This project aims to develop a comprehensive simulation testbed for the Boost-Agnostic (BA) hydrodynamic framework. We will implement a suite of numerical simulations to critically assess the predictions of BA theory, particularly in the context of collective motion phenomena such as flocking, swarming, and herding. These simulations will also serve as a versatile computational platform with potential interdisciplinary applications, including crowd dynamics and optimization algorithms.

A key focus is the Toner-Tu model, which effectively describes the large-scale behavior of flocking systems like those generated by the Vicsek model. Previous approaches lacked constraints one might derive from a hydrostatic generating functional. In earlier work, we showed that incorporating such constraints can impose non-trivial structure on transport coefficients. Notably, some coefficients remain invariant under Dynamical Renormalization Group (DRG) flow when noise correlations are fixed. To test this, we will develop a numerical testbed.

Another major component of the project is the development of the first numerical simulations of BA kinetic theory, which models gases of particles governed by generic, non-boost-invariant Hamiltonians. Such solvers will allow us to explore phenomena that include:

• steady state formation under persistent driving,

• domain wall formation in momentum space due to freezing transitions between particles obeying different dispersion relations,

• stochastic switching and coexisting phases in multi-dispersive systems.

By linking non-equilibrium field theory, stochastic dynamics, and real-world applications, "Simulating Swarms, Herds, and Flocks" aims to provide both theoretical insight and practical tools for understanding complex collective systems.

In this project, we explore the emergence and structure of relaxation and steady states in quantum field theories using the tools of gauge/gravity duality. In the past we have worked with Q-lattices and other bottom up models; we are currently interested in probe branes and analogues with a driving electric field. These holographic setups provide an ideal and highly controllable environment in which to study quasihydrodynamic (QH) theories, especially in driven, non-equilibrium regimes.

We are particularly interested in the following topics:

• the thermodynamic and effective field-theoretic structure of QH systems, and

• the instabilities and dynamical phenomena that emerge when such systems are continuously driven.

Probe branes and their analogues are uniquely suited to this investigation for two key reasons:

1. They offer analytic and numerically tractable access to a wide range of observables - including expectation values of currents and charges, two-point correlators, dispersion relations, and transport coefficients.

2. At large charge density and in the presence of strong electric fields, they are known to exhibit quasihydrodynamic behavior about electrically driven steady states, making them natural holographic duals for non-equilibrium systems.

Importantly, by working in the probe limit, we consistently decouple the dynamics of the bulk stress tensor. This allows us to focus on conserved U(1) sectors while truncating out the gravitational backreaction associated with temperature and fluid velocity profiles—simplifying the analysis and isolating the relevant relaxation dynamics.

Our goal is to use this framework to test and extend effective field theories for driven systems. In particular, we will analyze the role of long-lived modes and determine the relevant effective description. Through this, we aim to provide first-principles insight into the stability structure, response functions, and universal features of steady-state systems that lie outside traditional hydrodynamic regimes.

Ultimately, this project aims to connect holography, non-equilibrium effective theory, and real-world driven systems.

In this project, we aim to develop a theoretical framework that reveals how superconductors, long thought to be insensitive to external electric fields, may in fact host rich and measurable non-linear electrodynamic phenomena. Specifically, we investigate whether an analog of the Schwinger effect, originally proposed in the context of quantum electrodynamics (QED), can emerge within Bardeen-Cooper-Schrieffer (BCS) superconductors.

In QED, the Schwinger effect describes the spontaneous production of particle–antiparticle pairs from the vacuum when subjected to a strong electric field. While this effect remains experimentally inaccessible due to the enormous field strengths required (~10¹⁸ V/m), we propose that superconductors provide an accessible condensed matter analog. In these systems, a strong electrostatic field can excite quasiparticles out of the superconducting condensate, thereby weakening or even destroying the superconducting state. That strong electric fields have an effect on the superconductor has been observed experimentally in superconducting transistors, where an applied electric field was found to suppress the critical current - a phenomenon long lacking a satisfactory theoretical explanation.

We suggest that this suppression is not a surface effect or a byproduct of electrostatics, but rather a true dynamical instability akin to vacuum pair creation, now realized in a many-body ground state. Theoretically, this becomes evident through a deep analogy between the Dirac equation (describing relativistic fermions) and the Bogoliubov–de Gennes equations (describing quasiparticles in superconductors). Both admit non-linear dynamics where the vacuum - or condensate - can become unstable under strong external fields.

Our framework further predicts non-linear electrodynamic responses within superconductors, including possible modifications to Maxwell’s equations. These effects can be studied using tools from quantum field theory, adapted to the low-energy, non-relativistic regime of condensed matter. 

Ultimately, this project not only offers a first-principles explanation of recent experimental anomalies, but also proposes that Schwinger-like effects are not exclusive to high-energy physics; they are measurable in a controlled lab setting, through the lens of superconductivity. This opens a new frontier, with implications for quantum technology, nanoelectronics, and the foundational understanding of superconducting systems.

We study critical phenomena and topological phases of matter using tools from quantum field theory, statistical mechanics, and computational physics. Our work centers on systems near second-order phase transitions, where long-range correlations and scale invariance emerge. In this regime, we employ conformal field theories (CFTs) to describe universal features at criticality, using both perturbative approaches (e.g., conformal perturbation theory, renormalization group flows) and non-perturbative techniques such as dualities and exact results in low-dimensional systems.

To complement our analytic work, we use Monte Carlo simulations to test predictions and access strongly coupled regimes. Beyond criticality, we investigate topological quantum field theories (TQFTs), which describe phases of matter that defy the conventional symmetry-breaking paradigm. These include systems with topological order, such as fractional quantum Hall states and topological insulators, where ground-state degeneracy and long-range entanglement play central roles.

By combining theoretical and numerical methods, we aim to uncover the fundamental mechanisms driving emergent macroscopic behavior in complex many-body systems and to build models relevant for quantum materials and topological quantum computing.

A central aim of this project is to develop a systematic framework for multi-scale analysis in boost-agnostic (BA) theories, allowing us to connect microscopic particle dynamics with macroscopic hydrodynamic behavior in driven, non-equilibrium systems.

We begin with the development of BA kinetic theory, a generalization of Hamiltonian mechanics to Aristotelian manifolds, where time and space are fundamentally distinct and boost invariance is absent. This allows for the inclusion of arbitrary dispersion relations, including codominant dispersion structures. This freedom is essential for modeling systems in which different excitations propagate with distinct scaling laws. 

Concurrently, we aim to employ improvements in computer assisted algebra to develop Feyman diagram based renormalization group (RG) methods to track how fluid non-linearities evolve across scales. Crucially, we will show that certain non-linear structures in BA hydrodynamics remain perturbatively stable under RG flow.

This multiscale approach also feeds directly into applied problems. For example, in active matter, we will use our BA formalism to model interactions and instabilities in systems of self-driven particles - incorporating effects from both microscopic collision dynamics and long-wavelength collective motion. Such systems often exhibit emergent transport, spontaneous symmetry breaking, and non-equilibrium phase transitions, all of which require coordinated modeling across multiple scales.

By unifying kinetic theory, effective field theory, and renormalization, this project builds a general-purpose theoretical infrastructure for analyzing complex systems where driving, dissipation, and symmetry breaking interact across length and time scales. In doing so, it offers not only deep theoretical insight but also versatile computational tools that benefit a wide range of domains in modern physics.