Has the Local Area Network (LAN) the Same Characteristics With the Particle/field Entity? Recovering the Schwarzschild Metric in a Discrete and Flat Spacetime, Using a Diffusion-driven Impurity Model Produced by Partile/LAN Entities.

A local area network (LAN) consists typically of several telecommunication nodes, all of which share a public IP address and a single point of contact with the Internet, namely the router. For an outside observer, the whole LAN with all its nodes would look point-like (having one, shared, "public IP" address and a single connection with the Internet), but in its interactions it would appear field-like, as a LAN of several nodes, each with its own "private IP" address, has an internal structure and interacts with the outside world differently than a single node would. In this study, the above particle/LAN analogy will be used as a basis of Átmiton theory, according to which, elementary particles are made of LANs consisting of a type of telecommunication node - called átmiton - and space is a 3D network of átmita with the simple cubic topology. In this work, it is demonstrated that connecting a particle/LAN entity on the lattice of space distorts its local topology, effectively introducing a crystal defect to the lattice of space. This defect increases the distance between points lying at opposite sides of it. The internal interactions of any massive object should be producing constantly copious numbers of such space-defects, which diffuse away from their source, by means of a random walk. Here it is suggested that general relativity's notion of spacetime's curvature is equivalent to the aforementioned diffusion-driven impurity model in the flat, discrete lattice of space of Átmiton theory. Their equivalency is demonstrated for the specific case of a spherical mass, around which the Schwarzschild metric is shown to be valid.

Hidden Moments

This chapter traces Anderson’s work from his invention of an impurity model to understand the fate of a magnetic atom immersed in a non-magnetic metal to his solution of the Kondo problem using an early version of the renormalization group invented by him and later generalized by Ken Wilson. Important events on this path are the experimental impetus provided by Bernd Matthias, the Coulomb repulsion model of insulating behavior due to Nevill Mott, and Jacques Friedel’s ideas about treating atoms embedded in metals. Speculation is offered about the award of the 1977 Nobel Prize to Anderson, Mott, and Van Vleck.

Time dependent reduced density matrix functional theory at strong correlation: insights from a two-site Anderson impurity model

The one-body density matrix has recently attracted considerable attention as promising key quantity for the description of systems out of equilibrium. Its time evolution is given in terms of the...

Maximally Localized Dynamical Quantum Embedding for Solving Many-Body Correlated Systems

We present a quantum embedding methodology to resolve the Anderson impurity model in the context of dynamical mean-field theory, based on an extended exact diagonalization method. Our method provides a maximally localized quantum impurity model, where the non-local components of the correlation potential remain minimal. This comes at a large benefit, as the environment used in the quantum embedding approach is described by propagating correlated electrons and hence offers an exponentially increasing number of degrees of freedom for the embedding mapping, in contrast to traditional free-electron representation where the scaling is linear. We report that quantum impurity models with as few as 3 bath sites can reproduce both the Mott transition and the Kondo physics, thus opening a more accessible route to the description of time-dependent phenomena. Finally, we obtain excellent agreement for dynamical magnetic susceptibilities, poising this approach as a candidate to describe 2-particle excitations such as excitons in correlated systems. We expect that our approach will be highly beneficial for the implementation of embedding algorithms on quantum computers, as it allows for a fine description of the correlation in materials with a reduced number of required qubits.