Coherence and mixedness of neutrino oscillations in a magnetic field

In studies of neutrino electromagnetic properties we discuss three very inter- esting aspects related to neutrino spin oscillations. First we consider neutrino mixing and oscillations in the mass and flavour bases under the influence of a constant magnetic field with nonzero transversal and longitudinal components. Then we discuss the effect of neutrino spin oscillations induced by electroweak interactions of neutrino with mov- ing matter in case there is matter transversal current or polarization. In the final part of the paper we discuss recently developed approach to description of neutrino spin and spin-flavour oscillations in a constant magnetic field that is based on the use of the exact neutrino stationary states in the magnetic field.

A theoretical analysis of possible influence of neutrino magnetic moments on the propagation of ultrahigh-energy cosmic neutrinos in the interstellar space is carried out under the assumption of two-neutrino mixing. The exact solution of the effective equation for neutrino evolution in the presence of a magnetic field and matter is obtained, which accounts for four neutrino species corresponding to two different flavor states with positive and negative helicities. Using most stringent astrophysical bounds on the putative neutrino magnetic moment, probabilities of neutrino flavor and spin oscillations are calculated on the basis of the obtained exact solution. Specific patterns of spin-flavor oscillations are determined for neutrino-energy values characteristic of, respectively, the cosmogenic neutrinos, the Greisen-Zatsepin-Kuz'min (GZK) cutoff, and well above the cutoff.

We study spin and flavor oscillations of astrophysical neutrinos under the influence of external fields in curved spacetime. First, we consider spin oscillations in case of neutrinos gravitationally scattered off a rotating supermassive black hole surrounded by a thin magnetized accretion disk. We find that the gravitational interaction only does not result in the spin-flip of scattered ultrarelativistic neutrinos. Realistic magnetic fields lead to the significant reduction of the observed flux of neutrinos possessing reasonable magnetic moments. Second, we study neutrino flavor oscillations in stochastic gravitational waves (GWs). We derive the effective Hamiltonian for neutrinos interacting with a plane GW having an arbitrary polarization. Then, we consider stochastic GWs with arbitrary correlators of amplitudes. The equation for the density matrix for neutrino oscillations is solved analytically and the probabilities to detect certain neutrino flavors are derived. We find that the interaction of neutrinos, emitted by a core-collapsing supernova, with the stochastic GW background results in the several percent change of the neutrino fluxes. The observability of the predicted effects is discussed.

Spin-flavor oscillations of Dirac neutrinos in matter and a magnetic field\nare studied using the method of relativistic quantum mechanics. Using the exact\nsolution of the wave equation for a massive neutrino, taking into account\nexternal fields, the effective Hamiltonian governing neutrino spin-flavor\noscillations is derived. Then the The consistency of our approach with the\ncommonly used quantum mechanical method is demonstrated. The obtained\ncorrection to the usual effective Hamiltonian results in the appearance of the\nnew resonance in neutrino oscillations. Applications to spin-flavor neutrino\noscillations in an expanding envelope of a supernova are discussed. In\nparticular, transitions between right-polarized electron neutrinos and\nadditional sterile neutrinos are studied for realistic background matter and\nmagnetic field distributions. The influence of other factors such as the\nlongitudinal magnetic field, the matter polarization, and the non-standard\ncontributions to the neutrino effective potential, is also analyzed.\n

We study oscillations of Dirac neutrinos in background matter and a plane electromagnetic wave. First, we find the new exact solution of the Dirac-Pauli equation for a massive neutrino with the anomalous magnetic moment electroweakly interacting with matter under the influence of a plane electromagnetic wave with the circular polarization. We use this result to describe neutrino spin oscillations in the external fields in question. Then we consider several neutrino flavors and study neutrino spin-flavor oscillations in this system. For this purpose we formulate the initial condition problem and solve it accounting for the considered external fields. We derive the analytical expressions for the transition probabilities of spin-flavor oscillations for different types of neutrino magnetic moments. These analytical expressions are compared with the numerical solutions of the effective Schr\"odinger equation and with the findings of other authors. In particular, we reveal that a resonance in neutrino spin-flavor oscillations in the considered external fields cannot happen contrary to the previous claims. Finally, we briefly discuss some possible astrophysical applications.

