Amr Ahmadain

Our modern understanding of the forces of nature as described by quantum field theories is fundamentally based on symmetries and their associated conservation laws. Quantum anomalies occur when a symmetry of a classical field theory is violated upon quantization. Gravitational anomalies of one-loop quantum effective actions arise after coupling classical field theories to external background geometry and integrating out all dynamical matter fields in the partition function. A gravitational Weyl anomaly of a relativistic field theory is the statement that the quantum effective action is not invariant under local rescaling of the background geometry. In this work, we study Weyl anomalies in non-relativistic Lifshitz field theories in (1+1) and (2+1) dimensions. Lifshitz field theories introduce a degree of scaling anisotropy between space and time measured by the dynamical scaling exponent z. In 1+1 dimensions, we analyze and study the physical and mathematical nature of a particular ...

In this thesis, a strategy for constructing electric-magnetic (EM) duality-symmetric N = 2 supersymmetric infrared effective actions (IREAs) is presented using harmonic superspace. Our aim is to elevate the EM duality from being equivalent descriptions of distinct IREAs to a symmetry of a single IREA under Sp(2r,Z) transformations. Our strategy is to build the IREA out of geometric objects which are manifestly Sp(2r,Z) invariant. We conjecture that a manifestly EM duality-symmetric action can be constructed in this way on harmonic superspace. The main invariant geometric object is the total space, X , of the Coulomb branch moduli space of the IREA, which has a natural hyperkähler structure, and is thus a suitable manifold to act as the target space of an N = 2 supersymmetric nonlinear σ-model (nlsm). We build the IREA as a nlsm with target space the twistor space of X . The twistor space is a fiber bundle with base space the projective line, CP, and X as fiber. The nlsm action is formed by pulling back the invariant holomorphic two-form on twistor space by the hypermultiplet superfield in harmonic superspace, with the base CP identified with the internal CP of harmonic superspace. We also conjecture, but do not prove, that the pullback approach introduced in this thesis for constructing the hypermultiplet nlsm is equivalent to using the standard harmonic superspace procedure of constructing the nlsm action using a harmonic-analytic potential for the hypermultiplet superfields.

The nature of entanglement in many-body systems is a focus of intense research with the observation that entanglement holds interesting information about quantum correlations in large systems and their relation to phase transitions. In particular, it is well known that although generic, many-body states have large, extensive entropy, ground states of reasonable local Hamiltonians carry much smaller entropy, often associated with the boundary length through the so-called area law. Here we introduce a continuous family of frustration-free Hamiltonians with exactly solvable ground states and uncover a remarkable quantum phase transition whereby the entanglement scaling changes from area law into extensively large entropy. This transition shows that entanglement in many-body systems may be enhanced under special circumstances with a potential for generating "useful" entanglement for the purpose of quantum computing and that the full implications of locality and its restriction...

ABSTRACT Using the nanoMOS 2.5 simulator, we study the impact of varying the channel length, gate oxide thickness and dielectric constant, drain voltage, and temperature on the performance of a ballistic nanoscale MOSFET using quantum ballistic and classic ballistic transport models. Our key results show that the quantum ballistic (QB) transport model typically predicts a lower on-state current compared to the classical ballistic (CB) model except for a 5nm channel length where source-to-drain tunneling contributes approximately 35% to the on-state current. We also show that the off-state current is significantly affected by the gate oxide thickness, whereas the influence of varying the oxide dielectric constant on the off-state current was not as pronounced for a 1.5nm oxide thickness. Finally, we show that room temperature operation (T=300K) leads to an excessively high off-state current and a degraded subthreshold slope. For low temperatures, (T=100K), the QB and CB models predicts a seven orders of magnitude difference in the off-state current.

We introduce a continuous family of frustration-free Hamiltonians with exactly solvable ground states. We prove that the ground state of our model is non-degenerate and exhibits a novel quantum phase transition from bounded entan-glement entropy to a massively entangled state with volume entropy scaling. The ground state may be interpreted as a deformation away from the uniform super-position of colored Motzkin paths, showed by Movassagh and Shor [1] to have a large (square-root) but sub-extensive scaling of entanglement into a state with an extensive entropy.

ABSTRACT Using the nanoMOS 2.5 simulator, we study the impact of varying the channel length, gate oxide thickness and dielectric constant, drain voltage, and temperature on the performance of a ballistic nanoscale MOSFET using quantum ballistic and classic ballistic transport models. Our key results show that the quantum ballistic (QB) transport model typically predicts a lower on-state current compared to the classical ballistic (CB) model except for a 5nm channel length where source-to-drain tunneling contributes approximately 35% to the on-state current. We also show that the off-state current is significantly affected by the gate oxide thickness, whereas the influence of varying the oxide dielectric constant on the off-state current was not as pronounced for a 1.5nm oxide thickness. Finally, we show that room temperature operation (T=300K) leads to an excessively high off-state current and a degraded subthreshold slope. For low temperatures, (T=100K), the QB and CB models predicts a seven orders of magnitude difference in the off-state current.

In this thesis, a strategy for constructing electric-magnetic (EM) duality-symmetric N=2 supersymmetric infrared effective actions (IREAs) is presented using harmonic superspace. Our aim is to elevate the EM duality from being equivalent descriptions of distinct IREAs to a symmetry of a single IREA under Sp(2r,Z) transformations. Our strategy is to build the IREA out of geometric objects which are manifestly Sp(2r,Z) invariant. We conjecture that a manifestly EM duality-symmetric action can be constructed in this way on harmonic superspace. The main invariant geometric object is the total space,X, of the Coulomb branch moduli space of the IREA, which has a natural hyperkahler structure, and is thus a suitable manifold to act as the target space of an N=2 supersymmetric nonlinear σ-model (nlsm). We build the IREA as a nlsm with target space the twistor space of X. The twistor space is a fiber bundle with base space the projective line, CP1, and X as fiber. The nlsm action is formed by pulling back the invariant holomorphic two-form on twistor space by the hypermultiplet superfield in harmonic superspace, with the base CP1 identified with the internal CP1 of harmonic superspace. We also conjecture, but do not prove, that the pullback approach introduced in this thesis for constructing the hypermultiplet nlsm is equivalent to using the standard harmonic superspace procedure of constructing the nlsm action using a harmonic-analytic potential for the hypermultiplet superfields.