Physics Lecture Notes
2017
A Conceptual Introduction to Quantum Fields on a Lattice (pdf)
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Abstract
Topics covered include: fermion doubling and the ways around it, the Nielsen-Ninomiya theorem, Wilson loops, the gauge-invariant Haar measure.
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2018
Physics Bits #1 (pdf)
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Abstract
A collection of short (to varying degrees), technical yet maximally simple explanations for established concepts, effects and principles in various subfields of physics: from classical mechanics to quantum field theory.​
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2019
Physics Bits #2 (pdf)
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Abstract
A collection of short (to varying degrees), technical yet maximally simple explanations for established concepts, effects and principles in various subfields of physics: from classical mechanics to quantum field theory.​
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2019
A Conceptual Introduction to Modified Newtonian Dynamics (pdf)
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Abstract
I show that at least phenomenologically, Milgrom's formula follows from the observed flatness of rotation curves and the Tully-Fisher Law. I motivate proposed microscopic theories explaining Milgrom's law, showing how each modification is required to account for the experimental failure of its predecessors. Topics covered include: MOND, AQUAL, RAQUAL, TeVeS and their observational tests.
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2019
A Conceptual Introduction to Biological Network Motifs and Their Evolution (pdf)
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Abstract
In the first three parts of the lecture, I introduce Uri Alon's theory of network motifs in biological systems. In the fourth part, I propose a model for their evolution. I argue that since the motifs appear to be universal and to perform simple dynamical functions, they should arise regardless of specific details, simply because of the need of an organism to adapt itself to temporal patterns in its environment. I thus propose an evolutionary model in which the rate of reproduction depends on the similarity between an internal variable (e.g., the concentration of some protein) and an external, noise-like variable with some temporal correlations. When considering the simplest possible nontrivial noise (constant time-correlations), and for the rather narrow class of three node networks with a tree-like structure and given activation rates, I argue that a coherent feedforward loop with an AND gate evolves.
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2020
A Conceptual Introduction to Objective Collapse Models​ (pdf)
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Abstract
It is argued that, in a sense, quantum mechanics has no classical limit, and that fixing this requires nonlinearity. However, it is shown that nonlinearity usually allows superluminal signaling (and it is explained why this is a severe physical problem). The known class of models that overcome this are presented. Topics covered include: the QMUPL model, the CSL model, the Lindblad euqation, the process of measurement, experimental consequences and bounds.
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2020
A Conceptual Introduction to the KPZ Model​ (pdf)
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Abstract
Topics covered include: the superdiffusive propagation of fluctuations in surface growth and the nonlinearity it entails, the many faces of the KPZ equation, the exact 1D solution and the physics behind it, the renormalization group in a nutshell.
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2020
A Conceptual Introduction to Parallel Plane-Fronted Gravitational Waves​ (pdf)
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Abstract
Topics covered include: Generalized superposition principle for nonlinear matter and gravitational waves; the transformation to Brinkmann coordinates in the linearized and nonlinear theory; the Penrose limit; gravitational field generated by a photon and its effects on a passing particle.
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2020
A Conceptual Introduction to Matrix Models of 2D Quantum Gravity​ (pdf)
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Abstract
Topics covered include: The triviality of the Einstein-Hilbert action in two dimensions; the Liouville action and its relation to the Weyl anomaly; triangulations of spacetime and their matrix duals; the large N and continuum limit; the propagating matrix model, its interpretation in terms of fermions and critical behavior.
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2021
A Conceptual Introduction to the Integer Quantum Hall Effect (pdf)
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Abstract
Topics covered include: Spectral flow on a ring; Landau levels, spectral flow of Landau levels; the Kubo formula, quantization of Hall conductivity on a lattice; composite fermions.