1,474 research outputs found
Corrections to the energy levels of a spin-zero particle bound in a strong field
Formulas for the corrections to the energy levels and wave functions of a
spin-zero particle bound in a strong field are derived. General case of the sum
of a Lorentz-scalar potential and zero component of a Lorentz-vector potential
is considered. The forms of the corrections differ essentially from those for
spin-1/2 particles. As an example of application of our results, we evaluated
the electric polarizability of a ground state of a spin-zero particle bound in
a strong Coulomb field.Comment: 7 pages, 1 figur
Quasiclassical Green function in an external field and small-angle scattering
The quasiclassical Green functions of the Dirac and Klein-Gordon equations in
the external electric field are obtained with the first correction taken into
account. The relevant potential is assumed to be localized, while its spherical
symmetry is not required. Using these Green functions, the corresponding wave
functions are found in the approximation similar to the Furry-Sommerfeld-Maue
approximation. It is shown that the quasiclassical Green function does not
coincide with the Green function obtained in the eikonal approximation and has
a wider region of applicability. It is illustrated by the calculation of the
small-angle scattering amplitude for a charged particle and the forward photon
scattering amplitude. For charged particles, the first correction to the
scattering amplitude in the non-spherically symmetric potential is found. This
correction is proportional to the scattering angle. The real part of the
amplitude of forward photon scattering in a screened Coulomb potential is
obtained.Comment: 20 pages, latex, 1 figur
Charge asymmetry in high-energy photoproduction in the electric field of a heavy atom
The charge asymmetry in the differential cross section of high-energy
photoproduction in the electric field of a heavy atom is obtained.
This asymmetry arises due to the Coulomb corrections to the amplitude of the
process (next-to-leading term with respect to the atomic field). The deviation
of the nuclear electric field from the Coulomb field at small distances is
crucially important for the charge asymmetry. Though the Coulomb corrections to
the total cross section are negligibly small, the charge asymmetry is
measurable for selected final states of and . We further discuss
the feasibility for experimental observation of this effect.Comment: 6 pages, 3 figure
Mean-square approximation of Navier-Stokes equations with additive noise in vorticity-velocity formulation
We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions and additive noise in the vorticity-velocity formulation. The approximation is based on freezing the velocity on time subintervals resulting in a linear stochastic parabolic equation for vorticity. At each time step, the velocity is expressed via vorticity using a formula corresponding to the Biot-Savart-type law. We prove the first mean-square convergence order of the vorticity approximation
Probabilistic methods for the incompressible navier-stokes equations with space periodic conditions
We propose and study a number of layer methods for Navier-Stokes equations (NSEs) with spatial periodic boundary conditions. The methods are constructed using probabilistic representations of solutions to NSEs and exploiting ideas of the weak sense numerical integration of stochastic differential equations. Despite their probabilistic nature, the layer methods are nevertheless deterministic. © ?Applied Probability Trust 2013
Numerical construction of a hedging strategy against the European claim
For evaluating a hedging strategy we have to know at every instant the solution of the Cauchy problem for a parabolic equation (the value of the hedging portfolio) and its derivatives (the deltas). We suggest to find these magnitudes by Monte Carlo simulation of the corresponding system of stochastic differential equations using weak solution schemes. It turns out that with one and the same control function a variance reduction can be achieved simultaneously for the claim value as well as for the deltas. We consider asset models with an instantaneous saving bond and the Jamshidian LIBOR rate model
Uniform approximation of the CIR process via exact simulation at random times
In this paper we uniformly approximate the trajectories of the Cox-Ingersoll-Ross (CIR) process. At a sequence of random times the approximate trajectories will be even exact. In between, the approximation will be uniformly close to the exact trajectory. From a conceptual point of view the proposed method gives a better quality of approximation in a path-wise sense than standard, or even exact simulation of the CIR dynamics at some deterministic time grid
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