Parametric Resonance by the Matter Effect SATO, Joe (Saitama) Koike, Masafumi (Saitama) Ota, Toshihiko (Würzburg) Saito, Masako (Saitama) with Plan Introduction.

Slides:

Advertisements

Similar presentations

N.B. the material derivative, rate of change following the motion:

Advertisements

The Asymptotic Ray Theory

Gradient expansion approach to multi-field inflation Dept. of Physics, Waseda University Yuichi Takamizu 29 th JGRG21 Collaborators: S.Mukohyama.

Accretion in Binaries Two paths for accretion –Roche-lobe overflow –Wind-fed accretion Classes of X-ray binaries –Low-mass (BH and NS) –High-mass (BH and.

1 Parametric Sensitivity Analysis For Cancer Survival Models Using Large- Sample Normal Approximations To The Bayesian Posterior Distribution Gordon B.

Non-equilibrium dynamics in the Dicke model Izabella Lovas Supervisor: Balázs Dóra Budapest University of Technology and Economics

Lecture 2: Observational constraints on dark energy Shinji Tsujikawa (Tokyo University of Science)

CP-phase dependence of neutrino oscillation probability in matter 梅 (ume) 田 (da) 義 (yoshi) 章 (aki) with Lin Guey-Lin ( 林貴林 ) National Chiao-Tung University.

1 Shu-Hua Yang ( 杨书华 ) Hua Zhong Normal University The role of r-mode damping in the thermal evoltion of neutron stars.

Neutrino Oscillations Or how we know most of what we know.

DAMPING THE FLAVOR PENDULUM BY BREAKING HOMOGENEITY (Alessandro MIRIZZI, Hamburg U.) NOW 2014 Neutrino oscillation workshop Conca Specchiulla, September.

Carrier Wave Rabi Flopping (CWRF) Presentation by Nathan Hart Conditions for CWRF: 1.There must exist a one photon resonance with the ground state 2.The.

College and Engineering Physics Quiz 9: Simple Harmonic Motion 1 Simple Harmonic Motion.

Non-Gaussianities of Single Field Inflation with Non-minimal Coupling Taotao Qiu Based on paper: arXiv: [Hep-th] (collaborated with.

TeVPA 2012 TIFR Mumbai, India Dec 10-14, 2012 Walter Winter Universität Würzburg Neutrino physics with IceCube DeepCore-PINGU … and comparison with alternatives.

Probing the Octant of  23 with very long baseline neutrino oscillation experiments G.-L. Lin National Chiao-Tung U. Taiwan CYCU Oct Work done.

Layers of the Earth.

Black hole production in preheating Teruaki Suyama (Kyoto University) Takahiro Tanaka (Kyoto University) Bruce Bassett (ICG, University of Portsmouth)

Probing the Reheating with Astrophysical Observations Jérôme Martin Institut d’Astrophysique de Paris (IAP) 1 [In collaboration with K. Jedamzik & M. Lemoine,

Dark energy I : Observational constraints Shinji Tsujikawa (Tokyo University of Science)

1 The Earth’s Shells Quantitative Concepts and Skills Weighted average The nature of a constraint Volume of spherical shells Concept that an integral is.

A. Krawiecki , A. Sukiennicki

Today’s class Spline Interpolation Quadratic Spline Cubic Spline Fourier Approximation Numerical Methods Lecture 21 Prof. Jinbo Bi CSE, UConn 1.

The Earth Matter Effect in the T2KK Experiment Ken-ichi Senda Grad. Univ. for Adv. Studies.

Physics with a very long neutrino factory baseline IDS Meeting CERN March 30, 2007 Walter Winter Universität Würzburg.

A New Analytic Model for the Production of X-ray Time Lags in Radio Loud AGN and X-Ray Binaries John J. Kroon Peter A. Becker George Mason University MARLAM.

K. Ohnishi (TIT) K. Tsumura (Kyoto Univ.) T. Kunihiro (YITP, Kyoto) Derivation of Relativistic Dissipative Hydrodynamic equations by means of the Renormalization.

Two problems with gas discharges 1.Anomalous skin depth in ICPs 2.Electron diffusion across magnetic fields Problem 1: Density does not peak near the.

Pavel Stránský Complexity and multidiscipline: new approaches to health 18 April 2012 I NTERPLAY BETWEEN REGULARITY AND CHAOS IN SIMPLE PHYSICAL SYSTEMS.

