Eigenvalues and eigenstates of the many-body collective neutrino oscillation problem
arXiv:1905.04386 · doi:10.1103/PhysRevD.99.123013
Abstract
We demonstrate a method to systematically obtain eigenvalues and eigenstates of a many-body Hamiltonian describing collective neutrino oscillations. The method is derived from the Richardson-Gaudin framework, which involves casting the eigenproblem as a set of coupled nonlinear "Bethe Ansatz equations", the solutions of which can then be used to parametrize the eigenvalues and eigenvectors. The specific approach outlined in this paper consists of defining auxiliary variables that are related to the Bethe-Ansatz parameters, thereby transforming the Bethe-Ansatz equations into a different set of equations that are numerically better behaved and more tractable. We show that it is possible to express not only the eigenvalues, but also the eigenstates, directly in terms of these auxiliary variables without involving the Bethe Ansatz parameters themselves. In this paper, we limit ourselves to a two-flavor, single-angle neutrino system.
arXiv comment18 pages of RevTeX, 4 figures. v2: contains some additional text and references, matches journal version. v3: fixed a missing figure reference
References in corpus (70)
- Evidence for oscillation of atmospheric neutrinos
- Observation of electron-antineutrino disappearance at Daya Bay
- Measurement of the rate of nu_e + d --> p + p + e^- interactions produced by 8B solar neutrinos at the Sudbury Neutrino Observatory
- Collective Neutrino Oscillations
- Simulation of Coherent Non-Linear Neutrino Flavor Transformation in the Supernova Environment I: Correlated Neutrino Trajectories
- Cosmological bounds on neutrino degeneracy improved by flavor oscillations
- Self-induced conversion in dense neutrino gases: Pendulum in flavour space
- Collective Neutrino Flavor Transformation In Supernovae
- Speed-up of neutrino transformations in a supernova environment
- Collective neutrino flavor transitions in supernovae and the role of trajectory averaging
- Multiple Spectral Splits of Supernova Neutrinos
- Stringent Constraints on Cosmological Neutrino-Antineutrino Asymmetries from Synchronized Flavor Transformation
- Self-induced spectral splits in supernova neutrino fluxes
- Collective neutrino flavor conversion: Recent developments
- Coherent Development of Neutrino Flavor in the Supernova Environment
- Physics of Synchronized Neutrino Oscillations Caused by Self-Interactions
- Analysis of Collective Neutrino Flavor Transformation in Supernovae
- Adiabaticity and spectral splits in collective neutrino transformations
- Self-induced neutrino flavor conversion without flavor mixing
- Collective three-flavor oscillations of supernova neutrinos
- Invariants of Collective Neutrino Oscillations
- Neutrino Mass Hierarchy and Stepwise Spectral Swapping of Supernova Neutrino Flavors
- Neutrino-Neutrino Interactions and Flavor Mixing in Dense Matter
- Imprints of neutrino-pair flavor conversions on nucleosynthesis in ejecta from neutron-star merger remnants
- Fast neutrino conversions: Ubiquitous in compact binary merger remnants
- Non-Abelian Boltzmann Equation for Mixing and Decoherence
- Neutrino flavour transformation in supernovae
- Self-Maintained Coherent Oscillations in Dense Neutrino Gases
- Collisional triggering of fast flavor conversions of supernova neutrinos
- Gaudin models solver based on the Bethe ansatz/ordinary differential equations correspondence
- Neutrino oscillations above black hole accretion disks: disks with electron-flavor emission
- Simple Picture for Neutrino Flavor Transformation in Supernovae
- Self-refraction of supernova neutrinos: mixed spectra and three-flavor instabilities
- Neutrino flavor conversion in a neutrino background: single- versus multi-particle description
- Do many-particle neutrino interactions cause a novel coherent effect?
