554 research outputs found
Wave packet evolution in non-Hermitian quantum systems
The quantum evolution of the Wigner function for Gaussian wave packets
generated by a non-Hermitian Hamiltonian is investigated. In the semiclassical
limit this yields the non-Hermitian analog of the Ehrenfest
theorem for the dynamics of observable expectation values. The lack of
Hermiticity reveals the importance of the complex structure on the classical
phase space: The resulting equations of motion are coupled to an equation of
motion for the phase space metric---a phenomenon having no analog in Hermitian
theories.Comment: Example added, references updated, 4 pages, 2 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
Contact complete integrability
Complete integrability in a symplectic setting means the existence of a
Lagrangian foliation leaf-wise preserved by the dynamics. In the paper we
describe complete integrability in a contact set-up as a more subtle structure:
a flag of two foliations, Legendrian and co-Legendrian, and a
holonomy-invariant transverse measure of the former in the latter. This turns
out to be equivalent to the existence of a canonical
structure on the leaves of the co-Legendrian foliation. Further, the above
structure implies the existence of contact fields preserving a special
contact 1-form, thus providing the geometric framework and establishing
equivalence with previously known definitions of contact integrability. We also
show that contact completely integrable systems are solvable in quadratures. We
present an example of contact complete integrability: the billiard system
inside an ellipsoid in pseudo-Euclidean space, restricted to the space of
oriented null geodesics. We describe a surprising acceleration mechanism for
closed light-like billiard trajectories
Involutive orbits of non-Noether symmetry groups
We consider set of functions on Poisson manifold related by continues
one-parameter group of transformations. Class of vector fields that produce
involutive families of functions is investigated and relationship between these
vector fields and non-Noether symmetries of Hamiltonian dynamical systems is
outlined. Theory is illustrated with sample models: modified Boussinesq system
and Broer-Kaup system.Comment: LaTeX 2e, 10 pages, no figure
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Structural Analysis of Human Respiratory Syncytial Virus P Protein: Identification of Intrinsically Disordered Domains
Human Respiratory Syncytial Virus P protein plus the viral RNA, N and L viral proteins, constitute the viral replication complex. In this report we describe that HRSV P protein has putative intrinsically disordered domains predicted by in silico methods. These two domains, located at the amino and caboxi terminus, were identified by mass spectrometry analysis of peptides obtained from degradation fragments observed in purified P protein expressed in bacteria. The degradation is not occurring at the central oligomerization domain, since we also demonstrate that the purified fragments are able to oligomerize, similarly to the protein expressed in cells infected by HRSV. Disordered domains can play a role in protein interaction, and the present data contribute to the comprehension of HRSV P protein interactions in the viral replication complex
Bi-presymplectic chains of co-rank one and related Liouville integrable systems
Bi-presymplectic chains of one-forms of co-rank one are considered. The
conditions in which such chains represent some Liouville integrable systems and
the conditions in which there exist related bi-Hamiltonian chains of vector
fields are derived. To present the construction of bi-presymplectic chains, the
notion of dual Poisson-presymplectic pair is used and the concept of
d-compatibility of Poisson bivectors and d-compatibility of presymplectic forms
is introduced. It is shown that bi-presymplectic representation of related flow
leads directly to the construction of separation coordinates in purely
algorithmic way. As an illustration bi-presymplectic and bi-Hamiltonian chains
in are considered in detail
On the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models
We consider two families of commuting Hamiltonians on the cotangent bundle of
the group GL(n,C), and show that upon an appropriate single symplectic
reduction they descend to the spectral invariants of the hyperbolic Sutherland
and of the rational Ruijsenaars-Schneider Lax matrices, respectively. The
duality symplectomorphism between these two integrable models, that was
constructed by Ruijsenaars using direct methods, can be then interpreted
geometrically simply as a gauge transformation connecting two cross sections of
the orbits of the reduction group.Comment: 16 pages, v2: comments and references added at the end of the tex
On the notion of phase in mechanics
The notion of phase plays an esential role in both classical and quantum
mechanics.But what is a phase? We show that if we define the notion of phase in
phase (!) space one can very easily and naturally recover the Heisenberg-Weyl
formalism; this is achieved using the properties of the Poincare-Cartan
invariant, and without making any quantum assumption
A spinor approach to Walker geometry
A four-dimensional Walker geometry is a four-dimensional manifold M with a
neutral metric g and a parallel distribution of totally null two-planes. This
distribution has a natural characterization as a projective spinor field
subject to a certain constraint. Spinors therefore provide a natural tool for
studying Walker geometry, which we exploit to draw together several themes in
recent explicit studies of Walker geometry and in other work of Dunajski (2002)
and Plebanski (1975) in which Walker geometry is implicit. In addition to
studying local Walker geometry, we address a global question raised by the use
of spinors.Comment: 41 pages. Typos which persisted into published version corrected,
notably at (2.15
On the integrability of stationary and restricted flows of the KdV hierarchy.
A bi--Hamiltonian formulation for stationary flows of the KdV hierarchy is
derived in an extended phase space. A map between stationary flows and
restricted flows is constructed: in a case it connects an integrable
Henon--Heiles system and the Garnier system. Moreover a new integrability
scheme for Hamiltonian systems is proposed, holding in the standard phase
space.Comment: 25 pages, AMS-LATEX 2.09, no figures, to be published in J. Phys. A:
Math. Gen.
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