Spontaneous Parity Violation

We disprove the Vafa-Witten theorem on the impossibility of spontaneously breaking parity in vector-like gauge field theories, identifying a mechanism driven by quantum fluctuations. With the introduction of a meromorphic Lattice formulation, defined over 5 dimensions, we demonstrate that the minima of the free energy can be distinct from the maxima of the partition function : identifying and evaluating a suitable contour for the partition function defined such that asymptotic behaviour of the complex action is non-oscillatory.Comment: 6 page

Exact Nonperturbative Renormalization

We propose an exact renormalization group equation for Lattice Gauge Theories, that has no dependence on the lattice spacing. We instead relate the lattice spacing properties directly to the continuum convergence of the support of each local plaquette. Equivalently, this is formulated as a convergence prescription for a characteristic polynomial in the gauge coupling that allows the exact meromorphic continuation of a nonperturbative system arbitrarily close to the continuum limit.Comment: 12 page

Lorentz Covariance and the Dimensional Crossover of 2d-Antiferromagnets

We derive a lattice $\beta$-function for the 2d-Antiferromagnetic Heisenberg model, which allows the lattice interaction couplings of the nonperturbative Quantum Monte Carlo vacuum to be related directly to the zero-temperature fixed points of the nonlinear sigma model in the presence of strong interplanar and spin anisotropies. In addition to the usual renormalization of the gapful disordered state in the vicinity of the quantum critical point, we show that this leads to a chiral doubling of the spectra of excited states

The Lattice β\beta-function of Quantum Spin Chains

We derive the lattice $\beta$-function for quantum spin chains, suitable for relating finite temperature Monte Carlo data to the zero temperature fixed points of the continuum nonlinear sigma model. Our main result is that the asymptotic freedom of this lattice $\beta$-function is responsible for the nonintegrable singularity in $\theta$, that prevents analytic continuation between $\theta=0$ and $\theta=\pi$.Comment: 10 page

Enhancing Near Zero Volt Storage Tolerance of Lithium-ion Batteries

There are inherent safety risks associated with inactive lithium ion batteries leading to greater restrictions and regulations on shipping and storage. Maintaining all cells of a lithium ion battery at near zero voltage with an applied fixed resistive load is one promising approach which can lessen (and potentially eliminate) the risk of a lithium ion battery entering thermal runaway when in an inactive state. However, in a conventional lithium ion cell, a near zero cell voltage can be damaging if the anode electrochemical potential increases to greater than the potential where dissolution of the standard copper current collector occurs (i.e. ~3.1 V vs. Li/Li+ at room temperature). Past approaches to yield lithium ion cells that are resilient to a near zero volt state of charge involve use of secondary active materials or alternative current collectors which have anticipated tradeoffs in terms of cell performance and cost. In the the present dissertation work the approach of managing the amount of reversible lithium in a cell during construction to prevent the anode potential from increasing to greater than ~3.1 V vs. Li/Li+ during near zero volt storage is introduced. Anode pre-lithiation was used in LiCoO2/MCMB pouch cells to appropriately manage the amount of reversible lithium so that there is excess reversible lithium compared to the cathodes intercalation capacity (reversible lithium excess cell or RLE cell). RLE LiCoO2/MCMB cells maintained 99% of their original capacity after three, 3-day and three, 7-day storage periods at near zero volts under fixed load. A LiCoO2/MCMB pouch cell fabricated with a pre-lithiated anode also maintained its original discharge performance after three, 3-day storage periods under fixed load at 45°C. The strong recharge performance after near zero volt storage is attributed to the anode potential remaining below the copper dissolution potential during near zero volt storage as informed by reference electrode measurements. Pulse discharge measurements were performed and show that double layer capacitance likely plays a major role in determining the behavior of electrode potentials during near zero volt storage. To further the viability of the anode pre-lithiation method in LiCoO2/MCMB cells, stabilization coatings on the cathode materials are being investigated to increase the tolerance of the cathode to the low potentials it may experience during near zero volt storage of an RLE lithium ion cell. Results show that an AlPO4 coating prevents cation exhange in the cathode crystal structure and substantially increases the cathode’s resilience to low electrochemical potentials. Investigations into applying anode pre-lithiation to cells utilizing LiNiCoAlO2 (NCA) cathodes have also been initiated and found to maintain the anode potential below the copper dissolution potential during near zero volt storage. RLE NCA/MCMB cells showed strong recharge performance and improved rate capability retention over a conventional NCA/MCMB cell after ten, 3-day near zero volt storage periods. Scale up of reversible lithium management to NCA/MCMB x3450 pouch cells was achieved using bath lithium addition and rendered a cell that retained 100% of its discharge performance after a 14 day period at near zero volts under fixed load. The near zero volt storage tolerance of lithium ion cells utilizing an advanced, high energy density lithium rich cathode material (0.49Li2MnO3·0.51LiNi0.37Co0.24Mn0.39O2 or HE5050) has also been studied and found to be high at room temperature without the need for anode pre-lithiation. HE5050/MCMB cells maintained ~100% of their discharge capacity after five, 3-day and five, 7-day near zero volt storage periods at room temperature. HE5050/MCMB also maintained ~99% of their discharge capacity after two, 3-day near zero volt storage periods at 40°C. The high first cycle loss and lower intercalation potential of the HE5050 cathode lead to the anode potential remainin