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

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

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

Time-dependent Mechanics and Lagrangian submanifolds of Dirac manifolds

A description of time-dependent Mechanics in terms of Lagrangian submanifolds of Dirac manifolds (in particular, presymplectic and Poisson manifolds) is presented. Two new Tulczyjew triples are discussed. The first one is adapted to the restricted Hamiltonian formalism and the second one is adapted to the extended Hamiltonian formalism

Highly-efficient noise-assisted energy transport in classical oscillator systems

Photosynthesis is a biological process that involves the highly-efficient transport of energy captured from the sun to a reaction center, where conversion into useful biochemical energy takes place. Even though one can always use a quantum perspective to describe any physical process, since everything follows the laws of Quantum Mechanics, is the use of quantum theory imperative to explain this high efficiency? Making use of the quantum-classical correspondence of electronic energy transfer recently introduced by Eisfeld and Briggs [Phys. Rev. E 85, 046118 (2012)], we show here that the highly-efficient noise-assisted energy transport described by Rebentrost et al. [New J. Phys. 11, 033003 (2009)], and Plenio and Huelga [New J. Phys. 10, 113019 (2008)], as the result of the interplay between the quantum coherent evolution of the photosynthetic system and noise introduced by its surrounding environment, it can be found as well in purely classical systems. The wider scope of applicability of the enhancement of energy transfer assisted by noise might open new ways for developing new technologies aimed at enhancing the efficiency of a myriad of energy transfer systems, from information channels in micro-electronic circuits to long-distance high-voltage electrical lines.Comment: 4 pages, 3 figure

The Berry phase and the pump flux in stochastic chemical kinetics

We study a classical two-state stochastic system in a sea of substrates and products (absorbing states), which can be interpreted as a single Michaelis-Menten catalyzing enzyme or as a channel on a cell surface. We introduce a novel general method and use it to derive the expression for the full counting statistics of transitions among the absorbing states. For the evolution of the system under a periodic perturbation of the kinetic rates, the latter contains a term with a purely geometrical (the Berry phase) interpretation. This term gives rise to a pump current between the absorbing states, which is due entirely to the stochastic nature of the system. We calculate the first two cumulants of this current, and we argue that it is observable experimentally

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