Density Matrix Formalism for PT-Symmetric Non-Hermitian Hamiltonians with the Lindblad Equation

Ohlsson, Tommy; Zhou, Shun

doi:10.48550/arxiv.2006.02445

Cited by 4 publications

(4 citation statements)

References 43 publications

(81 reference statements)

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“…Neutrino decoherence is often represented using an open quantum system formalism [24,29,30,[36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55] considering both the neutrino and its environment. The stochastic processes we consider in this work cause our knowledge of the neutrino to degrade over time, which in the language of open quantum systems constitutes the evolution from an initially pure quantum state to a mixed quantum state.…”

Section: Analytic Decoherence Operatormentioning

confidence: 99%

Neutrino signals of lightcone fluctuations resulting from fluctuating space-time

Stuttard

2021

Preprint

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One of the most common expectations of a quantum theory of gravity is that space-time is uncertain or fluctuating at microscopic scales, making it a stochastic medium for particle propagation. Particles traversing this space-time may experience fluctuations in travel times or velocities, together referred to as lightcone fluctuations, with even very small effects potentially accumulating into observable signals over large distances. In this work we present a heuristic model of lightcone fluctuations and study the resulting modifications to neutrino propagation, including neutrino decoherence and arrival time spread. We show the expected scale of such effects due to 'natural' Planck scale physics and consider how they may be observed in neutrino detectors, and compare the potential of neutrinos to γ-ray astronomy. Using simulations of neutrino mass states propagating in a fluctuating environment, we determine an analytic decoherence operator in the framework of open quantum systems to quantitatively evaluate neutrino decoherence resulting from lightcone fluctuations, allowing experimental constraints on neutrino decoherence to be connected to Planck scale fluctuations in space-time and γ-ray results.

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Section: Analytic Decoherence Operatormentioning

confidence: 99%

Neutrino signals of lightcone fluctuations resulting from fluctuating space-time

Stuttard

2021

Preprint

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“…Obviously, the Lindblad operators characterize the dissipative effects on the subsystem described by the density matrix ρ(t). The applications of the Lindblad equation to neutrino oscillations with a Hermitian [45][46][47][48][49][50][51][52][53][54][55] or a non-Hermitian effective Hamiltonian [56] can be found in the literature. For three-flavor neutrino oscillations, the most general form of Eq.…”

Section: Lindblad Decoherencementioning

confidence: 99%

Cosmic Flavor Hexagon for Ultrahigh-energy Neutrinos and Antineutrinos at Neutrino Telescopes

Zhou¹

2020

Preprint

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In this paper, we propose a hexagonal description for the flavor composition of ultrahighenergy (UHE) neutrinos and antineutrinos, which will hopefully be determined at the future large neutrino telescopes. With such a geometrical description, we are able to clearly separate the individual flavor composition of neutrinos from that of antineutrinos in one single regular hexagon, which can be regarded as a natural generalization of the widely-used ternary plot. For illustration, we consider the pp or pγ collisions as the dominant production mechanism for UHE neutrinos and antineutrinos in the cosmic accelerator, and investigate how neutrino oscillations in the standard picture and in the presence of Lindblad decoherence could change the flavor composition of neutrinos and antineutrinos at neutrino telescopes.

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“…[1] that the apparent puzzles concerning the positivity of transition probabilities and unitarity found in Refs. [23,24] (cf. Ref.…”

Section: Introductionmentioning

confidence: 99%

Discrete spacetime symmetries, second quantization and inner products in a non-Hermitian Dirac fermionic field theory

Alexandre¹,

Ellis²,

Millington³

2022

Preprint

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We extend to a non-Hermitian fermionic quantum field theory with PT symmetry our previous discussion of second quantization, discrete symmetry transformations and inner products in a scalar field theory [1]. For illustration, we consider a prototype model containing a single Dirac fermion with a parity-odd, anti-Hermitian mass term. In the phase of unbroken PT symmetry, this Dirac fermion model is equivalent to a Hermitian theory under a similarity transformation, with the non-Hermitian nature of the model residing only in the spinor structure, whereas the algebra of the creation and annihilation operators is just that of a Hermitian theory.

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Density Matrix Formalism for PT-Symmetric Non-Hermitian Hamiltonians with the Lindblad Equation

Cited by 4 publications

References 43 publications

Neutrino signals of lightcone fluctuations resulting from fluctuating space-time

Neutrino signals of lightcone fluctuations resulting from fluctuating space-time

Cosmic Flavor Hexagon for Ultrahigh-energy Neutrinos and Antineutrinos at Neutrino Telescopes

Discrete spacetime symmetries, second quantization and inner products in a non-Hermitian Dirac fermionic field theory

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