arXiv subjects
Publications and source records attributed to A. Widom.
The real time exponential decay laws for meta-stable charged particles are shown to require radiative corrections. The methods employed are well known to be valid for radiatively correcting Breit-Wigner line shapes. Radiative corrections contribute substantially to precision life time measurements of muons and pions when initially stopped in condensed matter.
The recent real time KARMEN anomaly for the electron neutrino counting rates (obtained from stopped muon decays) is analyzed by employing a neutrino flavor rotation model in which the muon neutrino is in a superposition of only two mass eigenstates. On the basis of experimental electron neutrino counting oscillations, we find a neutrino mass splitting $|m_2^2-m_1^2|=(0.22\pm 0.02)(eV/c^2)^2$ and a flavor rotation angle $ϕ=0.34\pm 0.10$, both within a 95% confidence interval.
There is a long standing problem about how close a connection exists between superfluidity and Bose condensation. Employing recent technology, for the case of confined finite Bose condensed systems in TOP traps, these questions concerning superfluidity and Bose condensation can be partially resolved if the velocity profile of the trapped atoms can be directly measured.
The dynamical Casimir effect for the ideal case of two perfectly conducting non-charged parallel plates, is discussed using the zero-point energy summation method to the first order in perturbation theory. We show that it is possible to create photon radiation when the two plates are modulated rapidly in time. Moreover we point out that the static Casimir energy between two conducting non-charged parallel plates violates the thermodynamic stability condition normally associated with the second law of thermodynamics.
For spin one atoms localized in a quadrapole magnetic field gradient, the atoms may be impeded from spin flipping their way out from the center of the trap by the application of a rotating uniform magnetic field. From a quantum mechanical viewpoint, such a trap for a Bose condensate is equivalent to having a superfluid in a rotating bucket. Vorticity is then expected to be induced in the condensate fluid flow without the application of any further external perturbations.
One loop field theory calculations of free energies quite often yield violations of the stability conditions associated with the thermodynamic second law. Perhaps the best known example involves the equation of state of black holes. Here, it is pointed out that the Casimir force between two parallel conducting plates also violates a thermodynamic stability condition normally associated with the second law of thermodynamics.
There have been several experiments which hint at evidence for superluminal transport of electromagnetic energy through a material slab. On the theoretical side, it has appeared evident that acausal signals are indeed possible in quantum electrodynamics. However, it is unlikely that superluminal signals can be understood on the basis of a purely classical electrodynamic signals passing through a material. The classical and quantum theories represent quite different views, and it is the quantum view which may lead to violations of Einstein causality.
In experiments involving Bose condensed atoms trapped in magnetic bottles, plugging the hole in the bottle potential with a LASER beam produces a new potential with two minima, and thus a condensate order parameter (i.e. wave function) with two maxima. When the trapping potential is removed and the condensate explodes away from the trap, the two wave function maxima act as two coherent sources which exhibit amplitude interference. A simplified theoretical treatment of this experimental effect is provided by considering momentum distributions.
Acausal features of quantum electrodynamic processes are discussed. While these processes are not present for the classical electrodynamic theory, in the quantum electrodynamic theory, acausal processes are well known to exist. For example, any Feynman diagram with a ``loop'' in space-time describes a ``particle'' which may move forward in time or backward in time or in space-like directions. The engineering problems involved in experimentally testing such causality violations on a macroscopic scale are explored.
Standard statistical thermodynamic views of temperature fluctuations predict a magnitude $(\sqrt{<(ΔT)^2>}/T)\approx\sqrt{(k_B/C)}$ for a system with heat capacity $C$. The extent to which low temperatures can be well defined is discussed for those systems which obey the thermodynamic third law in the form $\lim_{(T\to 0)}C=0$. Physical limits on the notion of very low temperatures are exhibited for simple systems. Application of these concepts to bound Bose condensed systems are explored, and the notion of bound Boson superfluidity is discussed in terms of the thermodynamic moment of inertia.
We study in detail the contribution of heavy composite Majorana neutrinos to neutrino-less double beta decay. Our analysis confirms the result of a previous estimate by two of the authors. Excited neutrinos couple to the electroweak gauge bosons through a magnetic type effective Lagrangian. The relevant nuclear matrix element is related to matrix elements available in the literature and current bounds on the half-life of neutrino-less double beta decay are converted into bounds on the compositeness scale and/or the heavy neutrino mass. Our bounds are of the same order of magnitude as those available from accelerator experiments.
The thermodynamic equations of state for Majorana and Dirac fermions are quite different even in the limit of zero mass. The corresponding equations are derived from general principles, and then applied to neutrinos. The nature of the approach to equilibrium is explored, along with the subtleties of low or zero mass neutrinos interacting via purely left-handed currents. Possible applications to cosmology, supernovae, and supersymmetry are discussed.
A physical difference between Majorana neutrinos and Dirac neutrinos (which persists in the zero mass limit) is proved in two sentences.
The quantum theory of Brownian motion is discussed in the Schwinger version wherein the notion of a coordinate moving forward in time $x(t)$ is replaced by two coordinates, $x_+(t)$ moving forward in time and $x_-(t)$ moving backward in time. The role of the doubling of the degrees of freedom is illustrated for the case of electron beam two slit diffraction experiments. Interference is computed with and without dissipation (described by a thermal bath). The notion of a dissipative interference phase, closely analogous to the Aharonov-Bohm magnetic field induced phase, is explored.
Recent theoretical claims not withstanding, muons can and do oscillate. Muons produced in association with neutrinos (if masses and mixing angles are nonzero) exhibit a joint oscillating spatial distribution. The possible use of muon oscillations as a probe of neutrino mass and mixing parameters is discussed using very simple physical arguments. Space-time oscillations in the secondary decay vertices of muons (produced by pion decay) persist after summing over all undetected neutrinos.
Traditional analysis of $g=2(1+κ)$ experiments for charged leptons use a classical spin vector picture. For muons, we here employ a more exact Dirac quantum four component spinor theory. Survival probabilities (including wave packet effects) are computed. These oscillate with the frequency $Ω=(κeB/Mc)$ as has been assumed in previous muon $(g-2)$ experimental analyses; i.e. muon survival probability oscillations are already at the root of previous succesful $(g-2)$ measurements. Further oscillations should also be observed if mixed neutrino mass matrices were to enter into the reactions (e.g. $π^+ \to μ^+ +ν_μ$) producing muons.
A simple but general proof is presented to show that Lorents covariance and 4-momentum conservation alone are sufficient to obtain muon oscillations in the pion decay if the recoiling neutrinos oscillate.
The theory of neutrino flavor rotations is discussed in terms of wave function solutions to the Dirac equation with a neutrino mass matrix. We give a critical review of the nature of neutrino oscillations.