Original Research Papers
2018
On the Irreversible Approach to Reversibility: a Field Theory of Random Organization (pdf)
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Abstract
Colloids disperesed in viscous fluids sheared peridoically exhibit a second-order phase transition from asymptoitc reversiblity to asymptotic irreversibility. The order parameter of the transition is the asymptotic activity (fraction of active particles). In addition to the usual diverging correlation length, the vicinity of the transition is characterized by a diverging relaxation time of the macroscopic activity. I assume that the particles tend to move along flow lines but are repelled via a short range potential. To study the transition, I coarse-grain over short lengthscales and timescales to obtain a universal field theory directly from the microscopic model. The field thoery is shown to reproduce the qualitative behavior of the transition, and predicts critical exponents consistent with experimental measurements. It is argued that diffusion is relevant at the critical point where particles still randomly organize, providing a possible explanation for random organization. (Note (2020): This explanation is incorrect, as explained in the 2019 paper on absorbing state phase-transition. A consistent explanation must involve noise, and is provided in the aforementioned 2019 paper.)
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2018-2019
Notes on a Bunch of Stuff: Gravity From Dynamically Deformed Lattices; Quantum Theory From Dynamically Structured Lattices (pdf)
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Abstract
A spacetime lattice is proposed as a remedy for UV divergences, as has been done by many earlier authors. Lorentz invariance requires that the lattice be dynamical, which is shown to give rise to general relativity in the classical continuum limit, with lattice vectors giving rise to tetrads and angles between lattice sites giving rise to the connection. An analogous dynamical discretization of fields with internal symmetries is performed, arguably leading to gauge symmetries. An attempt to quantize the theory using the path integral formalism is made, and it is argued that to reproduce the correct continuum limit one must modify the action to energetically favor fluctuations in the spin-1 degrees of freedom of lattice vectors. To make the gravitational degrees of freedom themselves discrete, the Lorentz group is compactified by making it nonlinear.
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Based on the holographic principle, I argue, as did 't Hooft, that lattice sites must be encoded on on a two dimensional boundary. However, any way to slice a three dimensional object into a surface will generate nonlocalities—there is no way to preserve all nearest neighbors (assuming a point-to-point mapping between two and three dimensions). Moreover, such a slicing violates symmetries of three dimensional space (e.g., translational invarince along the direction that has been eliminated), Hence, I propose that no matter how performs the slicing, the result should remain unchanged—there is an exact symmetry under the interchange of any two points, no matter how far apart. This introduces a strong form of nonlocality, coined dislocality. Locality in the continuum limit is restored by dynamically breaking the relabelling symmetry, making a point interact more strongly with some points than with some other points based on degrees of freedom on the point. It is argued that “classical” models with such an interchange symmetry are an exact mean field theory and thus reproduce quantum mechanical configuration space, and by an appropriate choice of dynamics can be made to reproudce quantum mechanics in an appropriate limit. One specific class of such models is proposed, and is argued to reproduce the Born rule through a dynamical collapse of the emergent wavefunction.
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2019
Absorbing State Phase Transitions: Diverging From Microscopy to Macroscopy (pdf)
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Abstract
The mean field theory of random organization from [5] is reintroduced. I discuss the incorporation of noise into the field theory. I argue that when noise is considered, the model provides a natural explanation for hyperuniformity: at the critical density, noise persists so long as the distribution is non-uniform. To make this explanation more quantitative, I consider two toy models for fluctuations about uniformity and show that they asymptote to a uniform configuration. I extend the discussion to absorbing state phase transitions of colliding particles with nontrivial conservation laws. I show that on the mean-field level, all such transitions can be mapped to one another, possibly suggesting a reason why they are found to exhibit the same critical exponents in [4].
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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
The Quantum Limit of Classical Mechanics (pdf)
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Abstract
I discuss models that reproduce quantum mechanics in an appropriate limit, despite having no configuration space and in this sense being “classical.” The models cannot reproduce the exponential scaling of the number of degrees of freedom in the number of particles for arbitrarily large systems, and thus involve some truncation of such degrees of freedom. However, the exponential scaling observed in small-scale quantum experiments requires the introduction of hidden degrees of freedom. Three concrete models are presented: The first accounts for the excess of degrees of freedom by high-derivative fields, which is essentially a field-theoretic generalization of matrix product states; the second accounts for them through U(n) matrix indices; the third through structure fluctuations of extended objects.