scholarly journals Discerning the Nature of Neutrinos: Decoherence and Geometric Phases

Universe ◽  
2020 ◽  
Vol 6 (11) ◽  
pp. 207
Author(s):  
Antonio Capolupo ◽  
Salvatore Marco Giampaolo ◽  
Gaetano Lambiase ◽  
Aniello Quaranta
Keyword(s):  
Geometric Phase ◽  
Neutrino Oscillations ◽  
Phenomenological Analysis ◽  
Cpt Symmetry ◽  
Geometric Phases ◽  
Majorana Phase ◽  
New Approaches ◽  
Majorana Neutrinos ◽  
Mixing Matrix

We present new approaches to distinguish between Dirac and Majorana neutrinos. The first is based on the analysis of the geometric phases associated to neutrinos in matter, the second on the effects of decoherence on neutrino oscillations. In the former we compute the total and geometric phase for neutrinos, and find that they depend on the Majorana phase and on the parametrization of the mixing matrix. In the latter, we show that Majorana neutrinos might violate CPT symmetry, whereas Dirac neutrinos preserve CPT. A phenomenological analysis is also reported showing the possibility to highlight the distinctions between Dirac and Majorana neutrinos.

scholarly journals GEOMETRIC PHASES AND QUANTUM PHASE TRANSITIONS

2008 ◽  
Vol 22 (06) ◽  
pp. 561-581 ◽  
Author(s):  
SHI-LIANG ZHU
Keyword(s):  
Phase Transitions ◽  
Geometric Phase ◽  
Quantum Phase Transitions ◽  
Condensed Matter ◽  
Quantum Phase ◽  
Many Body ◽  
Scientific Communities ◽  
Geometric Phases ◽  
Many Body Systems ◽  
The Many

Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant relation was recognized before recent work. In this paper, we present a review of the connection recently established between these two interesting fields: investigations in the geometric phase of the many-body systems have revealed the so-called "criticality of geometric phase", in which the geometric phase associated with the many-body ground state exhibits universality, or scaling behavior in the vicinity of the critical point. In addition, we address the recent advances on the connection of some other geometric quantities and quantum phase transitions. The closed relation recently recognized between quantum phase transitions and some of the geometric quantities may open attractive avenues and fruitful dialogue between different scientific communities.

scholarly journals Unitarity of neutrino mixing matrix

2019 ◽  
Vol 206 ◽  
pp. 09009
Author(s):  
Ha Nguyen Thi Kim ◽  
Van Nguyen Thi Hong ◽  
Son Cao Van
Keyword(s):  
Cp Violation ◽  
Neutrino Oscillations ◽  
Graphical Form ◽  
Muon Neutrinos ◽  
Neutrino Mixing ◽  
Electron Neutrinos ◽  
Tau Neutrinos ◽  
The Matrix ◽  
Mixing Matrix ◽  
Unitary Triangle

Neutrinos are neutral leptons and there exist three types of neutrinos (electron neutrinos νe, muon neutrinos νµ and tau neutrinos ντ). These classifications are referred to as neutrinos’s “flavors”. Oscillations between the different flavors are known as neutrino oscillations, which occurs when neutrinos have mass and non-zero mixing. Neutrino mixing is governed by the PMNS mixing matrix. The PMNS mixing matrix is constructed as the product of three independent rotations. With that, we can describe the numerical parameters of the matrix in a graphical form called the unitary triangle, giving rise to CP violation. We can calculate the four parameters of the mixing matrix to draw the unitary triangle. The area of the triangle is a measure of the amount of CP violation.

THREE-NEUTRINO OSCILLATIONS IN MATTER, CP-VIOLATION AND TOPOLOGICAL PHASES

1992 ◽  
Vol 01 (02) ◽  
pp. 379-399 ◽  
Author(s):  
V.A. NAUMOV
Keyword(s):  
Evolution Operator ◽  
Adiabatic Approximation ◽  
Neutrino Oscillations ◽  
Topological Phases ◽  
Matrix Elements ◽  
Neutrino Mixing ◽  
Time Evolution Operator ◽  
Adiabatic Approach ◽  
Flavor Mixing ◽  
Mixing Matrix

The phenomenon of Dirac neutrino oscillations in medium of varying density and composition is studied for the case of three lepton generations using the Berry adiabatic approach. The expressions for the topological phases γN are derived. It is shown that the Berry phases, arising when matter parameters vary periodically, are equal to zero identically, while in the case of noncyclic evolution, γN≢0 (in a special gauge) under the condition that all matrix elements of the flavor-mixing matrix in vacuum, CP-violating (Dirac) phase and neutrino-mass-squares differences are not equal to zero simultaneously. Exact formulas for the neutrino-mixing matrix in matter and adiabatic time-evolution operator are obtained. The recursion algorithm for the calculation of corrections to the adiabatic approximation is given

BERRY PHASE IN COUPLED TWO-LEVEL SYSTEMS

2013 ◽  
Vol 27 (12) ◽  
pp. 1350088 ◽  
Author(s):  
X. Y. ZHANG ◽  
J. H. TENG ◽  
X. X. YI
Keyword(s):  
Asymptotic Behavior ◽  
Geometric Phase ◽  
Berry Phase ◽  
External Control ◽  
Control Parameters ◽  
Coupling Constant ◽  
Geometric Phases ◽  
Coupled Subsystems ◽  
Two Level Systems ◽  
The Individual

