Perturbative exponential expansion and matter neutrino oscillations

Supanitsky, A. D.; D’Olivo, Juan Carlos; Medina‐Tanco, G.

doi:10.1103/physrevd.78.045024

Cited by 19 publications

(19 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Eq. (55) reproduces the formula given in [10]. If |I V | << 1, we find making expansion in powers of I V P ν2→νe = sin 2 θ + I V sin 2θ sin φ + I 2 V cos 2θ (56) which exactly coincides with our result in [3] (see eq.…”

Section: Oscillation Probabilitiessupporting

confidence: 77%

“…The approach is based on the Magnus expansion [12], [13] which was previously used for description of the nonadiabatic neutrino conversion in medium with monotonously varying density [14], [15] [16]. Recently the first order Magnus expansion has been applied to the low energy neutrino oscillations in matter of the Earth [10]. The formula for the regeneration factor in the Earth has been obtained which generalizes our result in [3].…”

Section: Introductionmentioning

confidence: 79%

“…Since the Magnus expansion is an expansion in power of commutators, it is the second order that provides non-trivial new results. As a part of the present study we reproduce the formula from [10].…”

Section: Introductionmentioning

confidence: 99%

“…Several analytic and semi-analytic approaches to computing probabilities in matter with non-constant density have been developed recently which use various perturbation theories [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]. In the previous publications [2], [3], we have proposed a formalism which describes the neutrino oscillations in matter with low density.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Describing neutrino oscillations in matter with Magnus expansion

Ioannisian

Smirnov

2009

Nuclear Physics B

View full text Add to dashboard Cite

We present new formalism for description of the neutrino oscillations in matter with varying density. The formalism is based on the Magnus expansion and has a virtue that the unitarity of the S-matrix is maintained in each order of perturbation theory. We show that the Magnus expansion provides better convergence of series: the restoration of unitarity leads to smaller deviations from the exact results especially in the regions of large transition probabilities. Various expansions are obtained depending on a basis of neutrino states and a way one splits the Hamiltonian into the self-commuting and non-commuting parts. In particular, we develop the Magnus expansion for the adiabatic perturbation theory which gives the best approximation. We apply the formalism to the neutrino oscillations in matter of the Earth and show that for the solar oscillation parameters the second order Magnus adiabatic expansion has better than 1% accuracy for all energies and trajectories. For the atmospheric ∆m 2 and small 1-3 mixing the approximation works well (< 3% accuracy for sin 2 θ13 = 0.01) outside the resonance region (2.7 -8) GeV.

show abstract

Section: Oscillation Probabilitiessupporting

confidence: 77%

Section: Introductionmentioning

confidence: 79%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Describing neutrino oscillations in matter with Magnus expansion

Ioannisian

Smirnov

2009

Nuclear Physics B

View full text Add to dashboard Cite

show abstract

“…Mathematically it is similar to the two level system studied in Section 3. The reader is referred to [67,68,69,222] for details of the calculations for two and three generations.…”

Section: Quantum Field Theory and High Energy Physicsmentioning

confidence: 99%

The Magnus expansion and some of its applications

Blanes¹,

Casas²,

Oteo³

et al. 2009

Physics Reports

1,091

1,300

View full text Add to dashboard Cite

Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in operator or matrix form, the Magnus expansion furnishes an elegant setting to built up approximate exponential representations of the solution of the system. It provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory. Every Magnus approximant corresponds in Perturbation Theory to a partial re-summation of infinite terms with the important additional property of preserving at any order certain symmetries of the exact solution.The goal of this review is threefold. First, to collect a number of developments scattered through half a century of scientific literature on Magnus expansion. They concern the methods for the generation of terms in the expansion, estimates of the radius of convergence of the series, generalizations and related non-perturbative expansions. Second, to provide a bridge with its implementation as generator of especial purpose numerical integration methods, a field of intense activity during the last decade. Third, to illustrate with examples the kind of results one can expect from Magnus expansion in comparison with those from both perturbative schemes and standard numerical integrators. We buttress this issue with a revision of the wide range of physical applications found by Magnus expansion in the literature.

show abstract

Extreme high energy proton-gamma discrimination from space observations

Supanitsky

Medina‐Tanco

2011

Astroparticle Physics

Self Cite

View full text Add to dashboard Cite

The origin of the highest energy cosmic rays is still unknown. At present, the major uncertainties are located at energies above ∼ 10 19.5 eV, the expected beginning of the GZK suppression. This is mainly due to the low statistics available, a problem that will be addressed in unprecedented way by the upcoming orbital detectors like JEM-EUSO. The detection of very high energy photons is of great relevance for the understanding of the origin of this extreme energy cosmic rays (EECR), due to the astrophysical information content. However, their discrimination is an experimental challenge for current and future cosmic ray detectors. In this work we study the statistical separation between hadron and photon showers from space observations at energies where both, the Landau-Pomeranchuk-Migdal (LPM) effect and magnetospheric interactions are important for the development of the cascades. We base our analysis on the X max parameter, which is already a well known composition discrimination parameter for ground based fluorescence observatories. Our analysis applies to orbiting detectors in general. Nevertheless, we exemplify the practical utilization of our technique by estimating a general upper limit to the photon fraction in the integral flux, attainable by an ideal orbital detector with characteristics similar to JEM-EUSO. In the process we describe the resultant asymmetry in the photon-hadron discrimination efficiency in galactic coordinates.

show abstract

Perturbative exponential expansion and matter neutrino oscillations

Cited by 19 publications

References 15 publications

Describing neutrino oscillations in matter with Magnus expansion

Describing neutrino oscillations in matter with Magnus expansion

The Magnus expansion and some of its applications

Extreme high energy proton-gamma discrimination from space observations

Contact Info

Product

Resources

About