Related papers: Liouville equations for neutrino distribution matr…
There is an accepted approach to calculation of the neutrino flavor density-matrix in the halo of a supernova, in which neutrino amplitudes, not cross-sections, need to be followed carefully in the region above the region of frequent…
Liouville equation is a fundamental one in statistical mechanics. It is rooted in ensemble theory. By ensemble theory, the variation of the system's microscopic state is indicated by the moving of the phase point, and the moving trajectory…
Collective neutrino oscillations are typically studied using the lowest-order quantum kinetic equation, also known as the mean-field approximation. However, some recent quantum many-body simulations suggest that quantum entanglement among…
A flavor-dependent model (FDM) is proposed in this work. The model extends the Standard Model by an extra $U(1)_F$ local gauge group, two scalar doublets, one scalar singlet and two right-handed neutrinos, where the additional $U(1)_F$…
The standard theory of neutrino oscillations is reviewed, highlighting the main assumptions: the definition of the flavor states, the equal-momentum assumption and the time = distance assumption. It is shown that the standard flavor states…
The Liouville equation differs from the von Neumann equation 'only' by a characteristic superoperator. We demonstrate this for Hamiltonian dynamics, in general, and for the Jaynes-Cummings model, in particular. -- Employing superspace…
Neutrino flavour transmutations in nonuniform matter are described by a Schr\"{o}dinger-like evolution equation with coordinate-dependent potential. In all the derivations of this equation it is assumed that the potential, which is due to…
This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of…
We presented a general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and Zubarev's nonequilibrium…
The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining…
The flavor evolution of neutrinos in environments with large neutrino number densities is an open problem at the nexus of astrophysics and neutrino flavor physics. Among the many unanswered questions pertaining to this problem, it remains…
We describe our recent proposal of a path integral formulation of classical Hamiltonian dynamics. Which leads us here to a new attempt at hybrid dynamics, which concerns the direct coupling of classical and quantum mechanical degrees of…
The quantum Liouville equation, which describes the phase space dynamics of a quantum system of fermions, is analyzed from statistical point of view as a particular example of the Kramers-Moyal expansion. Quantum mechanics is extended to…
The flavor composition of high-energy astrophysical neutrinos can reveal the physics governing their production, propagation, and interaction. The IceCube Collaboration has published the first experimental determination of the ratio of the…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. In particular, a local quantum field theory is presented which is a supersymmetric classical model. -- The Hilbert space approach of Koopman…
Density matrices are powerful mathematical tools for the description of closed and open quantum systems. Recently, methods for the direct computation of density matrix elements in scalar quantum field theory were developed based on thermo…
Neutrino flavor oscillations are discussed in terms of two coupled Dirac fields. The interacting Lagrangian is diagonalized to obtain the exact eigenvalues and eigenfunctions. Flavor wave functions are then derived directly from the…
We extend a previously developed description of the flavour parameters in the charged fermion sector, based on a U(2) flavour symmetry, to include two main features of the neutrino sector seemingly implied by recent data: a large mixing…
We explore the non-singlet sector of matrix quantum mechanics dual to $c=1$ Liouville theory. The non-singlets are obtained by adding $N_{f}\times N$ bi-fundamental fields in the gauged matrix quantum mechanics model as well as a one…
Neutrino oscillation is phenomenon of random transition from a flavor state of neutrino to another, and should obey quantum statistics theory, and constitutes Markoffian process. The process is depicted by method of CTRW (continuous time…