Chiral oscillations

We report about recent results on Dirac wave packets in the treatment of neutrino flavor oscillation where the initial localization of a spinor state implies an interference between positive and negative energy components of mass-eigenstate wave packets. A satisfactory description of fermionic particles requires the use of the Dirac equation as evolution equation for the mass-eigenstates. In this context, a new flavor conversion formula can be obtained when the effects of chiral oscillation are taken into account. Our study leads to the conclusion that the fermionic nature of the particles, where chiral oscillations and the interference between positive and negative frequency components of mass-eigenstate wave packets are implicitly assumed, modifies the standard oscillation probability. Nevertheless, for ultra-relativistic particles and sharply peaked momentum distributions, we can analytically demonstrate that these modifications introduce correction factors proportional to (m12/p0) square which are practically un-detectable by any experimental analysis

Equilibrium thermodynamics only retains its validity as long as the molecular internal degrees of freedom of the considered system do not attain a primary macroscopic relevance. This condition is fulfilled if the macroscopic perturbation of the system occurs so slowly (quasi-static) that the statistical equilibrium of the internal degrees of freedom is not disturbed during the perturbation. The system is then in a so-called internal equilibrium. In this case, the internal degrees of freedom are not explicitly noticeable, but only become globally apparent, for example, by a change dQ of the heat content of the system. This condition, however, is also fulfilled if the macroscopic perturbation occurs so quickly that one or more of the molecular internal degrees of freedom do not have time to react to the perturbation. The degrees of freedom concerned then appear frozen with respect to the macroscopic perturbation. Provided that the other part of the internal degrees of freedom is still able to restore equilibrium practically instantaneously during the perturbation (so that we can still talk about a thermodynamic equilibrium), the system is in a so-called arrested equilibrium with respect to the frozen degrees of freedom for the duration of the perturbation. Arrested (frozen) internal degrees of freedom do not exhibit any macroscopic effects. They can be ignored as long as different arrested states do not have to be compared with each other or with other states. How fast a system must be perturbed so that an internal degree of freedom appears arrested with respect to the perturbation naturally depends on the degree of freedom itself, but also on the physical environment in which it is embedded. Some internal degrees of freedom can, in certain temperature and pressure ranges, still be regarded as being at least approximately arrested, even in the case of a quasistatic perturbation. Two typical examples are the degrees of freedom of the diffusive translational motion of the molecules in a glass and the degree of advancement of the reaction in an oxygen and hydrogen gas mixture.

Levitation optomechanics exploits the unique mechanical properties of trapped nano-objects in vacuum to address some of the limitations of clamped nanomechanical resonators. In particular, its performance is foreseen to contribute to a better understanding of quantum decoherence at the mesoscopic scale as well as to lead to novel ultrasensitive sensing schemes. While most efforts have focused so far on the optical trapping of low-absorption silica particles, further opportunities arise from levitating objects with internal degrees of freedom, such as color centers. Nevertheless, inefficient heat dissipation at low pressures poses a challenge because most nano-objects, even with low-absorption materials, experience photodamage in an optical trap. Here, by using a Paul trap, we demonstrate levitation in vacuum and center-of-mass feedback cooling of a nanodiamond hosting a single nitrogen-vacancy center. The achieved level of motion control enables us to optically interrogate and characterize the emitter response. The developed platform is applicable to a wide range of other nano-objects and represents a promising step toward coupling internal and external degrees of freedom.

Internal degrees of freedom in a thermodynamical model for intracell biological transport

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.

Solving the Dirac equation is a formidable task due to the high frequency and the degrees of freedom involved. However, this high frequency allows one to obtain an approximation to the equation. Here, we directly solve the Dirac equation using an envelope method and derive analytical solutions of Dirac wave packets to first order for the small momentum spread. We apply the insight gained from this solution to the Zitterbewegung behavior in a Dirac-like system, where we show that it is crucial to include the first-order term in our solution to correctly describe a Dirac packet.

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 $\Delta m_{21}^2$.