CP violation in the neutrino sector Lecture 3: Matter effects in neutrino oscillations, extrinsic CP violation Walter Winter Nikhef, Amsterdam,

Annual and semi-annual variations of equatorial Atlantic circulation associated with basin mode resonance Peter Brandt 1, Martin Claus 1, Richard J. Greatbatch.

Gravimetry Geodesy Rotation

Effect of nonlinearity on Head-Tail instability 3/18/04.

K S Cheng Department of Physics University of Hong Kong Collaborators: W.M. Suen (Wash. U) Lap-Ming Lin (CUHK) T.Harko & R. Tian (HKU)

Optimization of a neutrino factory for non-standard neutrino interactions IDS plenary meeting RAL, United Kingdom January 16-17, 2008 Walter Winter Universität.

The relationship between the properties of matter and the structure of the Earth. -mass, volume, density, Earth’s interior, atmosphere.

Three theoretical issues in physical cosmology I. Nonlinear clustering II. Dark matter III. Dark energy J. Hwang (KNU), H. Noh (KASI)

Math 445: Applied PDEs: models, problems, methods D. Gurarie.

Differential Equations Linear Equations with Variable Coefficients.

Random Matter Density Perturbations and LMA N. Reggiani Pontifícia Universidade Católica de Campinas - Campinas SP Brazil M.

Gravitational Waves from primordial density perturbations Kishore N. Ananda University of Cape Town In collaboration with Chris Clarkson and David Wands.

The earth matter effect in T2KK Based on work with K. Hagiwara, N. Ken-ichi Senda Grad. Univ. for Adv. Studies &KEK.

Neutrino Oscillation in Dense Matter Speaker: Law Zhiyang, National University of Singapore.

Moscow State Institute for Steel and Alloys Department of Theoretical Physics Analytical derivation of thermodynamic characteristics of lipid bilayer Sergei.

Oscillations and Resonances PHYS 5306 Instructor : Charles Myles Lee, EunMo.

Introduction to Coherence Spectroscopy Lecture 1 Coherence: “A term that's applied to electromagnetic waves. When they "wiggle" up and down together they.

PHY221 Ch21: SHM 1.Main Points: Spring force and simple harmonic motion in 1d General solution a Cos  t+  Plot x, v, a 2.Example Vertical spring with.

Matter Effects on Neutrino Oscillations By G.-L. Lin NCTU Nov. 20, 04 AS.

Basudeb Dasgupta, JIGSAW 2007 Mumbai Phase Effects in Neutrinos Conversions at a Supernova Shockwave Basudeb Dasgupta TIFR, Mumbai Joint Indo-German School.

1 Driven Oscillations Driven Oscillators –Equation of motion –Algebraic solution –Complex algebra solution Phase and amplitude of particular solution –Algebraic.

Lyα Forest Simulation and BAO Detection Lin Qiufan Apr.2 nd, 2015.

Design for a 2 MW graphite target for a neutrino beam Jim Hylen Accelerator Physics and Technology Workshop for Project X November 12-13, 2007.

Statistics and probability Dr. Khaled Ismael Almghari Phone No:

Evolution of the poloidal Alfven waves in 3D dipole geometry Jiwon Choi and Dong-Hun Lee School of Space Research, Kyung Hee University 5 th East-Asia.

Forced Oscillation 1. Equations of Motion Linear differential equation of order n=2 2.

Collapse of Small Scales Density Perturbations

Enhancement of CP Violating terms

Diffusion over potential barriers with colored noise

Progressive Waves Standing Waves T Stretched string Wave Equation

Peter Brandt (1), Martin Claus (1), Richard J

Event Rates vs Cross Sections

Perturbation Methods Jeffrey Eldred

TAV / PIRATA-17 Meeting, Kiel, Germany

4n + 2 1st term = 4 × = 6 2nd term = 4 × = 10 3rd term

10.4 Parametric Equations Parametric Equations of a Plane Curve

The impact of non-linear evolution of the cosmological matter power spectrum on the measurement of neutrino masses ROE-JSPS workshop Edinburgh.

hep-ph Prog. Theor. Phys. 117 Takashi Shimomura (Saitama Univ.)

