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Many physical problems such as Allen-Cahn flows have natural maximum principles which yield strong point-wise control of the physical solutions in terms of the boundary data, the initial conditions and the operator coefficients.…
We propose a novel idea to construct an effective interaction under energy-density-functional (EDF) theories which is adaptive to the enlargement of the model space. Guided by effective field theory principles, iterations of interactions as…
In mathematics or theoretical physics one is often interested in obtaining an exact analytic description of some data which can be produced, in principle, to arbitrary accuracy. For example, one might like to know the exact analytical form…
We reinvestigate the large degeneracy solution of the multichannel Kondo problem, and show how in the universal regime the complicated integral equations simplifying the problem can be mapped onto a first order differential equation. This…
In the first part of this paper, we apply a well known discrete-to-continuum approach to a Frenkel-Kontorova-type model of an infinitely long one-dimensional chain of atoms weakly interacting with a line of fixed atoms. The rescaled model…
Downfolding coupled cluster (CC) techniques are powerful tools for reducing the dimensionality of many-body quantum problems. This work investigates how ground-state downfolding formalisms can target excited states using non-Aufbau…
We describe a new technique for computing lower-bounds on the minimum energy configuration of a planar Markov Random Field (MRF). Our method successively adds large numbers of constraints and enforces consistency over binary projections of…
The stability, robustness, accuracy, and efficiency of space-time finite element methods crucially depend on the choice of approximation spaces for test and trial functions. This is especially true for high-order, mixed finite element…
The formalism based on correlated basis functions and the cluster expansion technique has been recently employed to derive an effective interaction from a realistic nuclear hamiltonian. To gauge the reliability of this scheme, we perform a…
The numerical solution of the many-body problem of interacting electrons and ions is a key challenge in condensed matter physics, chemistry, and materials science. Traditional methods to solve the multi-component quantum Hamiltonian are…
We project the Wilson/Polchinski renormalization group equation onto its uniform external field dependent effective free energy and connected Green's functions. The result is a hierarchy of equations which admits a choice of "natural"…
In this work we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the…
The ever-increasing parameter counts of deep learning models necessitate effective compression techniques for deployment on resource-constrained devices. This paper explores the application of information geometry, the study of…
It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…
Ground-state Kohn-Sham density functional theory provides, in principle, the exact ground-state energy and electronic spin-densities of real interacting electrons in a static external potential. In practice, the exact density functional for…
I discuss many-body models for interacting fermions in two space dimensions which can be solved exactly using group theory. The simplest example is a model of a quantum Hall system: 2D fermions in a constant magnetic field and a particular…
We treat low-energy $^3$He-$\alpha$ elastic scattering in an Effective Field Theory (EFT) that exploits the separation of scales in this reaction. We compute the amplitude up to Next-to-Next-to-Leading Order (NNLO), developing a hierarchy…
We analyze the renormalization of systems whose effective degrees of freedom are described in terms of fluctuations which are ``environment'' dependent. Relevant environmental parameters considered are: temperature, system size, boundary…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
Effective field theory (EFT) is generalized to investigate the rotational motion of triaxially deformed even-even nuclei. A Hamiltonian, called the triaxial rotor model (TRM), is obtained up to next-to-leading order (NLO) within the EFT…