In this talk, we consider the interplay of fundamental and matter-induced T-violating effects in neutrino oscillations in matter. We present a simple approximative analytical formula for the T-violating probability asymmetry for three flavor neutrino oscillations in matter with an arbitrary density profile. We also discuss some implications of the obtained results. Since there are no T-violating effects in two flavor neutrino case (in the limit of vanshing $\theta_{13}$ or $\Delta m_{21}^2$, the three flavor neutrino oscillations reduces to the two flavor ones), the T-violating probability asymmetry can, in principle, provide a way to measure $\theta_{13}$ and $\Delta m_{21}^2$.

T-violating effects in neutrino oscillations with three flavors in matter

We analyze the evolution of a neutrino in an inhomogeneous electromagnetic field. Based on exact solutions to the equation describing both flavor oscillations and spin rotation, we obtain the probabilities of neutrino spin–flavor transitions. The propagation of a neutrino in the field of a point magnetic dipole is considered in detail. It is shown that in this case, the total probability of spin rotation depends on the angle between the direction of the neutrino velocity and the dipole axis. The results of analysis show that the effective reduction of the left-polarized neutrino flux from an astrophysical object with a high magnetic field or at the final stage of supernova collapse can be due to spin rotation both in the region with a high density of matter and during further propagation of the neutrino in the field surrounding the object.

The ultra high energy (UHE) cosmic neutrinos are expected to play a pivotal role in the disquisition of physics beyond the standard model of particle physics as well as serve as an ideal cosmic messengers. This epitomizes the selling point of several currently running or planned neutrino telescopes. The UHE cosmic neutrinos usually perambulate gargantuan scales in the extragalactic universe having a magnetic field. If neutrinos have a finite magnetic moment (μν) owing to quantum loop corrections, this may result in spin-flavor oscillations, which can affect the cosmic neutrino flux. Using the current limit and assuming neutrinos to be Dirac particles, we show that the flux of cosmic neutrinos will reduce by half if they traverse few Mpcs through the intergalactic magnetic field, in the range of μG to nG. Moreover, one can safely neglect the effect of μν if the current upper bound is improved by a few orders of magnitude even if the neutrinos travel through the size of the visible universe.

We study the gravitational scattering of ultrarelativistic neutrinos off a rotating supermassive black hole (BH) surrounded by a thick magnetized accretion disk. Neutrinos interact electroweakly with background matter and with the magnetic field in the disk since neutrinos are supposed to possess nonzero magnetic moments. The interaction with external fields results in neutrino spin oscillations. We find that the toroidal magnetic field, inherent in the magnetized Polish doughnut, does not cause a significant spin-flip for any reasonable strengths of the toroidal component. The reduction of the observed neutrino flux, owing to neutrino spin oscillations, is predicted. A poloidal component of the magnetic field gives the main contribution to the modification of the observed flux. The neutrino interaction with matter, rotating with relativistic velocities, also changes the flux of neutrinos. We briefly discuss the idea of the neutrino tomography of magnetic field distributions in accretion disks near BHs.

