3,804 research outputs found
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
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
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
Coherent delocalization: Views of entanglement in different scenarios
The concept of entanglement was originally introduced to explain correlations
existing between two spatially separated systems, that cannot be described
using classical ideas. Interestingly, in recent years, it has been shown that
similar correlations can be observed when considering different degrees of
freedom of a single system, even a classical one. Surprisingly, it has also
been suggested that entanglement might be playing a relevant role in certain
biological processes, such as the functioning of pigment-proteins that
constitute light-harvesting complexes of photosynthetic bacteria. The aim of
this work is to show that the presence of entanglement in all of these
different scenarios should not be unexpected, once it is realized that the very
same mathematical structure can describe all of them. We show this by
considering three different, realistic cases in which the only condition for
entanglement to exist is that a single excitation is coherently delocalized
between the different subsystems that compose the system of interest
Nonholonomic constraints in -symplectic Classical Field Theories
A -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
On the Hamilton-Jacobi Theory for Singular Lagrangian Systems
We develop a Hamilton-Jacobi theory for singular lagrangian systems using the
Gotay-Nester-Hinds constraint algorithm. The procedure works even if the system
has secondary constraints.Comment: 36 page
Higher-order Mechanics: Variational Principles and other topics
After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the
Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we
state a unified geometrical version of the Variational Principles which allows
us to derive the Lagrangian and Hamiltonian equations for these kinds of
systems. Then, the standard Lagrangian and Hamiltonian formulations of these
principles and the corresponding dynamical equations are recovered from this
unified framework.Comment: New version of the paper "Variational principles for higher-order
dynamical systems", which was presented in the "III Iberoamerican Meeting on
Geometry, Mechanics and Control" (Salamanca, 2012). The title is changed. A
detailed review is added. Sections containing results about variational
principles are enlarged with additional comments, diagrams and summarizing
results. Bibliography is update
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