Engineering topics

Wilczek, Frank

Publications and source records attributed to Wilczek, Frank.

8 records

DOE OSTI2025

Quantum Hamiltonian algorithms for maximum independent sets

ABSTRACT We compare two quantum Hamiltonian algorithms that address the maximum independent set problem: one based on the emergent non-Abelian gauge matrix in adiabatic evolution of an energetically isolated manifold of states; the other based on designed application of single-qubit operations. We demonstrate that they are mathematically equivalent in the sense that one is the other’s interaction picture. Despite their mathematical equivalence, our numerical simulations show significant differences between them in performance, which is explained analytically. Intriguingly, this equivalence unveils that the PXP model, recently prominent in quantum dynamics research, can be viewed as quantum diffusion over the median graph of all independent sets governed by the non-Abelian gauge matrix.

Science & Technology - Other Topics↗

NASA NTRS1991

Inflationary axion cosmology

If Peccei-Quinn (PQ) symmetry is broken after inflation, the initial axion angle is a random variable on cosmological scales; based on this fact, estimates of the relic-axion mass density give too large a value if the axion mass is less than about 10 to the -6th eV. This bound can be evaded if the universe underwent inflation after PQ-symmetry breaking and if the observable universe happens to be a region where the initial axion angle was atypically small. Consideration of fluctuations induced during inflation severely constrains the latter alternative is shown.

Turner, Michael S.↗

NASA NTRS1990

Relic gravitational waves and extended inflation

In extended inflation, a new version of inflation where the transition from an inflationary to a radiation-dominated universe is accomplished by bubble nucleation, bubble collisions supply a potent - and potentially detectable - source of gravitational waves. The energy density in relic gravitons from bubble collisions is expected to be about 0.00005 of closure density. Their characteristic wavelength depends on the reheating temperature. If black holes are produced by bubble collisions, they will evaporate, producing shorter-wavelength gravitons.

Turner, Michael S.↗

NASA NTRS1990

Relic gravitational waves and extended inflation

In extended inflation, a new version of inflation where the transition from the false-vacuum phase to a radiation-dominated Universe is accomplished by bubble nucleation and percolation, bubble collisions supply a potent-and potentially detectable-source of gravitational waves. The present energy density in relic gravity waves from bubble collisions is expected to be about 10(exp -5) of closure density-many orders of magnitude greater than that of the gravity waves produced by quantum fluctuations. Their characteristic wavelength depends upon the reheating temperature T(sub RH): lambda is approximately 10(exp 4) cm (10(exp 14) GeV/T(sub RH)). If large numbers of black holes are produced, a not implausible outcome, they will evaporate producing comparable amounts of shorter wavelength waves, lambda is approximately 10(exp -6) cm (T(sub RH)/10(exp 14) GeV).

Turner, Michael S.↗

NASA NTRS1989

Positron line radiation from halo WIMP annihilations as a dark matter signature

We suggest a new signature for dark matter annihilation in the halo: high energy positron line radiation. Because the cosmic ray positron spectrum falls rapidly with energy, e+'s from halo WIMP annihilations can be a significant, clean signal for very massive WIMP's (approx. greater than 30 GeV). In the case that the e+e- annihilation channel has an appreciable branch, the e+ signal should be above background in a future detector, such as have been proposed for ASTROMAG, and of potential importance as a dark matter signature. A significant e+e- branching ratio can occur for neutralinos or Dirac neutrinos. High-energy, continuum positron radiation may also be an important signature for massive neutralino annihilations, especially near or above the threshold of the W+W- and ZoZo annihilation channels.

Turner, Michael S.↗

NASA NTRS1988

Supervised learning of probability distributions by neural networks

Supervised learning algorithms for feedforward neural networks are investigated analytically. The back-propagation algorithm described by Werbos (1974), Parker (1985), and Rumelhart et al. (1986) is generalized by redefining the values of the input and output neurons as probabilities. The synaptic weights are then varied to follow gradients in the logarithm of likelihood rather than in the error. This modification is shown to provide a more rigorous theoretical basis for the algorithm and to permit more accurate predictions. A typical application involving a medical-diagnosis expert system is discussed.

Baum, Eric B.↗

NASA NTRS1987

Lattice fermions

A simple heuristic proof of the Nielsen-Ninomaya theorem is given. A method is proposed whereby the multiplication of fermion species on a lattice is reduced to the minimal doubling, in any dimension, with retention of appropriate chiral symmetries. Also, it is suggested that use of spatially thinned fermion fields is likely to be a useful and appropriate approximation in QCD - in any case, it is a self-checking one.

Wilczek, Frank↗

NASA NTRS1987

Two applications of axion electrodynamics

The equations of axion electrodynamics are studied. Variations in the axion field can give rise to peculiar distributions of charge and current. These effects provide a simple understanding of the fractional electric charge on dyons and of some recently discovered oddities in the electrodynamics of antiphase boundaries in PbTe. Some speculations regarding the possible occurrence of related phenomena in other solids are presented.

Wilczek, Frank↗