Entropic uncertainty relation in neutrino oscillations

The European Physical Journal C - We study the isentropic evolution of the matter produced in relativistic heavy-ion collisions for various values of the entropy-per-baryon ratio of interest for...     

The time-energy uncertainty relation

A discussion is presented of the formulations of the time and energy uncertainty principle given by Mandelstam, Tamm, Wigner, and the one proposed recently by the present authors, based on the concept of the equivalent width. In the case of the free particle, all three formulations give essentially the same result, while in the problem of the lifetime-width relation for a decaying state, only the one based on the equivalent width concept is applicable. This is also the case in the energy-measurement process, when it is formulated as a transition produced by an external interaction of finite duration.     

On the Lorentz-invariant time-energy uncertainty relation for a relativistic photon

The time-energy uncertainty relation is discussed for a relativistic massless particle. The Lorentz-invariant uncertainty relation is obtained between the root-mean-square energy deviation and the scatter of registration time. The interconnection between this uncertainty relation and its classical analogue is established.     

Physical basis for minimal time-energy uncertainty relation

A physical basis for the minimal time-energy uncertainty relation is formulated from basic high-energy hadronic properties such as the resonance mass spectrum, the form factor behavior, and the peculiarities of Feynman's parton picture. It is shown that the covariant oscillator formalism combines covariantly this time-energy uncertainty relation with Heisenberg's space-momentum uncertainty relation. A pictorial method is developed to describe the spacetime distribution of the localized probability density.     

On the failure of the time-energy uncertainty principle

We establish, for the quantum system made up of a single free particle, the formula E t(v/c) , where E is the precision to whichE can be ascertained in time t. The measurement can be carried out with zero disturbance inE itself.     

On the theory of neutrino mixing and oscillations

A brief review of the status of neutrino oscillations is given. The phenomenology of neutrino mixing and the standard seesaw mechanism of neutrino mass generation is discussed. Different approaches to neutrino oscillations are considered and compared. The role of the Heisenberg space-momentum uncertainty relation and the Mandelstam-Tamm time-energy uncertainty relation in neutrino oscillations is discussed in some detail.     

Resonant neutrino oscillations and the neutrino signature of supernovae

We examine the effects of resonant neutrino oscillations, proposed as a solution to the solar neutrino puzzle, on the neutrino signature of a Type II supernova. We find that, for parameters corresponding to an adiabatic conversion of most of the ⁸B neutrino flux, the supernova neutrino signal in a water-Čerenkov detector is altered in the following way: (1) The isotropic-to-directional event ratio increases; (2) The short time scale neutronization burst signal decreases by a factor 7, perhaps rendering it unobservable. Detection of these changes would allow one to distinguish between neutrino oscillations and solar model alterations as solutions to the solar neutrino problem. We also note that mixing of the higher energy ν_μ and ν_r's to ν_e's will enhance detection of the thermally produced ν-flux.     

On vacuum oscillations solution of the solar neutrino problem

Experimental signatures of vacuum oscillations solution of the solar neutrino problem are considered. This solution predicts a strict correlation between a distortion of the neutrino energy spectrum and an amplitude of seasonal variations of the neutrino flux. The slope parameter which characterizes a distortion of the recoil electron energy spectrum in the Super-Kamiokande experiment and the seasonal asymmetry of the signal have been calculated in a wide range of oscillation parameters. The correlation of the slope and asymmetry gives crucial criteria for identification or exclusion of this solution. For the positive slope indicated by preliminary Super-Kamiokande data we predict (40 – 60) % enhancement of the seasonal variations.     

"Weighing" a closed system and the time-energy uncertainty principle

A gedanken experiment is proposed for "weighing" the total mass of a closed system from within the system. We prove that for an internal observer the time tau, required to measure the total energy with accuracy DeltaE, is bounded according to tauDeltaE>Planck's over 2pi. This time-energy uncertainty principle for a closed system follows from the measurement backreaction on the system. We generally examine what other conserved observables are in principle measurable within a closed system and what are the corresponding uncertainty relations.     

Charged lepton and neutrino oscillations

Problems long present in the conventional formalism employed for neutrino oscillations are discussed. We here develop a more satisfactory framework based on the Dirac equation and its propagators. When 4-momentum conservation is strictly enforced, there will be induced oscillations in space (but not between generations) for the charged leptons, e.g. and , produced in association with the neutrinos. The oscillations are computed explicitly for the pion decay . Leptonic decays of the are also briefly discussed. Received: 15 October 1996 / Revised version: 15 June 1997 / Published online: 20 February 1998     

Lepton mixing and neutrino oscillations

The present article is a review of phenomena connected with neutrino oscillations. Mixing of two neutrinos (Majorana as well as Dirac) with masses m₁ and m₂ is considered in detail. It is shown that the hypothesis of lepton mixing is not in contradiction with the existing data if |m₁²?m₂²| ? 1 (eV)². Possible experiments designed to reveal neutrino oscillations at reactor, meson factory and high energy accelerator facilities are considered. In such experiments oscillation might be found if $\text{|m}{}_1{}^2\text{?m}{}_2{}^2\text{| ? 0.01}\text{(eV)}{}^2$. The possibilities of searching for oscillations by experiments on cosmic ray neutrinos and especially on solar neutrinos are discussed in detail. The last experiments have an incredible high sensitivity from the point of view of testing the lepton mixing hypothesis (oscillation effects might be observable if $\text{|m}{}_1{}^2\text{?m}{}_2{}^2\text{| ? 10}{}^{\mathrm{?12}}\text{(eV)}{}^2$). The “solar neutrino puzzle” is also discussed from the point of view of lepton mixing. Neutrino oscillations are considered then in the case where in nature there exist N ? 2 neutrino types.In conclusion the case of heavy lepton mixing is considered. It is shown that in a concrete scheme with right-handed currents, the probabilities of such processes as μ → eγ, μ → 3e etc. can be close to existing experimental upper limits, provided the heavy lepton masses are of an order of a few GeV, whereas the probabilities of the above processes are entirely negligible if only neutrinos are mixed.     

CP violation and neutrino oscillations

We review the basic mechanisms of neutrino mass generation and the corresponding structure of the lepton mixing matrix. We summarize the status of three-neutrino oscillation parameters as determined from current observations, using state-of-the-art solar and atmospheric neutrino fluxes, as well as latest experimental data as of September 2007. We also comment on recent attempts to account for these results and to understand flavour from first principles. We discuss extensively the prospects of probing the strength of CP violation in two near term accelerator neutrino oscillation experiments, T2K and , as well as possible extensions such as T2KK and a second large off-axis detector near the detector. We also briefly discuss the possibility of probing the effect of Majorana phases in future neutrinoless double beta decay searches and discuss other implications of leptonic CP violation such as leptogenesis. Finally we comment on the issue of robustness of the current oscillation interpretation and possible ways of probing for non-standard neutrino interactions in precision oscillation studies.