Relativistic Wigner function approach to neutrino propagation in matter

Sirera, M.; Perez, A.

doi:10.1103/physrevd.59.125011

Cited by 19 publications

(39 citation statements)

References 40 publications

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“…[8] and references therein). It is thus interesting from an academic point of view how this oscillation phenomenon is described by the generalized Boltzmann equations [9][10][11][12][13][14]. It is also important from a practical point of view for those who are interested in the possible significant consequences the oscillation might give in astrophysical events [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

“…This might be done in a couple of ways. Sirera and Pérez [14], for instance, based their derivation on the relativistic Wigner function approach in the mean field approximation. Although they took the relativistic kinematics properly into account, they did not obtain the collision terms, since it is difficult to go beyond the mean field approximation in their formalism.…”

Section: Introductionmentioning

confidence: 99%

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Boltzmann equations for neutrinos with flavor mixings

Yamada

2000

Phys. Rev. D

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With a view of applications to the simulations of supernova explosion and proto neutron star cooling, we derive the Boltzmann equations for the neutrino transport with the flavor mixing based on the real time formalism of the nonequilibrium field theory and the gradient expansion of the Green function. The relativistic kinematics is properly taken into account. The advection terms are derived in the mean field approximation for the neutrino self-energy whiles the collision terms are obtained in the Born approximation. The resulting equations take the familiar form of the Boltzmann equation with corrections due to the mixing both in the advection part and in the collision part. These corrections are essentially the same as those derived by Sirera et al. for the advection terms and those by Raffelt et al. for the collision terms, respectively, though the formalism employed here is different from theirs. The derived equations will be easily implemented in numerical codes employed in the simulations of supernova explosions and proto neutron star cooling.14.60.Pq 11.10.Wx 97.60.Bw 97.60.Jd

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Boltzmann equations for neutrinos with flavor mixings

Yamada

2000

Phys. Rev. D

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“…Under these conditions, we obtain that the equation of motion for the Wigner Function of the neutrinos in equilibrium is [11] (…”

Section: Neutrino Gas In the Hartree Approximationmentioning

confidence: 99%

“…These statistical averages are called Wigner functions [11], and are the analogous to the distribution functions we need to describe many-particles systems. These are, in general, complex functions, and also contain a Lorentz structure.…”

Section: Equations For Wigner Functionsmentioning

confidence: 99%

“…As we will show, the equilibrium features, such as the effective masses and mixing angles, are modified when the interactions among neutrinos are considered, due to the non-diagonal nature of the self-term. To this end, we use a method based on Wigner Functions, which has been shown to be appropriate to describe both the equilibrium and kinematics of many-particle neutrino mixing [11].…”

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confidence: 99%

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Equilibrium properties of self-interacting neutrinos in the quasi-particle approach

Sirera¹,

Perez²

2004

J. Phys. G: Nucl. Part. Phys.

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In this work a neutrino gas in equilibrium is studied both at T = 0 and at finite temperature.Neutrinos are treated as massive Dirac quasi-particles with two generations. We include selfinteractions among the neutrinos via neutral currents, as well as the interaction with a background of matter. To obtain the equilibrium properties we use Wigner function techniques. To account for corrections beyond the Hartree approximation, we also introduce correlation functions. We prove that, under the quasi-particle approximation, these correlation functions can be expressed as products of Wigner functions. We analyze the main properties of the neutrino eigenmodes in the medium, such as effective masses and mixing angle. We show that the formulae describing these quantities will differ with respect to the case with no self-interactions.

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Overview of the Phase Space Formulation of Quantum Mechanics with Application to Quantum Technologies

Rundle

Everitt

2021

Adv Quantum Tech

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The phase‐space formulation of quantum mechanics has recently seen increased use in testing quantum technologies, including methods of tomography for state verification and device validation. Here, an overview of quantum mechanics in phase space is presented. The formulation to generate a generalized phase‐space function for any arbitrary quantum system is shown, such as the Wigner and Weyl functions along with the associated Q and P functions. Examples of how these different formulations are used in quantum technologies are provided, with a focus on discrete quantum systems, qubits in particular. Also provided are some results that, to the authors' knowledge, have not been published elsewhere. These results provide insight into the relation between different representations of phase space and how the phase‐space representation is a powerful tool in understanding quantum information and quantum technologies.

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Relativistic Wigner function approach to neutrino propagation in matter

Cited by 19 publications

References 40 publications

Boltzmann equations for neutrinos with flavor mixings

Boltzmann equations for neutrinos with flavor mixings

Equilibrium properties of self-interacting neutrinos in the quasi-particle approach

Overview of the Phase Space Formulation of Quantum Mechanics with Application to Quantum Technologies

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