Band structure in classical field theory

Classical Field Theory

a) Energy-momentum Based on Noether’s theorem, construct the energy-momentum tensor for classical electromagnetism from the above Lagrangian. Note that the usual procedure does not result in a symmetric tensor. To remedy that, we can add to T μν a term of the form ∂λK λμν , where K is antisymmetric in its first two indices. Such an object is automatically divergenceless, so T̂ μν = T μν + ∂λK λμ...

Symmetric Criticality in Classical Field Theory

This is a brief overview of work done by Ian Anderson, Mark Fels, and myself on symmetry reduction of Lagrangians and Euler-Lagrange equations, a subject closely related to Palais’ Principle of Symmetric Criticality. After providing a little history, I describe necessary and sufficient conditions on a group action such that reduction of a group-invariant Lagrangian by the symmetry group yields ...

Classical chaotic trajectories in quantum field theory

Trajectories in the space of the unitarily inequivalent representations of the canonical commutation relations are shown to be classical trajectories. Under convenient conditions, they may exhibit properties typical of chaotic behavior in classical nonlinear dynamics. Quantum noise in fluctuating random force in the system–environment coupling and system–environment entanglement is also discussed.

Asymptotic Conservation Laws in Classical Field Theory.

Field modulation in bilayer graphene band structure.

Using an external electric field, one can modulate the band gap of Bernal stacked bilayer graphene by breaking the A-[Formula: see text] symmetry. We analyze strain effects on the bilayer graphene using the extended Hückel theory and find that reduced interlayer distance results in higher band gap modulation, as expected. Furthermore, above about 2.5 Å interlayer distance, the band gap is direc...