Undamped Forced Oscillations

Intae Yu Sungkyunkwan University (SKKU), Korea KNO 2nd KNU, Nov

Linear Vector Space and Matrix Mechanics

Presentation transcript:

Parametric Resonance by the Matter Effect SATO, Joe (Saitama) Koike, Masafumi (Saitama) Ota, Toshihiko (Würzburg) Saito, Masako (Saitama) with Plan Introduction Two-Flavor Oscillation Parametric Resonance in Neutrino Oscillation More on Parametric Resonance Summary

Introduction

Parametric resonance of neutrino oscillation (Akhmedov, 1999) Matter with periodic density profile causes parametric resonance of the neutrino oscillation. Neutrino oscillation through the Earth may indicate this effect. We show how the effect of parametric resonance emerges in neutrino oscillation in a general matter profile.

Interior of the Earth

crust mantle outer core Interior of the Earth inner core Preliminary Reference Earth Model Depth

Matter Density Profile

Constant-Density Approximation

Matter Density Profile

Inhomogeneous Matter Koike,Sato 1999 Ota,Sato 2001

Parametric Resonance in Neutrino Oscillation Ermilova et al. (1986) Akhmedov, Akhmedov et al. (1988 — Present) others “Castle-wall” matter profile (Akhmedov, 1998) Fourier decomposition (Present approach) Mode 1 Mode 2 Mode 3

Two-Flavor Oscillation

Second-order equation in dimensionless variables Dimensionless variables Initial conditions, Matter effect Evolution equation of the two-flavor neutrino

MSW-resonance peak. Peaks and dips of the oscillation spectrum Simple solution when: Appearance probability at the endpoint of the baseline (n+1)-th oscillation peak. n-th oscillation dip. Constant-Density Oscillation

id numbers of the oscillation peaks Constant-Density Oscillation Neutrino Energy / [GeV] Appearance Prob

Parametric Resonance in Neutrino Oscillation

Matter Density Profile

Evolution Equation Inhomogeneity Fourier expansion Effect of the n-th Fourier mode on the oscillation Mathieu Equation

Modes of Matter Profile Matter profile in Fourier series Mode 1 Mode 5 Mode 2 Mode 3 Mode 4

Pow ! Parametric Resonance Periodic Motion Oscillation of Oscillation Parameter in classical mechanics We kick a swing twice in a period of motion. Mathieu Equation

Pow ! Parametric Resonance Periodic Motion Oscillation of Oscillation Parameter Parametric Resonance in classical mechanics We kick a swing twice in a period of motion. Parametric Resonance Condition

Parametric Resonance Neutrino Oscillation Fourier modes of matter effect in neutrino oscillation

Parametric Resonance Neutrino Oscillation Fourier modes of matter effect Parametric Resonance in neutrino oscillation Parametric Resonance Condition n-th oscillation dip

Effect of the Mode 1 Neutrino Energy / [GeV] Appearance Prob Sizable effect at 1st peak (n=0) and 2nd peak (n=1) 0 g/cm g/cm g/cm g/cm g/cm g/cm

Mode 1: Possible Large Effect Earth models suggestfor a through-Earth path 0 g/cm g/cm g/cm g/cm g/cm g/cm

Mode 1: Possible Large Effect Earth models suggestfor a through-Earth path 0 g/cm g/cm g/cm g/cm g/cm g/cm

Effect of the Mode 2 Neutrino Energy / [GeV] Appearance Prob Sizable at 2nd (n=1) and 3rd (n=2) peaks 0 g/cm g/cm g/cm g/cm g/cm g/cm

Effect of the Mode 3 Neutrino Energy / [GeV] Appearance Prob Sizable at 3rd (n=2) and 4th (n=3) peaks 0 g/cm g/cm g/cm g/cm g/cm g/cm

More on the Parametric Resonance

Resonant Enhancement

Resonant enhancement of apparance probability, even for a small Fourier coefficient n = 1 n = 2 n = 3 Fictious repetition of the matter profile Matter profile (Arbitrary vertical scale) Oscillation “dip” at 0 g/cm g/cm g/cm

Large-Scale Oscillation

Summary Neutrino oscillation across the Earth Deviation from the constant density Fourier analysis Parametric resonance Frequency matching of the matter distribution and the neutrino energy Mathieu-like equation provides an analytic description Matter distributionn-th Fourier mode Appearance probabilityn-th dip and neighbor