The application of geometric phases into robust control of quantal systems has triggered exploration of the geometric phase for coupled subsystems. Earlier studies have mainly focused on the situation where the external control parameters are in the free Hamiltonian of the subsystems, i.e. the controls exert only on the individual subsystems. Here we consider another circumstance that we can control the coupling geiϕ between the subsystems. By changing only the phase ϕ in the coupling constant, we derive the Berry phase acquired by the system and compare it to the geometric phase acquired by changing the coupling strength g. We find that the asymptotic behavior of the Berry phase depends on the relative Rabi frequency of the two subsystems, and it approaches π when the amplitude of the coupling tends to infinity.

scholarly journals Sub-Geometric Phases in Density Matrices

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Zheng-Chuan Wang
Keyword(s):  
Mixed State ◽  
Geometric Phase ◽  
Density Matrices ◽  
Geometric Phases

Abstract This study presents the generalization of geometric phases in density matrices. We show that the extended sub-geometric phase has an unified expression during the adiabatic or nonadiabatic process and establish the relations between them and the usual Berry or Aharonov-Anandan phases. We also demonstrate the influence of sub-geometric phases on the physical observables. Finally, the above treatment is used to investigate the geometric phase in a mixed state.

scholarly journals Gravity-Induced Geometric Phases and Entanglement in Spinors and Neutrinos: Gravitational Zeeman Effect

Universe ◽  
2020 ◽  
Vol 6 (10) ◽  
pp. 160
Author(s):  
Banibrata Mukhopadhyay ◽  
Soumya Kanti Ganguly
Keyword(s):  
Electromagnetic Field ◽  
Gravitational Field ◽  
Geometric Phase ◽  
Zeeman Effect ◽  
Relative Strength ◽  
Entangled States ◽  
Neutrino Masses ◽  
Geometric Phases ◽  
Aharonov Bohm ◽  
Gravitational Background

We show Zeeman-like splitting in the energy of spinors propagating in a background gravitational field, analogous to the spinors in an electromagnetic field, otherwise termed the Gravitational Zeeman Effect. These spinors are also found to acquire a geometric phase, in a similar way as they do in the presence of magnetic fields. However, in a gravitational background, the Aharonov-Bohm type effect, in addition to Berry-like phase, arises. Based on this result, we investigate geometric phases acquired by neutrinos propagating in a strong gravitational field. We also explore entanglement of neutrino states due to gravity, which could induce neutrino-antineutrino oscillation in the first place. We show that entangled states also acquire geometric phases which are determined by the relative strength between gravitational field and neutrino masses.

scholarly journals Geometric phases for mixed states of the Kitaev chain

2016 ◽  
Vol 374 (2068) ◽  
pp. 20150231 ◽  
Author(s):  
Ole Andersson ◽  
Ingemar Bengtsson ◽  
Marie Ericsson ◽  
Erik Sjöqvist
Keyword(s):  
Finite Temperature ◽  
Geometric Phase ◽  
Berry Phase ◽  
Condensed Matter ◽  
Order Parameters ◽  
Topological Order ◽  
Mixed States ◽  
Geometric Phases

The Berry phase has found applications in building topological order parameters for certain condensed matter systems. The question whether some geometric phase for mixed states can serve the same purpose has been raised, and proposals are on the table. We analyse the intricate behaviour of Uhlmann's geometric phase in the Kitaev chain at finite temperature, and then argue that it captures quite different physics from that intended. We also analyse the behaviour of a geometric phase introduced in the context of interferometry. For the Kitaev chain, this phase closely mirrors that of the Berry phase, and we argue that it merits further investigation.

scholarly journals TEV NEUTRINO PHYSICS AT THE LARGE HADRON COLLIDER

2009 ◽  
Vol 24 (18n19) ◽  
pp. 3286-3296 ◽  
Author(s):  
ZHI-ZHONG XING
Keyword(s):  
Neutrino Physics ◽  
Large Hadron Collider ◽  
Particle Physics ◽  
Degrees Of Freedom ◽  
Neutrino Oscillations ◽  
Hadron Collider ◽  
Higgs Bosons ◽  
Type I ◽  
Seesaw Mechanism ◽  
Majorana Neutrinos

I argue that TeV neutrino physics might become an exciting frontier of particle physics in the era of the Large Hadron Collider (LHC). The origin of non-zero but tiny masses of three known neutrinos is probably related to the existence of some heavy degrees of freedom, such as heavy Majorana neutrinos or heavy Higgs bosons, via a TeV-scale seesaw mechanism. I take a few examples to illustrate how to get a balance between theoretical naturalness and experimental testability of TeV seesaws. Besides possible collider signatures at the LHC, new and non-unitary CP-violating effects are also expected to show up in neutrino oscillations for type-I, type-(I+II) and type-III seesaws at the TeV scale.

scholarly journals THE MASS DIFFERENCE OF $F-\bar{F}$ WITH SO(3) FAMILY GAUGE SYMMETRY

2012 ◽  
Vol 27 (20) ◽  
pp. 1250107 ◽  
Author(s):  
HONG-LEI LI ◽  
SHOU-SHAN BAO ◽  
ZONG-GUO SI
Keyword(s):  
Gauge Symmetry ◽  
Mass Difference ◽  
Simple Extension ◽  
Gauge Bosons ◽  
Majorana Neutrinos ◽  
Mixing Matrix ◽  
Gauge Interaction

As a simple extension, a non-Abelian family gauge symmetry SO(3), as well as three family Majorana neutrinos, was introduced to explain the tri-bimaximal mixing matrix of neutrinos. We discuss the effect of the possible SO(3) family gauge interaction to the mass differences of [Formula: see text] and [Formula: see text], and get the constrains to the new gauge bosons.

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