4,831 research outputs found
Discrete approximations for strict convex continuous time problems and duality
We propose a discrete approximation scheme to a class of Linear Quadratic Continuous Time Problems. It is shown, under positiveness of the matrix in the integral cost, that optimal solutions of the discrete problems provide a sequence of bounded variation functions which converges almost everywhere to the unique optimal solution. Furthermore, the method of discretization allows us to derive a number of interesting results based on finite dimensional optimization theory, namely, Karush-Kuhn-Tucker conditions of optimality and weak and strong duality. A number of examples are provided to illustrate the theory.8110
Phase diagram of a random-anisotropy mixed-spin Ising model
We investigate the phase diagram of a mixed spin-1/2--spin-1 Ising system in
the presence of quenched disordered anisotropy. We carry out a mean-field and a
standard self-consistent Bethe--Peierls calculation. Depending on the amount of
disorder, there appear novel transition lines and multicritical points. Also,
we report some connections with a percolation problem and an exact result in
one dimension.Comment: 8 pages, 4 figures, accepted for publication in Physical Review
Ab-initio study of the relation between electric polarization and electric field gradients in ferroelectrics
The hyperfine interaction between the quadrupole moment of atomic nuclei and
the electric field gradient (EFG) provides information on the electronic charge
distribution close to a given atomic site. In ferroelectric materials, the loss
of inversion symmetry of the electronic charge distribution is necessary for
the appearance of the electric polarization. We present first-principles
density functional theory calculations of ferroelectrics such as BaTiO3, KNbO3,
PbTiO3 and other oxides with perovskite structures, by focusing on both EFG
tensors and polarization. We analyze the EFG tensor properties such as
orientation and correlation between components and their link with electric
polarization. This work supports previous studies of ferroelectric materials
where a relation between EFG tensors and polarization was observed, which may
be exploited to study ferroelectric order when standard techniques to measure
polarization are not easily applied.Comment: 9 pages, 6 figures, 5 tables, corrected typos, as published in Phys.
Rev.
On the exact Foldy-Wouthuysen transformation for a Dirac spinor in torsion and other CPT and Lorentz violating backgrounds
We discuss the possibility to perform and use the exact Foldy-Wouthuysen
transformation (EFWT) for the Dirac spinor coupled to different CPT and Lorentz
violating terms. The classification of such terms is performed, selecting those
of them which admit EFWT. For the particular example of an axial vector field,
which can be associated with the completely antisymmetric torsion, we construct
an explicit EFWT in the case when only a timelike component of this axial
vector is present. In the cases when EFWT is not possible, one can still use
the corresponding technique for deriving the perturbative Foldy-Wouthuysen
transformation, as is illustrated in a particular example in the Appendix
Vector Meson Production in Ultraperipheral Heavy Ion Collisions
The ultraperipheral heavy ion collisions (UPC's) are an important alternative
to study the QCD dynamics until the next generation of
colliders become reality. Due to the coherent action of all the protons in the
nucleus, the electromagnetic field is very strong and the resulting flux of
equivalent photons is large, which allows to study two-photon as well as
photonuclear interactions at high energies. In this paper we present a brief
review of the vector meson production in UPC's at high energies using the QCD
color dipole approach to describe their photonuclear production and the
perturbative QCD Pomeron (BFKL dynamics) to describe the double meson
production in photon-photon process. Predictions for rates and integrated cross
sections are presented for energies of RHIC and LHC.Comment: 16 pages, 1 figure. Version to be published in Journal of Physics G:
Nuclear and Particle Physic
Exact Foldy-Wouthuysen transformation for gravitational waves and magnetic field background
We consider an exact Foldy-Wouthuysen transformation for the Dirac spinor
field on the combined background of a gravitational wave and constant uniform
magnetic field. By taking the classical limit of the spinor field Hamiltonian
we arrive at the equations of motion for the non-relativistic spinning
particle. Two different kinds of the gravitational fields are considered and in
both cases the effect of the gravitational wave on the spinor field and on the
corresponding spinning particle may be enforced by the sufficiently strong
magnetic field. This result can be relevant for the astrophysical applications
and, in principle, useful for creating the gravitational wave detectors based
on atomic physics and precise interferometry
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