I have dedicated most of my research to exploring the foundational principles underpinning physical theories, emphasizing the integration of mathematical tools across various sub-disciplines and energy scales.
I am focused primarily on refining the concept of locality within field theories and establishing a rigorous mathematical framework for studying nonlocality. Concurrently, I am exploring potential solutions to the black hole information paradox, leveraging the methodologies of algebraic quantum field theory and geometric analysis.
Outside of physics, I am interested in both the formal aspects and the practice of statistical learning theory, especially in the realm of quantitative finance. I have a particular fondness of applying differentiable programming techniques in adaptive, domain specific ways.
My current ongoing personal projects focus on modeling information-time volatility dynamics and price-discovery with self-growing tensor networks, time-nonlocal feature engineering and optimal transport in the contexts of risk and arbitrage.
Bora Basa, Gabriele La Nave, and Philip W. Phillips
Phys. Rev. B 106, 125109 – Published 9 September 2022
The topological nontriviality of insulating phases of matter are by now well understood through topological K theory where the indices of the Dirac operators are assembled into topological classes. We consider in the context of the Kitaev chain a notion of a generalized Dirac operator where the associated Clifford algebra is centrally extended. We demonstrate that the central extension is achieved via taking rational operator powers of Pauli matrices that appear in the corresponding BdG Hamiltonian. Doing so introduces a pseudometallic component to the topological phase diagram within which the winding number is valued in $\mathbb Q$. We find that this phase hosts a mode that remains extended in the presence of weak disorder, motivating a topological interpretation of a nonintegral winding number. We remark that this is in correspondence with recent paper demonstrating that projective Dirac operators defined in the absence of $\text{spin}^\mathbb C$ structure have rational indices.
Bora Basa, Gabriele La Nave, and Philip W. Phillips
preprint arXiv:2011.04662
Using the recently developed fractional Virasoro algebra, we construct a class of nonlocal CFTs with graded OPEs that lead to a state-dependent central charge. Our work indicates that only those theories which are nonlocal have state-dependent central charges, regardless of the pseudo-differential operator content of their action. All others, including certain fractional Laplacian theories, can be mapped onto an equivalent local one using a suitable covering/field redefinition. In addition, we discuss various perturbative implications of deformations of fractional CFTs that realize a fractional Virasoro algebra through the lense of a degree/state-dependent refinement of the 2 dimensional C-theorem.
Bora Basa, Gabriele La Nave, and Philip W. Phillips
Phys. Rev. D 101, 106006 – Published 6 May 2020
From the partition function for two classes of classically nonlocal actions containing the fractional Laplacian, we show that as long as there exists a suitable (nonlocal) Hilbert-space transform the underlying action can be mapped onto a purely local theory. In all such cases the partition function is equivalent to that of a local theory and an area law for the entanglement entropy obtains. When such a reduction fails, the entanglement entropy deviates strongly from an area law and can in some cases scale as the volume. As these two criteria are coincident, we conjecture that they are equivalent and provide the ultimate test for locality of Gaussian theories rather than a simple inspection of the explicit operator content.
Mark R Hirsbrunner, Timothy M Philip, Bora Basa, Youngseok Kim, Moon Jip Park and Matthew J Gilbert
Reports on Progress in Physics, 2019- Published 5 March 2019
As experimental probes have matured to observe ultrafast transient and high frequency responses of materials and devices, so to have the theoretical methods to numerically and analytically simulate time- and frequency-resolved transport. In this review article, we discuss recent progress in the development of the time-dependent and frequency-dependent non-equilibrium Green function (NEGF) technique. We begin with an overview of the theoretical underpinnings of the underlying Kadanoff–Baym equations and derive the fundamental NEGF equations in the time and frequency domains. We discuss how these methods have been applied to a variety of condensed matter systems such as molecular electronics, nanoscale transistors, and superconductors. In addition, we survey the application of NEGF in fields beyond condensed matter, where it has been used to study thermalization in ultra-cold atoms and to understand leptogenesis in the early universe. Throughout, we pay special attention to the challenges of incorporating contacts and interactions, as the NEGF method is uniquely capable of accounting for such features.
Moon Jip Park, Bora Basa, and Matthew J. Gilbert
Phys. Rev. B 95, 094201 – Published 2 March 2017
Weyl semimetals are a newly discovered class of materials that host relativistic massless Weyl fermions as their low-energy bulk excitations. Among this new class of materials, there exist two general types of semimetals that are of particular interest: type-I Weyl semimetals, which have broken inversion or time-reversal symmetry, and type-II Weyl semimetals, which additionally break Lorentz invariance. In this work, we use the Born approximation to analytically demonstrate that the type-I Weyl semimetals may undergo a quantum phase transition to type-II Weyl semimetals in the presence of the finite charge and magnetic disorder when nonzero tilt exists. The phase transition occurs when the disorder renormalizes the topological mass, thereby reducing the Fermi velocity near the Weyl cone below the tilt of the cone. We also confirm the presence of the disorder-induced phase transition in Weyl semimetals by using exact diagonalization of a three-dimensional tight-binding model to calculate the resultant phase diagram of the type-I Weyl semimetal.