The full Schwinger-Dyson tower for random tensor models

We treat random rank-$D$ tensor models as $D$-dimensional quantum field theories---tensor field theories (TFT)---and review some of their non-perturbative methods. We classify the correlation functions of complex tensor field theories by boundary graphs, sketch the derivation of the Ward-Takahashi identity and stress its relevance in the derivation of the tower of exact, analytic Schwinger-Dyson equations for all the correlation functions (with connected boundary) of TFTs with quartic pillow-like interactions.Comment: Proceedings: Corfu 2017 Training School "Quantum Spacetime and Physics Models

Mixed weak type estimates: Examples and counterexamples related to a problem of E. Sawyer

We study mixed weighted weak-type inequalities for families of functions, which can be applied to study classical operators in harmonic analysis. Our main theorem extends the key result from D. Cruz-Uribe, J.M. Martell and C. Perez, Weighted weak-type inequalities and a conjecture of Sawyer, Int. Math. Res. Not., V. 30, 2005, 1849-1871.Comment: Colloquium Mathematicum, to appea

Cellular Automata as a Model of Physical Systems

Cellular Automata (CA), as they are presented in the literature, are abstract mathematical models of computation. In this pa- per we present an alternate approach: using the CA as a model or theory of physical systems and devices. While this approach abstracts away all details of the underlying physical system, it remains faithful to the fact that there is an underlying physical reality which it describes. This imposes certain restrictions on the types of computations a CA can physically carry out, and the resources it needs to do so. In this paper we explore these and other consequences of our reformalization.Comment: To appear in the Proceedings of AUTOMATA 200

What is a quantum computer, and how do we build one?

The DiVincenzo criteria for implementing a quantum computer have been seminal in focussing both experimental and theoretical research in quantum information processing. These criteria were formulated specifically for the circuit model of quantum computing. However, several new models for quantum computing (paradigms) have been proposed that do not seem to fit the criteria well. The question is therefore what are the general criteria for implementing quantum computers. To this end, a formal operational definition of a quantum computer is introduced. It is then shown that according to this definition a device is a quantum computer if it obeys the following four criteria: Any quantum computer must (1) have a quantum memory; (2) facilitate a controlled quantum evolution of the quantum memory; (3) include a method for cooling the quantum memory; and (4) provide a readout mechanism for subsets of the quantum memory. The criteria are met when the device is scalable and operates fault-tolerantly. We discuss various existing quantum computing paradigms, and how they fit within this framework. Finally, we lay out a roadmap for selecting an avenue towards building a quantum computer. This is summarized in a decision tree intended to help experimentalists determine the most natural paradigm given a particular physical implementation

Tornadoes in a Microchannel

In non-dilute colloidal suspensions, gradients in particle volume fraction result in gradients in electrical conductivity and permittivity. An externally applied electric field couples with gradients in electrical conductivity and permittivity and, under some conditions, can result in electric body forces that drive the flow unstable forming vortices. The experiments are conducted in square 200 micron PDMS microfluidic channels. Colloidal suspensions consisted of 0.01 volume fraction of 2 or 3 micron diameter polystyrene particles in 0.1 mM Phosphate buffer and 409 mM sucrose to match particle-solution density. AC electric fields at 20 Hz and strength of 430 to 600 V/cm were used. We present a fluid dynamics video that shows the evolution of the particle aggregation and formation of vortical flow. Upon application of the field particles aggregate forming particle chains and three dimensional structures. These particles form rotating bands where the axis of rotation varies with time and can collide with other rotating bands forming increasingly larger bands. Some groups become vortices with a stable axis of rotation. Other phenomena showed include counter rotating vortices, colliding vortices, and non-rotating particle bands with internal waves