Short Range Interactions in the Hydrogen Atom

In calculating the energy corrections to the hydrogen levels we can identify two different types of modifications of the Coulomb potential $V_{C}$, with one of them being the standard quantum electrodynamics corrections, $\delta V$, satisfying $\left|\delta V\right|\ll\left|V_{C}\right|$ over the whole range of the radial variable $r$. The other possible addition to $V_{C}$ is a potential arising due to the finite size of the atomic nucleus and as a matter of fact, can be larger than $V_{C}$ in a very short range. We focus here on the latter and show that the electric potential of the proton displays some undesirable features. Among others, the energy content of the electric field associated with this potential is very close to the threshold of $e^+e^-$ pair production. We contrast this large electric field of the Maxwell theory with one emerging from the non-linear Euler-Heisenberg theory and show how in this theory the short range electric field becomes smaller and is well below the pair production threshold

The geometric tensor for classical states

We use the Liouville eigenfunctions to define a classical version of the geometric tensor and study its relationship with the classical adiabatic gauge potential (AGP). We focus on integrable systems and show that the imaginary part of the geometric tensor is related to the Hannay curvature. The singularities of the geometric tensor and the AGP allows us to link the transition from Arnold-Liouville integrability to chaos with some of the mathematical formalism of quantum phase transitions

The Schwinger action principle for classical systems

We use the Schwinger action principle to obtain the correct equations of motion in the Koopman-von Neumann operational version of classical mechanics. We restrict our analysis to non-dissipative systems and velocity-independent forces. We show that the Schwinger action principle can be interpreted as a variational principle in these special cases

Projective representation of the Galilei group for classical and quantum-classical systems

A physically relevant unitary irreducible non-projective representation of the Galilei group is possible in the Koopman-von Neumann formulation of classical mechanics. This classical representation is characterized by the vanishing of the central charge of the Galilei algebra. This is in contrast to the quantum case where the mass plays the role of the central charge. Here we show, by direct construction, that classical mechanics also allows for a projective representation of the Galilei group where the mass is the central charge of the algebra. We extend the result to certain kind of quantum-classical hybrid systems

Reconfigurable interconnects in DSM systems: a focus on context switch behavior

Recent advances in the development of reconfigurable optical interconnect technologies allow for the fabrication of low cost and run-time adaptable interconnects in large distributed shared-memory (DSM) multiprocessor machines. This can allow the use of adaptable interconnection networks that alleviate the huge bottleneck present due to the gap between the processing speed and the memory access time over the network. In this paper we have studied the scheduling of tasks by the kernel of the operating system (OS) and its influence on communication between the processing nodes of the system, focusing on the traffic generated just after a context switch. We aim to use these results as a basis to propose a potential reconfiguration of the network that could provide a significant speedup

Adiabatic driving and parallel transport for parameter-dependent Hamiltonians

We use the Van Vleck-Primas perturbation theory to study the problem of parallel transport of the eigenvectors of a parameter-dependent Hamiltonian. The perturbative approach allows us to define a non-Abelian connection $\mathcal{A}$ that generates parallel translation via unitary transformation of the eigenvectors. It is shown that the connection obtained via the perturbative approach is an average of the Maurer-Cartan 1-form of the one-parameter subgroup generated by the Hamiltonian. We use the Yang-Mills curvature and the non-Abelian Stokes' theorem to show that the holonomy of the connection $\mathcal{A}$ is related to the Berry phase