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A nonlinear parabolic equation of sixth order is analyzed. The equation arises as a reduction of a model from quantum statistical mechanics, and also as the gradient flow of a second-order information functional with respect to the…
We describe in detail a simple and efficient Green Function Monte Carlo technique for computing both the ground state energy and the ground state properties by the ``forward walking'' scheme. The simplicity of our reconfiguration process,…
Classical density-functional theory provides an efficient alternative to molecular dynamics simulations for understanding the equilibrium properties of inhomogeneous fluids. However, application of density-functional theory to multi-site…
We propose a density functional to find the ground state energy and density of interacting particles, where both the density and the pair density can adjust in the presence of an inhomogeneous potential. As a proof of principle we formulate…
Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…
We develop an analytical and numerical framework based on the disentanglement approach to study the ground states of many-body quantum spins systems. In this approach, observables are expressed as functional integrals over scalar fields,…
Groundwater flow in Washington DC greatly influences the surface water quality in urban areas. The current methods of flow estimation, based on Darcy's Law and the groundwater flow equation, can be described by the diffusion equation (the…
Block-Oriented Nonlinear (BONL) models, particularly Wiener models, are widely used for their computational efficiency and practicality in modeling nonlinear behaviors in physical systems. Filtering and smoothing methods for Wiener systems,…
Classical density functional theory (DFT) is a powerful framework to study inhomogeneous fluids. Its standard form is based on the knowledge of a generating free energy functional. If this is known exactly, then the results obtained by…
Following an approach based on generating function method phase space characteristics of Landau system are studied in the autonomous framework of deformation quantization. Coherent state property of generating functions is established and…
The $L^2$ gradient flow of the Ginzburg-Landau free energy functional leads to the Allen Cahn equation that is widely used for modeling phase separation. Machine learning methods for solving the Allen-Cahn equation in its strong form suffer…
The quasiprobability distribution of the discrete Wigner function provides a complete description of a quantum state and is, therefore, a useful alternative to the usual density matrix description. Moreover, the experimental quantum state…
This paper establishes the applicability of density functional theory methods to quantum computing systems. We show that ground-state and time-dependent density functional theory can be applied to quantum computing systems by proving the…
Diagrammatic summation is a common bottleneck in modern applications of projected entangled-pair states, especially in computing low-energy excitations of a two-dimensional quantum many-body system. To solve this problem, here we extend the…
The recently developed Wigner functional theory is used to formulate an evolution equation for arbitrary multi-photon states, propagating through a turbulent atmosphere under arbitrary conditions. The resulting evolution equation, which is…
In this paper, we analyze the polymer representation of the real-valued scalar field theory within the deformation quantization formalism. Specifically, we obtain the polymer Wigner functional by taking the limit of Gaussian measures in the…
A Density Matrix Functional theory is constructed semi-empirically for the two-level Lipkin model. This theory, based on natural orbitals and occupation numbers, is shown to provide a good description for the ground state energy of the…
We present a method to compute the many-body real-time Green's function using an adaptive variational quantum dynamics simulation approach. The real-time Green's function involves the time evolution of a quantum state with one additional…
This paper introduces a new Windowed Green Function (WGF) method for the numerical integral-equation solution of problems of electromagnetic scattering by obstacles in presence of dielectric or conducting half-planes. The WGF method, which…
In this work we have explored few tools in Quantum State Tomography for Continuous Variable Systems. The concept of quantum states in phase space representation is introduced in a simple manner by using a few statistical concepts. Unlike…