- Spectral split in prompt supernova neutrino burst: Analytic three-flavor treatment
- Fast neutrino flavor conversion: roles of dense matter and spectrum crossing
- A particle-number-conserving solution to the generalized pairing problem
- Stepwise Spectral Swapping with Three Neutrino Flavors
- A few moments to diagnose fast flavor conversions of supernova neutrinos
- Neutrino mass hierarchy and three-flavor spectral splits of supernova neutrinos
- Matter Neutrino Resonance Transitions above a Neutron Star Merger Remnant
- On Fast Neutrino Flavor Conversion Modes in the Nonlinear Regime
- An eigenvalue-based method and determinant representations for general integrable XXZ Richardson-Gaudin models
- Bethe Ansatz and Ordinary Differential Equation Correspondence for Degenerate Gaudin Models
- On the Bethe Ansatz for the Jaynes-Cummings-Gaudin model
- Symmetric and Standard Matter-Neutrino Resonances Above Merging Compact Objects
- Speed-up through entanglement -- many-body effects in neutrino processes
- Fast Neutrino Flavor Conversion as Oscillations in a Quartic Potential
- Neutrino Flavor Evolution in Binary Neutron Star Merger Remnants
- Physics of neutrino flavor transformation through matter-neutrino resonances
- Multi-azimuthal-angle effects in self-induced supernova neutrino flavor conversions without axial symmetry
- New effects of non-standard self-interactions of neutrinos in a supernova
- The neutrino spectral split in core-collapse supernovae: a magnetic resonance phenomenon
- Neutrino Spectral Split in the Exact Many Body Formalism
- Nonstandard Neutrino Interactions in Supernovae
- Multi-azimuthal-angle instability for different supernova neutrino fluxes
- Neutrino Flavor Evolution in Neutron Star Mergers
- Neutrino flavor transformation in the lepton-asymmetric universe
- Non-standard neutrino self-interactions in a supernova and fast flavor conversions
- Uncovering the Matter-Neutrino Resonance
- Inner products in integrable Richardson-Gaudin models
- Matter-neutrino resonance in a multi-angle neutrino bulb model
- Self-induced temporal instability from a neutrino antenna
- Neutrino Oscillations in the Early Universe: A Real Time Formulation
- Collective neutrino oscillations with the halo effect in single-angle approximation
- Multi-angle calculation of the matter-neutrino resonance near an accretion disk
- Spectra and Symmetry in Nuclear Pairing
- Spectral splits of neutrinos as a BCS-BEC crossover type phenomenon
- Richardson-Gaudin models and broken integrability
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- New Developments in Flavor Evolution of a Dense Neutrino Gas
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- Fast neutrino flavor instability and neutrino flavor lepton number crossings
- Neutrino Flavor Conversions in High-Density Astrophysical and Cosmological Environments
- Entanglement and collective flavor oscillations in a dense neutrino gas
- Collective Neutrino Flavor Instability Requires a Crossing
- Exact solution of multi-angle quantum many-body collective neutrino flavor oscillations
- Spectral splits and entanglement entropy in collective neutrino oscillations
- Role of non-gaussian quantum fluctuations in neutrino entanglement
- Collective neutrino oscillations with tensor networks using a time-dependent variational principle
- Classical and Quantum Evolution in a Simple Coherent Neutrino Problem
- General-Relativistic Quantum-Kinetics Neutrino Transport
- Entanglement in three-flavor collective neutrino oscillations
- Many-body effects of collective neutrino oscillations
- Quantum information and quantum simulation of neutrino physics
- Tri-Partite entanglement in Neutrino Oscillations
- Qutrit and Qubit Circuits for Three-Flavor Collective Neutrino Oscillations
- Many-body collective neutrino oscillations: recent developments
- Supernova Neutrinos: flavour conversion mechanisms and new physics scenarios
- Collective Neutrino Oscillations in Three Flavors on Qubit and Qutrit Processors
- Exploring entanglement and spectral split correlations in three-flavor collective neutrino oscillations
- Inference finds consistency between a neutrino flavor evolution model and Earth-based solar neutrino measurements
- Interactions of Neutrino Wave Packets