A new non-perturbative approach to quantum field theory -D-theory -is proposed, in which continuous classical fields are replaced by discrete quantized variables which undergo dimensional reduction. The 2-d classical O(3) model emerges from the (2 + 1)-d quantum Heisenberg model formulated in terms of quantum spins. Dimensional reduction is demonstrated explicitly by simulating correlation lengths up to 350,000 lattice spacings using a loop cluster algorithm. In the framework of D-theory, gauge theories are formulated in terms of quantum links -the gauge analogs of quantum spins. Quantum links are parallel transporter matrices whose elements are non-commuting operators. They can be expressed as bilinears of anticommuting fermion constituents. In quantum link models dimensional reduction to four dimensions occurs, due to the presence of a 5-d Coulomb phase, whose existence is confirmed by detailed simulations using standard lattice gauge theory. Using Shamir's variant of Kaplan's fermion proposal, in quantum link QCD quarks appear as edge states of a 5-d slab. This naturally protects their chiral symmetries without fine-tuning. The first efficient cluster algorithm for a gauge theory with a continuous gauge group is formulated for the U (1) quantum link model. Improved estimators for Wilson loops are constructed, and dimensional reduction to ordinary lattice QED is verified numerically.

Functional materials for energy conversion and storage exhibit strong coupling between electrochemistry and mechanics. For example, ceramics developed as electrodes for both solid oxide fuel cells and batteries exhibit cyclic volumetric expansion upon reversible ion transport. Such chemomechanical coupling is typically far from thermodynamic equilibrium, and thus is challenging to quantify experimentally and computationally. In situ measurements and atomistic simulations are under rapid development to explore how this coupling can be used to potentially improve both device performance and durability. Here, we review the commonalities of coupling between electrochemical and mechanical states in fuel cell and battery materials, illustrating with specific cases the progress in materials processing, in situ characterization, and computational modeling and simulation. We also highlight outstanding questions and opportunities in these applications -both to better understand the limiting mechanisms within the materials and to significantly advance the durability and predictability of device performance required for renewable energy conversion and storage.

We study the Abelian projection of an instanton in R 3 × S 1 as a function of temperature (T) and non-trivial holonomic twist (ω) of the Polyakov loop at infinity. These parameters interpolate between the circular monopole loop solution at T = 0 and the static 't Hooft-Polyakov monopole/anti-monopole pair at high temperature.

We study the heavy quark potential in the instanton liquid model by carefully measuring Wilson loops out to a distance of order 3$fm$. A random instanton ensemble with a fixed radius $\rho$ = 1/3$fm$ generates a potential $V(R)$ growing very slowly at large $R$. In contrast, a more realistic size distribution growing as $\rho^6$ at small $\rho$ and decaying as $\rho^{-5}$ at large $\rho$, leads to a potential which grows linearly with $R$. The string tension, however, is only about 1/10 of the phenomenological value.Comment: LATTICE98(confine

No abstract