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11 papers · 1 filter
Classical and relativistic fluids as intermediate integrals of finite dimensional mechanical systems
Ricardo J. Alonso-Blanco
We explore the relationship between mechanical systems describing the motion of a particle with the mechanical systems describing a continuous medium. More specifically, we will st…
Continuous-time random walks with reset events: Historical background and new perspectives
Miquel Montero, Axel Masó-Puigdellosas, Javier Villarroel
In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensio…
The geometry of real reducible polarizations in quantum mechanics
Carlos Tejero Prieto, Raffaele Vitolo
The formulation of Geometric Quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedu…
Miura-reciprocal transformations for non-isospectral Camassa-Holm hierarchies in dimensions
P. G. Estévez, C. Sardón
We present two hierarchies of partial differential equations in dimensions. Since there exist reciprocal transformations that connect these hierarchies to the Calogero-Bogoya…
On the geometry of the energy operator in quantum mechanics
Carlos Tejero Prieto, Raffaele Vitolo
We analyze the different ways to define the energy operator in geometric theories of quantum mechanics. In some formulations the operator contains the scalar curvature as a multipl…
On Lie systems and Kummer-Schwarz equations
J. de Lucas, C. Sardón
A Lie system is a system of first-order differential equations admitting a superposition rule, i.e., a map that expresses its general solution in terms of a generic family of parti…