Classical and Quantum Physics: 60 Years Alberto Ibort Fest Geometry, Dynamics, and Control

Description

This proceedings is based on the interdisciplinary workshop held in Madrid, 5-9 March 2018, dedicated to Alberto Ibort on his 60th birthday. Alberto has great and significantly contributed to many fields of mathematics and physics, always with highly original and innovative ideas.Most of Albertos’s scientific activity has been motivated by geometric ideas, concepts and tools that are deeply related to the framework of classical dynamics and quantum mechanics.Let us mention some of the fields of expertise of Alberto Ibort:Geometric Mechanics; Constrained Systems; Variational Principles; Multisymplectic structures for field theories; Super manifolds; Inverse problem for Bosonic and Fermionic systems; Quantum Groups, Integrable systems, BRST Symmetries; Implicit differential equations; Yang-Mills Theories; BiHamiltonian Systems; Topology Change and Quantum Boundary Conditions; Classical and Quantum Control; Orthogonal Polynomials; Quantum Field Theory and Noncommutative Spaces; Classical and Quantum Tomography; Quantum Mechanics on phase space; Wigner-Weyl formalism; Lie-Jordan Algebras, Classical and Quantum; Quantum-to-Classical transition; Contraction of Associative Algebras; contact geometry, among many others.In each contribution, one may find not only technical novelties but also completely new way of looking at the considered problems. Even an experienced reader, reading Alberto's contributions on his field of expertise, will find new perspectives on the considered topic.His enthusiasm is happily contagious, for this reason he has had, and still has, very bright students wishing to elaborate their PhD thesis under his guidance.What is more impressive, is the broad list of rather different topics on which he has contributed. Front Matter ....Pages i-xxvi On a New Asymptotic Behaviour of Toeplitz Determinants (Filiberto Ares, José G. Esteve, Fernando Falceto)....Pages 1-16 Bulk-Edge Dualities in Topological Matter (Manuel Asorey)....Pages 17-28 Near-Horizon Modes and Self-adjoint Extensions of the Schrödinger Operator (A. P. Balachandran, A. R. de Queiroz, Alberto Saa)....Pages 29-39 The Gauss Law: A Tale (A. P. Balachandran, A. F. Reyes-Lega)....Pages 41-55 Quantum Control at the Boundary (A. Balmaseda, J. M. Pérez-Pardo)....Pages 57-84 Application of Lie Systems to Quantum Mechanics: Superposition Rules (José F. Cariñena, Jesús Clemente-Gallardo, Jorge A. Jover-Galtier, Javier de Lucas)....Pages 85-119 Killing Vector Fields and Quantisation of Natural Hamiltonians (José F. Cariñena, Manuel F. Rañada, Mariano Santander)....Pages 121-145 Conditions for Legitimate Memory Kernel Master Equation (Dariusz Chruściński)....Pages 147-162 From Classical Trajectories to Quantum Commutation Relations (F. M. Ciaglia, G. Marmo, L. Schiavone)....Pages 163-185 On the Thermodynamics of Supersymmetric Haldane–Shastry Spin Chains (F. Finkel, A. González-López, I. León, M. A. Rodríguez)....Pages 187-201 Towards a Quantum Sampling Theory: The Case of Finite Groups (Antonio G. García, Miguel A. Hernández-Medina, Alberto Ibort)....Pages 203-223 On the Kinematics of the Last Wigner Particle (José M. Gracia-Bondía, Joseph C. Várilly)....Pages 225-242 Dimensional Deception for the Noncommutative Torus (Fedele Lizzi, Alexandr Pinzul)....Pages 243-257 Notions of Infinity in Quantum Physics (Fernando Lledó, Diego Martínez)....Pages 259-273 Poisson-Nijenhuis Manifolds, Classical Yang-Baxter Equations, and Frobenius Algebras (F. Magri, T. Marsico)....Pages 275-287 Hermite Polynomial Representation of Qubit States in Quantum Suprematism Picture (Margarita A. Man’ko, Vladimir I. Man’ko)....Pages 289-303 On Sympletic Lifts of Actions for Complete Lagrangian Fibrations (Juan Carlos Marrero, Edith Padrón)....Pages 305-324 Some Properties of Multisymplectic Manifolds (Narciso Román-Roy)....Pages 325-336 A Simple Model of Double Dynamics on Lie Groups (Patrizia Vitale)....Pages 337-359 Loops of Legendrians in Contact 3-Manifolds (Eduardo Fernández, Javier Martínez-Aguinaga, Francisco Presas)....Pages 361-372 Back Matter ....Pages 373-374