On flavor violation for massive and mixed neutrinos

We study the effects of neutrino lensing induced by a Damour–Solodukhin wormhole on the neutrino oscillation. We derive and calculate the flavour transition probabilities in the presence of Damour–Solodukhin factor $$\Lambda $$ Λ as a shift in the massive source to show that the neutrino flavour oscillation is also sensitive not only to the sign of difference between the squared masses but also to the individual mass of neutrinos in both the two-flavour and the three-flavour cases. As a consequence of parameter $$\Lambda $$ Λ within a region, a series of curves of probability function versus the azimuthal angle $$\phi $$ ϕ with definite masses of neutrino can be plotted and their shapes resemble each other in the case of two-flavoured neutrinos and of three-flavoured ones. In view of the probability functions due to the wormhole, we reveal that the contribution of the factor $$\Lambda $$ Λ is novel. Based on our analytical and numerical discussions on the probability expressions, the difference of the neutrino flavour oscillation arising from the shift in the wormhole factor $$\Lambda $$ Λ is detectable. It is crucial that the $$\Lambda $$ Λ as deviation from the black holes can change the shapes of the curves greatly, in the case of three-flavoured neutrinos in particular. The detailed comparisons can be made among our estimations depicted in the figures for neutrino oscillations and the measurements from the detector, which open a new window for judging whether the remote star as lens is black-hole-like wormhole or spherically symmetric black hole and further the wormhole factor $$\Lambda $$ Λ can be estimated.

The model predictions for the flux of low energy neutrinos produced in the solar core are now rather firm. This allows reliable tests of neutrino properties in solar neutrino experiments; neutrino propagation can be studied with a baseline of 150 million kilometers. Experimental data are available from three radiochemical detectors (Homestake, Gallex, and Sage) and from two real-time detectors (Kamiokande and Superkamiokande). Taking all experimental data together, it appears that the abundant pp-neutrinos are entirely present, the moderately abundant 7Be-neutrinos are strongly or totally suppressed and the rare 8B-neutrinos are partially reduced, by a factor ≈ 2. This pattern can not be explained by modifications of the stellar model but it is consistent with neutrino flavor oscillations that occur on the way between the solar core and the detector. If this applies, a non-vanishing neutrino restmass follows. The evidence is summarized.

Since quantum coherence is an undoubted characteristic trait of quantum\nphysics, the quantification and application of quantum coherence has been one\nof the long-standing central topics in quantum information science. Within the\nframework of a resource theory of quantum coherence proposed recently, a\n\\textit{fiducial basis} should be pre-selected for characterizing the quantum\ncoherence in specific circumstances, namely, the quantum coherence is a\n\\textit{basis-dependent} quantity. Therefore, a natural question is raised:\nwhat are the maximum and minimum coherences contained in a certain quantum\nstate with respect to a generic basis? While the minimum case is trivial, it is\nnot so intuitive to verify in which basis the quantum coherence is maximal.\nBased on the coherence measure of relative entropy, we indicate the particular\nbasis in which the quantum coherence is maximal for a given state, where the\nFourier matrix (or more generally, \\textit{complex Hadamard matrices}) plays a\ncritical role in determining the basis. Intriguingly, though we can prove that\nthe basis associated with the Fourier matrix is a stationary point for\noptimizing the $l_1$ norm of coherence, numerical simulation shows that it is\nnot a global optimal choice.\n

We introduce and study a generalization of majorization called relative submajorization and show that it has many applications to the resource theories of thermodynamics, bipartite entanglement, and quantum coherence. Relative majorization is an ordering on pairs of vectors induced by stochastic transformations: One pair of vectors relatively majorizes another when there exists a stochastic transformation taking the former to the latter. Relative submajorization is a weakened version in which a substochastic matrix need only generate a vector pair obeying certain positivity conditions relative to the input pair. In the context of resource theories, we show that the relative submajorization characterizes both the probability and approximation error that can be obtained when transforming one resource to another, also when assisted by additional standard resources such as useful work or maximally entangled states. These characterizations have a geometric formulation as the ratios or differences, respectively, between the Lorenz curves associated with the input and output resources, making them efficient to compute. We also find several interesting bounds on the reversibility of a given transformation in terms of the properties of the forward transformation. The main technical tool used to establish these results is the linear programming duality, which is used to show that any instance of relative submajorization can be “dilated” to an instance of strict relative majorization.