In this work (arXiv:2309.15305), PT-symmetric Hamiltonians defined on quantum sl(2,ℝ) algebras are presented. We study the spectrum of a family of non-Hermitian Hamiltonians written in terms of the generators of the non-standard Uz(sl(2,ℝ)) Hopf algebra deformation of sl(2,ℝ). By making use of a particular boson representation of the generators of Uz(sl(2,ℝ)), both the co-product and the commutation relations of the quantum algebra are shown to be invariant under the PT-transformation. In terms of these operators, we construct several finite dimensional PT-symmetry Hamiltonians, whose spectrum is analytically obtained for any arbitrary dimension. In particular, we show the appearance of Exceptional Points in the space of model parameters and we discuss the behaviour of the spectrum both in the exact PT-symmetry and the broken PT-symmetry dynamical phases. As an application, we show that this non-standard quantum algebra can be used to define an effective model Hamiltonian describing accurately the experimental spectra of three-electron hybrid qubits based on asymmetric double quantum dots. Remarkably enough, in this effective model, the deformation parameter z has to be identified with the detuning parameter of the system.

Pointlike systems coupled to quantum fields are often employed as toy models for measurements in quantum field theory. In this paper (arXiv:2308.14718), we identify the field observables recorded by such models. We show that in models that work in the strong coupling regime, the apparatus is correlated with smeared field amplitudes, while in models that work in weak coupling the apparatus records particle aspects of the field, such as the existence of a particle-like time of arrival and resonant absorption. Then, we develop an improved field-detector interaction model, adapting the formalism of Quantum Brownian motion, that is exactly solvable. This model confirms the association of field and particle properties in the strong and weak coupling regimes, respectively. Further, it can also describe the intermediate regime, in which the field-particle characteristics `merge’. In contrast to standard perturbation techniques, this model also recovers the relativistic Breit-Wigner resonant behavior in the weak coupling regime. The modulation of field-particle-duality by a single tunable parameter is a novel feature that is, in principle, experimentally accessible.

In this paper (arXiv:2305.02281), the spectrum of bound and scattering states of the one dimensional Dirac Hamiltonian describing fermions distorted by a static background built from two Dirac delta potentials is studied. A distinction will be made between mass-spike and electrostatic Dirac delta-potentials. The second quantisation is then performed to promote the relativistic quantum mechanical problem to a relativistic quantum field theory and study the quantum vacuum interaction energy for fermions confined between opaque plates. The work presented here is a continuation of [Guilarte et al 2019 Front. Phys. 7 109].

These lecture notes (arXiv:2307.08460) cover materials exposed by Luca Ciambelli at the 59 Winter School of Theoretical Physics and third COST Action CA18108 Training School “Gravity — Classical, Quantum and Phenomenology”, held in Palac Wojanów, Poland, 12-21 Feb 2023.
After introducing the covariant phase space calculus, Noether’s theorems are discussed, with particular emphasis on Noether’s second theorem and the role of gauge symmetries. This is followed by the enunciation of the theory of asymptotic symmetries, and later its application to gravity. Specifically, we review how the BMS group arises as the asymptotic symmetry group of gravity at null infinity. Symmetries are so powerful and constraining that memory effects and soft theorems can be derived from them. The lectures end with more recent developments in the field: the corner proposal as a unified paradigm for symmetries in gravity, the extended phase space as a resolution to the problem of charge integrability, and eventually the implications of the corner proposal on quantum gravity.

In the past decade, significant efforts have been devoted to the study of Relative Locality, which aims to generalize the kinematics of relativistic particles to a nonlocal framework by introducing a nontrivial geometry for momentum space. This paper (arXiv:2306.11451) builds upon a recent proposal to extend the theory to curved spacetimes and investigates the behavior of horizons in certain spacetimes with this nonlocality framework. Specifically, we examine whether nonlocality effects weaken or destroy the notion of horizon in these spacetimes. Our analysis indicates that, in the chosen models, the nonlocality effects do not disrupt the notion of horizon and that it remains as robust as it is in General Relativity.

Recent studies have demonstrated the possibility to uphold classical determinism within gravitational singularities, showcasing the ability to uniquely extend Einstein’s equations across the singularity in certain symmetry-reduced models. This extension can be achieved by allowing the orientation of spatial hypersurfaces to dynamically change. Furthermore, a crucial aspect of the analysis revolves around the formulation of the dynamical equations in terms of physical degrees of freedom, demonstrating their regularity at the singularity. Remarkably, singular behavior is found to be confined solely to the gauge/unphysical degrees of freedom. This paper (arXiv:2306.02941) extends these results to gravity coupled with Abelian and non-Abelian gauge fields in a symmetry-reduced model (homogeneous anisotropic universe). Near the Big Bang, the dynamics of the geometry and the gauge fields is reformulated in a way that shows that determinism is preserved, assuming a change in orientation at the singularity. The gauge fields are demonstrated to maintain their orientation throughout the singularity, indicating that the predicted orientation change of spatial hypersurfaces holds physical significance. This observation suggests that an observer can discern the specific side of the Big Bang they inhabit.

In this paper (arXiv:2304.08843), by using the theory of Lie-Hamilton systems, formal generalized stochastic Hamiltonian systems that enlarge a recently proposed stochastic SIS epidemic model with a variable infection rate are considered. It is shown that, independently on the particular interpretation of the time-dependent coefficients, these systems generally admit an exact solution, up to the case of the maximal extension within the classification of Lie-Hamilton systems, for which a superposition rule is constructed. The method provides the algebraic frame to which any SIS epidemic model that preserves the above mentioned properties is subjected. In particular, we obtain exact solutions for generalized SIS Hamitonian models based on the book and oscillator algebras, denoted respectively by 𝔟2 and 𝔥4. The last generalization corresponds to a SIS system possessing the so-called two-photon algebra symmetry 𝔥6, according to the embedding chain 𝔟2⊂𝔥4⊂𝔥6, for which an exact solution cannot generally be found, but a nonlinear superposition rule is explicitly given.

In this paper (arXiv:2303.08220), we will discuss the notion of curved momentum space, as it arises in the discussion of noncommutative or doubly special relativity theories. We will illustrate it with two simple examples, the Casimir effect in anti-Snyder space and the introduction of fermions in doubly special relativity. We will point out the existence of intriguing results, which suggest nontrivial connections with spectral geometry and Hopf algebras.

Doubly special relativity considers a deformation of the special relativistic kinematics parametrized by a high-energy scale, in such a way that it preserves a relativity principle. When this deformation is assumed to be applied to any interaction between particles, one faces some inconsistencies. In order to avoid them, in this paper we propose a new perspective where the deformation affects only the interactions between elementary particles. A consequence of this proposal is that the deformation cannot modify the special relativistic energy–momentum relation of a particle.

In the last few years, much attention has been paid to the exotic properties that graphene nanostructures exhibit, especially those emerging upon deforming the material. In this new paper we present a study of the mechanical and electronic properties of bent hexagonal graphene quantum dots employing density functional theory. We explore three different kinds of surfaces with Gaussian curvature exhibiting different shapes—spherical, cylindrical, and one-sheet hyperboloid—used to bend the material, and several boundary conditions regarding what atoms are forced to lay on the chosen surface. In each case, we study the curvature energy and two quantum regeneration times (classic and revival) for different values of the curvature radius. A strong correlation between Gaussian curvature and these regeneration times is found, and a special divergence is observed for the revival time for the hyperboloid case, probably related to the pseudo-magnetic field generated by this curvature being capable of causing a phase transition.