Locally covariant quantum field theory with external sources

We provide a detailed analysis of the classical and quantized theory of a multiplet of inhomogeneous Klein-Gordon fields, which couple to the spacetime metric and also to an external source term; thus the solutions form an affine space. Following the formulation of affine field theories in terms of presymplectic vector spaces as proposed in [Annales Henri Poincare 15, 171 (2014)], we determine the relative Cauchy evolution induced by metric as well as source term perturbations and compute the automorphism group of natural isomorphisms of the presymplectic vector space functor. Two pathological features of this formulation are revealed: the automorphism group contains elements that cannot be interpreted as global gauge transformations of the theory; moreover, the presymplectic formulation does not respect a natural requirement on composition of subsystems. We therefore propose a systematic strategy to improve the original description of affine field theories at the classical and quantized level, first passing to a Poisson algebra description in the classical case. The idea is to consider state spaces on the classical and quantum algebras suggested by the physics of the theory (in the classical case, we use the affine solution space). The state spaces are not separating for the algebras, indicating a redundancy in the description. Removing this redundancy by a quotient, a functorial theory is obtained that is free of the above mentioned pathologies. These techniques are applicable to general affine field theories and Abelian gauge theories. The resulting quantized theory is shown to be dynamically local.Comment: v2: 42 pages; Appendix C on deformation quantization and references added. v3: 47 pages; compatible with version to appear in Annales Henri Poincar

Working with Nonassociative Geometry and Field Theory

We review aspects of our formalism for differential geometry on noncommutative and nonassociative spaces which arise from cochain twist deformation quantization of manifolds. We work in the simplest setting of trivial vector bundles and flush out the details of our approach providing explicit expressions for all bimodule operations, and for connections and curvature. As applications, we describe the constructions of physically viable action functionals for Yang-Mills theory and Einstein-Cartan gravity on noncommutative and nonassociative spaces, as first steps towards more elaborate models relevant to non-geometric flux deformations of geometry in closed string theory.Comment: 20 pages; v2: Reference added; Contribution to the proceedings of the Corfu Summer Institute on Elementary Particle Physics and Gravity, September 1-26, 2015, Corfu, Greece; Final version published in Proceedings of Scienc

Cheeger-Simons differential characters with compact support and Pontryagin duality

By adapting the Cheeger-Simons approach to differential cohomology, we establish a notion of differential cohomology with compact support. We show that it is functorial with respect to open embeddings and that it fits into a natural diagram of exact sequences which compare it to compactly supported singular cohomology and differential forms with compact support, in full analogy to ordinary differential cohomology. We prove an excision theorem for differential cohomology using a suitable relative version. Furthermore, we use our model to give an independent proof of Pontryagin duality for differential cohomology recovering a result of [Harvey, Lawson, Zweck - Amer. J. Math. 125 (2003) 791]: On any oriented manifold, ordinary differential cohomology is isomorphic to the smooth Pontryagin dual of compactly supported differential cohomology. For manifolds of finite-type, a similar result is obtained interchanging ordinary with compactly supported differential cohomology.Comment: 33 pages, no figures - v3: Final version to be published in Communications in Analysis and Geometr

Processing Issues in Top-Down Approaches to Quantum Computer Development in Silicon

We describe critical processing issues in our development of single atom devices for solid-state quantum information processing. Integration of single 31P atoms with control gates and single electron transistor (SET) readout structures is addressed in a silicon-based approach. Results on electrical activation of low energy (15 keV) P implants in silicon show a strong dose effect on the electrical activation fractions. We identify dopant segregation to the SiO2/Si interface during rapid thermal annealing as a dopant loss channel and discuss measures of minimizing it. Silicon nanowire SET pairs with nanowire width of 10 to 20 nm are formed by electron beam lithography in SOI. We present first results from Coulomb blockade experiments and discuss issues of control gate integration for sub-40nm gate pitch levels

Detection of low energy single ion impacts in micron scale transistors at room temperature

We report the detection of single ion impacts through monitoring of changes in the source-drain currents of field effect transistors (FET) at room temperature. Implant apertures are formed in the interlayer dielectrics and gate electrodes of planar, micro-scale FETs by electron beam assisted etching. FET currents increase due to the generation of positively charged defects in gate oxides when ions (121Sb12+, 14+, Xe6+; 50 to 70 keV) impinge into channel regions. Implant damage is repaired by rapid thermal annealing, enabling iterative cycles of device doping and electrical characterization for development of single atom devices and studies of dopant fluctuation effects