Constraint algorithm for k-presymplectic Hamiltonian systems. Application to singular field theories

The k-symplectic formulation of field theories is especially simple, since only tangent and cotangent bundles are needed in its description. Its defining elements show a close relationship with those in the symplectic formulation of mechanics. It will be shown that this relationship also stands in the presymplectic case. In a natural way,one can mimick the presymplectic constraint algorithm to obtain a constraint algorithmthat can be applied to k-presymplectic field theory, and more particularly to the Lagrangian and Hamiltonian formulations offield theories defined by a singular Lagrangian, as well as to the unified Lagrangian-Hamiltonian formalism (Skinner--Rusk formalism) for k-presymplectic field theory. Two examples of application of the algorithm are also analyzed.

Classical solutions of the leading-logarithm approximation with non-trivial topology

Exact solutions of the classical equations corresponding to the leading-logarithm approximation are obtained. They are classified by an (integer) topological number.

Classical anisotropies in models of open inflation

In the simplest model of open inflation there are two inflaton fields decoupled from each other. One of them, the tunneling field, produces a first stage of inflation which prepares the ground for the nucleation of a highly symmetric bubble. The other, a free field, drives a second period of slow-roll inflation inside the bubble. However, the second field also evolves during the first stage of inflation, which to some extent breaks the needed symmetry. We show that this generates large supercurvature anisotropies which, together with the results of Tanaka and Sasaki, rule out this class of simple models (unless, of course, Omega0 is sufficiently close to 1). The problem does not arise in modified models where the second field does not evolve in the first stage of inflation.

A new efficient approach to the direct restricted active space self-consistent field method

An implicitly parallel method for integral-block driven restricted active space self-consistent field (RASSCF) algorithms is presented. The approach is based on a model space representation of the RAS active orbitals with an efficient expansion of the model subspaces. The applicability of the method is demonstrated with a RASSCF investigation of the first two excited states of indole

Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defind by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincare-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.

Generating functions for the numbers of Abelian extensions of a local field

The aim of this paper is to give an explicit formula for the num- bers of abelian extensions of a p-adic number field and to study the generating function of these numbers. More precisely, we give the number of abelian ex- tensions with given degree and ramification index, and the number of abelian extensions with given degree of any local field of characteristic zero. Moreover, we give a concrete expression of a generating function for these last numbers

Continuum Double Exchange Model

We present a continuum model for doped manganites which consist of two species of quantum spin-1 / 2 fermions interacting with classical spin fields. The phase structure at zero temperature turns out to be considerably rich: antiferromagnetic insulator, antiferromagnetic two band conducting, canted two band conducting, canted one band conducting, and ferromagnetic one band conducting phases are identified, all of them being stable against phase separation. There are also regions in the phase diagram where phase separation occurs

Influence of the driving mechanism on the response of systems with athermal dynamics: The example of the random-field Ising model

We investigate the influence of the driving mechanism on the hysteretic response of systems with athermal dynamics. In the framework of local mean-field theory at finite temperature (but neglecting thermally activated processes), we compare the rate-independent hysteresis loops obtained in the random field Ising model when controlling either the external magnetic field H or the extensive magnetization M. Two distinct behaviors are observed, depending on disorder strength. At large disorder, the H-driven and M-driven protocols yield identical hysteresis loops in the thermodynamic limit. At low disorder, when the H-driven magnetization curve is discontinuous (due to the presence of a macroscopic avalanche), the M-driven loop is reentrant while the induced field exhibits strong intermittent fluctuations and is only weakly self-averaging. The relevance of these results to the experimental observations in ferromagnetic materials, shape memory alloys, and other disordered systems is discussed.

Atomic parity nonconservation, neutron radii, and effective field theories of nuclei

Accurately calibrated effective field theories are used to compute atomic parity nonconserving (APNC) observables. Although accurately calibrated, these effective field theories predict a large spread in the neutron skin of heavy nuclei. Whereas the neutron skin is strongly correlated to numerous physical observables, in this contribution we focus on its impact on new physics through APNC observables. The addition of an isoscalar-isovector coupling constant to the effective Lagrangian generates a wide range of values for the neutron skin of heavy nuclei without compromising the success of the model in reproducing well-constrained nuclear observables. Earlier studies have suggested that the use of isotopic ratios of APNC observables may eliminate their sensitivity to atomic structure. This leaves nuclear structure uncertainties as the main impediment for identifying physics beyond the standard model. We establish that uncertainties in the neutron skin of heavy nuclei are at present too large to measure isotopic ratios to better than the 0.1% accuracy required to test the standard model. However, we argue that such uncertainties will be significantly reduced by the upcoming measurement of the neutron radius in 208^Pb at the Jefferson Laboratory.

Particle in an electromagnetic field: The Lorentz-Dirac equation

A new method to solve the Lorentz-Dirac equation in the presence of an external electromagnetic field is presented. The validity of the approximation is discussed, and the method is applied to a particle in the presence of a constant magnetic field.