Unified formalism for higher-order non-autonomous dynamical systems

This work is devoted to giving a geometric framework for describing higher-order non-autonomous mechanical systems. The starting point is to extend the Lagrangian-Hamiltonian unified formalism of Skinner and Rusk for these kinds of systems, generalizing previous developments for higher-order autonomous mechanical systems and first-order non-autonomous mechanical systems. Then, we use this unified formulation to derive the standard Lagrangian and Hamiltonian formalisms, including the Legendre-Ostrogradsky map and the Euler-Lagrange and the Hamilton equations, both for regular and singular systems. As applications of our model, two examples of regular and singular physical systems are studied.Comment: 43 pp. We have corrected and clarified the statement of Propositions 2 and 3. A remark is added after Proposition

Geometric aspects of nonholonomic field theories

A geometric model for nonholonomic Lagrangian field theory is studied. The multisymplectic approach to such a theory as well as the corresponding Cauchy formalism are discussed. It is shown that in both formulations, the relevant equations for the constrained system can be recovered by a suitable projection of the equations for the underlying free (i.e. unconstrained) Lagrangian system.Comment: 29 pages; typos remove

Spectral analysis of Markarian 421 and Markarian 501 with HAWC

The Hight Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory monitors the gamma-ray sky in the energy range from 100 GeV to 100 TeV and has detected two very high energy (VHE) blazars: Markarian 421 (Mrk 421) and Markarian 501 (Mrk 501) in 1.5 years of observations. In this work, we present the spectral analysis above 1 TeV of both sources using a maximum likelihood method and an artificial neural network as an energy estimator. The main objectives are to constrain the spectral curvature of Mrk 421 and Mrk 501 at $\sim$5 TeV using the EBL models from Gilmore et al. (2012) and Franceschini et al. (2008).Comment: Presented at the 35th International Cosmic Ray Conference (ICRC2017), Bexco, Busan, Korea. See arXiv:1708.02572 for all HAWC contribution

Hamilton-Jacobi Theory in k-Symplectic Field Theories

In this paper we extend the geometric formalism of Hamilton-Jacobi theory for Mechanics to the case of classical field theories in the k-symplectic framework

Sequential Quantum Cloning

Not all unitary operations upon a set of qubits can be implemented by sequential interactions between each qubit and an ancillary system. We analyze the specific case of sequential quantum cloning 1->M and prove that the minimal dimension D of the ancilla grows linearly with the number of clones M. In particular, we obtain D = 2M for symmetric universal quantum cloning and D = M+1 for symmetric phase-covariant cloning. Furthermore, we provide a recipe for the required ancilla-qubit interactions in each step of the sequential procedure for both cases.Comment: 4 pages, no figures. New version with changes. Accepted in Physical Review Letter

Population bound effects on bosonic correlations in non-inertial frames

We analyse the effect of bounding the occupation number of bosonic field modes on the correlations among all the different spatial-temporal regions in a setting in which we have a space-time with a horizon along with an inertial observer. We show that the entanglement between A (inertial observer) and R (uniformly accelerated observer) depends on the bound N, contrary to the fermionic case. Whether or not decoherence increases with N depends on the value of the acceleration a. Concerning the bipartition A-antiR (Alice with an observer in Rindler's region IV), we show that no entanglement is created whatever the value of N and a. Furthermore, AR entanglement is very quickly lost for finite N and for infinite N. We will study in detail the mutual information conservation law found for bosons and fermions. By means of the boundary effects associated to N finiteness, we will show that for bosons this law stems from classical correlations while for fermions it has a quantum origin. Finally, we will present the strong N dependence of the entanglement in R-antiR bipartition and compare the fermionic cases with their finite N bosonic analogs. We will also show the anti-intuitive dependence of this entanglement on statistics since more entanglement is created for bosons than for their fermion counterparts.Comment: revtex 4, 12 pages, 10 figures. Added Journal ref

Unified formalism for the generalized kth-order Hamilton-Jacobi problem

The geometric formulation of the Hamilton-Jacobi theory enables us to generalize it to systems of higher-order ordinary differential equations. In this work we introduce the unified Lagrangian-Hamiltonian formalism for the geometric Hamilton-Jacobi theory on higher-order autonomous dynamical systems described by regular Lagrangian functions.Comment: 9pp. Revised version: Minor corrections done. Second part of our previous work arXiv:1309.2166. arXiv admin note: substantial text overlap with arXiv:1309.216

Nonholonomic constraints in kk-symplectic Classical Field Theories

A $k$-symplectic framework for classical field theories subject to nonholonomic constraints is presented. If the constrained problem is regular one can construct a projection operator such that the solutions of the constrained problem are obtained by projecting the solutions of the free problem. Symmetries for the nonholonomic system are introduced and we show that for every such symmetry, there exist a nonholonomic momentum equation. The proposed formalism permits to introduce in a simple way many tools of nonholonomic mechanics to nonholonomic field theories.Comment: 27 page