cosmic neutrinos as a window to departures from special relativity

In this paper (arXiv:2206.14257) we review the peculiarities that make neutrino a very special cosmic messenger in high-energy astrophysics, and, in particular, to provide possible indications of deviations from special relativity, as it is suggested theoretically by quantum gravity models. In this respect, we examine the effects that one could expect in the production, propagation, and detection of neutrinos, not only in the well-studied scenario of Lorentz Invariance Violation, but also in models which maintain, but deform, the relativity principle, such as those considered in the framework of Doubly Special Relativity. We discuss the challenges and the promising future prospects offered by this phenomenological window to physics beyond special relativity.

Space-time thermodynamics in momentum dependent geometries

A possible way to capture the effects of quantum gravity in spacetime at a mesoscopic scale, for relatively low energies, is through an energy dependent metric, such that particles with different energies probe different spacetimes. In this context, a clear connection between a geometrical approach and modifications of the special relativistic kinematics has been shown in the last few years. In this work (arXiv:2206.14096), we focus on the geometrical interpretation of the relativistic deformed kinematics present in the framework of doubly special relativity, where a relativity principle is present. In this setting, we study the effects of a momentum dependence of the metric for a uniformly accelerated observer. We show how the local Rindler wedge description gets affected by the proposed observer dependent metric, while the local Rindler causal structure is not, leading to a standard local causal horizon thermodynamic description. For the proposed modified metric, we can reproduce the derivation of Einstein’s equations as the equations of state for the thermal Rindler wedge. The conservation of the Einstein tensor leads to the same privileged momentum basis obtained in other works of some of the present authors, so supporting its relevance.

Higher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike system

In this paper (arXiv:2206.12717) we consider an N-dimensional multiparametric generalization of the classical Zernike system. We prove that it always provides a superintegrable system by obtaining the corresponding constants of the motion explicitly, which turn out to be of higher-order in the momenta. Such generic results are not only applied to the Euclidean plane, but also to the sphere and the hyperbolic plane. In the latter curved spaces, the Hamiltonian is expressed in geodesic polar coordinates showing that such a new superintegrable Hamiltonian can be regarded as a superposition of the isotropic 1:1 curved (Higgs) oscillator with even-order anharmonic curved oscillators plus another superposition of higher-order momentum-dependent potentials. Furthermore, the Racah algebra determined by the constants of the motion is also studied, giving rise to a (2N−1)th-order polynomial algebra. As a byproduct, the Hamiltonian is interpreted as a family of superintegrable perturbations of the classical Zernike system. Finally, it is shown that this new Hamiltonian (and so the Zernike system as well) is endowed with a Poisson 𝔰𝔩(2,ℝ)-coalgebra symmetry which would allow for further possible generalizations that are also discussed.

Quantum revivals in curved graphene nanoflakes

Graphene nanostructures have attracted a lot of attention in recent years due to their unconventional properties. In this paper we have employed Density Functional Theory to study the mechanical and electronic properties of curved graphene nanoflakes. We explore hexagonal flakes relaxed with different boundary conditions: (i) all atoms on a perfect spherical sector, (ii) only border atoms forced to be on the spherical sector, and (iii) only vertex atoms forced to be on the spherical sector. For each case, we have analysed the behaviour of curvature energy and of quantum regeneration times (classical and revival) as the spherical sector radius changes. Revival time presents in one case a divergence usually associated with a phase transition, probably caused by the pseudomagnetic field created by the curvature. This could be the first case of a phase transition in graphene nanostructures without the presence of external electric or magnetic fields.

Astrophysical sources and acceleration mechanisms

In these lecture notes (arXiv:2202.09170) it is reviewed how multi-messenger astronomy provides for the observation of the same astronomical event with different kind of telescopes at the same time: optical observations, X-rays, gamma-ray bursts, neutrinos and, most recently, gravitational waves are just few examples of the several points of view from which an astronomical event can be observed and analyzed. Cosmic rays play an important role in multi-messenger astronomy and, for this reason, it is important to deepen the study of their sources and to understand the mechanisms behind their acceleration in astronomical environments.

XIV International Summer School on Geometry, Mechanics and Control

The XIV International Summer School on Geometry, Mechanics and Control will be held in Burgos, Spain, from July 4 to July 8, 2022. The School is organised by the Geometry, Mechanics and Control (GMC) Network and the Mathematical Physics Group of the Universidad de Burgos.

This school is oriented to young researchers, Ph.D. and postdoctoral students in Mathematics, Physics and Engineering, whose research topics deal with Geometry, Mechanics and Control Theory. In particular, this year the courses of the School will be focused in spectral geometry, Lie systems and their geometric structures, quantum groups and non-commutative geometry and geometric control. These courses are intended to present an up-to-date introduction to these topics, and also to bring the participant´s attention to some open problems, in particular those ones related to applications. Undegraduate students and master students are also welcome. Participants are encouraged to present oral or poster contributions.

Geometrize and conquer: the Klein-Gordon and Dirac equations in Doubly Special Relativity

In this work (arXiv: 2203.12286) we discuss the deformed relativistic wave equations, namely the Klein–Gordon and Dirac equations in a Doubly Special Relativity scenario. We employ what we call a geometric approach, based on the geometry of a curved momentum space, which should be seen as complementary to the more spread algebraic one. In this frame we are able to rederive well-known algebraic expressions, as well as to treat yet unresolved issues, to wit, the explicit relation between both equations, the discrete symmetries for Dirac particles, the fate of covariance, and the formal definition of a Hilbert space for the Klein–Gordon case.