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 nucleus is represented as a Kerr-Newman source, under the assumption that the angular momentum of the source is equal to the intrinsic spin angular momentum of the nucleus. The theoretical values of the hyperfine splitting obtained from a solution of Dirac's equation for this model of the muon, the positron, and the proton agree with the observed values in muonium, positronium, and hydrogen, to within the uncertainty in the respective QED corrections---except for an unaccounted factor of 2. In hydrogen one also has to introduce the observed value of the magnetic moment of the proton. The singularity in Dirac's radial differential equations is shifted from the origin, where it is located in the case of flat space, to a pair of conjugate points on the imaginary axis of the radial coordinate. Consequently, the energy eigenvalues have a trace of an imaginary part, making the bound states of our model unstable.

In the binary-driven hypernova model of long gamma-ray bursts, a carbon–oxygen star explodes as a supernova in the presence of a neutron star binary companion in close orbit. Hypercritical (i.e., highly super-Eddington) accretion of the ejecta matter onto the neutron star sets in, making it reach the critical mass with consequent formation of a Kerr black hole. We have recently shown that, during the accretion process onto the neutron star, fast neutrino flavor oscillations occur. Numerical simulations of the above system show that a part of the ejecta stays bound to the newborn Kerr black hole, leading to a new process of hypercritical accretion. We address herein, also for this phase of the binary-driven hypernova, the occurrence of neutrino flavor oscillations given the extreme conditions of high density (up to 1012 g cm−3) and temperatures (up to tens of MeV) inside this disk. We estimate the behavior of the electronic and non-electronic neutrino content within the two-flavor formalism (νeνx) under the action of neutrino collective effects by neutrino self-interactions. We find that in the case of inverted mass hierarchy, neutrino oscillations inside the disk have frequencies between ∼(105–109) s−1, leading the disk to achieve flavor equipartition. This implies that the energy deposition rate by neutrino annihilation (ν+ν¯→e−+e+) in the vicinity of the Kerr black hole is smaller than previous estimates in the literature not accounting for flavor oscillations inside the disk. The exact value of the reduction factor depends on the νe and νx optical depths but it can be as high as ∼5. The results of this work are a first step toward the analysis of neutrino oscillations in a novel astrophysical context, and as such, deserve further attention.

HIGH ENERGY ELECTRON SCATTERING FROM A TWO CENTER POTENTIAL

We numerically solve the evolution equations of neutrino three-flavor density matrices, and show that, even if neutrino oscillations mix neutrino flavors, large lepton number asymmetries are still allowed in certain limits by big bang nucleosynthesis.

We study decoherence effects in neutrino flavor oscillations in curved spacetime with particular emphasis on the lensing in a Schwarzschild geometry. Assuming Gaussian wave packets for neutrinos, we argue that the decoherence length derived from the exponential suppression of the flavor transition amplitude depends on the proper time of the geodesic connecting the events of the production and detection in general gravitational setting. In the weak gravity limit, the proper time between two events of given proper distance is smaller than that in the flat spacetime. Therefore, in presence of a Schwarzschild object, the neutrino wave packets have to travel relatively more physical distance in space to lapse the same amount of proper time before they decoher. For nonradial propagation applicable to the lensing phenomena, we show that the decoherence, in general, is sensitive to the absolute values of neutrino masses as well as the classical trajectories taken by neutrinos between the source and detector along with the spatial widths of neutrino wave packets. At distances beyond the decoherence length, the probability of neutrino flavor transition due to lensing attains a value which depends only on the leptonic mixing parameters. Hence, the observability of neutrino lensing significantly depends on these parameters and in-turn the lensing can provide useful information about them.

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.

Maxwell's equations, Lorentz's equations of motion, and Dirac's equations are investigated on a cosmological background. Maxwell's equations are conform invariant and the equations of motion can easily be made conform invariant. Then, without introducing any new assumptions, Dirac's equations are seen to be conform invariant. In open universes the solutions of Maxwell's and Dirac's equations are the same as in flat Minkowski space. The behavior of these equations is different in closed universes by reasons of topology. In closed universes both Maxwell's and Dirac's equations provide new eigenvalue problems. Dirac's equations exhibit a marked difference between an elliptic and a spherical closed universe.