75 research outputs found
Hamiltonian Multivector Fields and Poisson Forms in Multisymplectic Field Theory
We present a general classification of Hamiltonian multivector fields and of
Poisson forms on the extended multiphase space appearing in the geometric
formulation of first order classical field theories. This is a prerequisite for
computing explicit expressions for the Poisson bracket between two Poisson
forms.Comment: 50 page
Singular factorizations, self-adjoint extensions, and applications to quantum many-body physics
We study self-adjoint operators defined by factorizing second order
differential operators in first order ones. We discuss examples where such
factorizations introduce singular interactions into simple quantum mechanical
models like the harmonic oscillator or the free particle on the circle. The
generalization of these examples to the many-body case yields quantum models of
distinguishable and interacting particles in one dimensions which can be solved
explicitly and by simple means. Our considerations lead us to a simple method
to construct exactly solvable quantum many-body systems of Calogero-Sutherland
type.Comment: 17 pages, LaTe
Strukturelles Design auf der Nanometerskala
For numerous technical applications, condensed materials must be specifically produced and manipulated on the nanometre scale. This frequently means the creation of an order with characteristic lengths in the range of extension of single atoms. Besides the possibility of constructing a solid "atom by atom" with suitable procedures, specific local transformations driven by energy input can also produce modified structures which display new and technically utilisable properties.Für zahlreiche technische Anwendungen müssen kondensierte Materialien auf der Nanometerskala gezielt hergestellt und manipuliert werden. Dies bedeutet häufig die Schaffung einer Ordnung mit charakteristischen Längen in der Größenordnung der Ausdehnung einzelner Atome. Neben der Möglichkeit, den Festkörper „Atom für Atom“ mit geeigneten Verfahren aufzubauen, können auch gezielte lokale Umwandlungen durch Energieeintrag modifizierte Strukturen, welche neuartige und technisch nutzbare Eigenschaften aufweisen, hervorbringen
Lagrangian-Hamiltonian unified formalism for field theory
The Rusk-Skinner formalism was developed in order to give a geometrical
unified formalism for describing mechanical systems. It incorporates all the
characteristics of Lagrangian and Hamiltonian descriptions of these systems
(including dynamical equations and solutions, constraints, Legendre map,
evolution operators, equivalence, etc.).
In this work we extend this unified framework to first-order classical field
theories, and show how this description comprises the main features of the
Lagrangian and Hamiltonian formalisms, both for the regular and singular cases.
This formulation is a first step toward further applications in optimal control
theory for PDE's.Comment: LaTeX file, 23 pages. Minor changes have been made. References are
update
Temperature and pressure evolution of the crystal structure of Ax(Fe1-ySe)2 (A = Cs, Rb, K) studied by synchrotron powder diffraction
Temperature-dependent synchrotron powder diffraction on Cs0.83(Fe0.86Se)2
revealed first order I4/m to I4/mmm structural transformation around 216{\deg}C
associated with the disorder of the Fe vacancies. Irreversibility observed
during the transition is likely associated with a mobility of intercalated
Alkali atoms. Pressure-dependent synchrotron powder diffraction on
Cs0.83(Fe1-ySe)2, Rb0.85(Fe1-ySe)2 and K0.8(Fe1-ySe)2 (y ~ 0.14) indicated that
the I4/m superstructure reflections are present up to pressures of 120 kbar.
This may indicate that the ordering of the Fe vacancies is present in both
superconducting and non-superconductive states.Comment: 11 pages, 5 figures, 1 tabl
On the k-Symplectic, k-Cosymplectic and Multisymplectic Formalisms of Classical Field Theories
The objective of this work is twofold: First, we analyze the relation between
the k-cosymplectic and the k-symplectic Hamiltonian and Lagrangian formalisms
in classical field theories. In particular, we prove the equivalence between
k-symplectic field theories and the so-called autonomous k-cosymplectic field
theories, extending in this way the description of the symplectic formalism of
autonomous systems as a particular case of the cosymplectic formalism in
non-autonomous mechanics. Furthermore, we clarify some aspects of the geometric
character of the solutions to the Hamilton-de Donder-Weyl and the
Euler-Lagrange equations in these formalisms. Second, we study the equivalence
between k-cosymplectic and a particular kind of multisymplectic Hamiltonian and
Lagrangian field theories (those where the configuration bundle of the theory
is trivial).Comment: 25 page
Invariant Forms and Automorphisms of Locally Homogeneous Multisymplectic Manifolds
It is shown that the geometry of locally homogeneous multisymplectic
manifolds (that is, smooth manifolds equipped with a closed nondegenerate form
of degree > 1, which is locally homogeneous of degree k with respect to a local
Euler field) is characterized by their automorphisms. Thus, locally homogeneous
multisymplectic manifolds extend the family of classical geometries possessing
a similar property: symplectic, volume and contact. The proof of the first
result relies on the characterization of invariant differential forms with
respect to the graded Lie algebra of infinitesimal automorphisms, and on the
study of the local properties of Hamiltonian vector fields on locally
multisymplectic manifolds. In particular it is proved that the group of
multisymplectic diffeomorphisms acts (strongly locally) transitively on the
manifold. It is also shown that the graded Lie algebra of infinitesimal
automorphisms of a locally homogeneous multisymplectic manifold characterizes
their multisymplectic diffeomorphisms.Comment: 25 p.; LaTeX file. The paper has been partially rewritten. Some
terminology has been changed. The proof of some theorems and lemmas have been
revised. The title and the abstract are slightly modified. An appendix is
added. The bibliography is update
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