Related papers: New Numerical Methods for Iterative or Perturbativ…
Using stochastic quantization method we derive gauge-invariant equations, connecting multilocal vacuum correlators of nonperturbative field configurations immersed into the quantum background. Three alternative methods of stochastic…
This is a collection of various result and notes, addressing the sum-of-squares hierarchy for spin and fermion systems using some ideas from quantum field theory, including higher order perturbation theory, critical phenomena, nonlocal…
The canonical front form Hamiltonian for non-Abelian SU(N) gauge theory in 3+1 dimensions is mapped on an effective Hamiltonian which acts only in the Fock space of one quark and one antiquark. The approach is non-perturbative and exact. It…
Deep neural networks are powerful tools for approximating functions, and they are applied to successfully solve various problems in many fields. In this paper, we propose a neural network-based numerical method to solve partial differential…
This paper proposes a general framework for nonperturbatively defining continuum quantum field theories. Unlike most such frameworks, the one offered here is finitary: continuum theories are defined by reducing large but finite quantum…
A weak Galerkin (WG) finite element method for solving the stationary Stokes equations in two- or three- dimensional spaces by using discontinuous piecewise polynomials is developed and analyzed. The variational form we considered is based…
Simulating the real-time dynamics of quantum field theories (QFTs) is one of the most promising applications of quantum simulators. Regularizing a bosonic QFT for quantum simulation purposes typically involves a truncation in Hilbert space…
Conformal truncation is a powerful numerical method for solving generic strongly-coupled quantum field theories based on purely field-theoretic technics without introducing lattice regularization. We discuss possible speedups for performing…
This thesis develops advanced Tensor Network (TN) methods to address Hamiltonian Lattice Gauge Theories (LGTs), overcoming limitations in real-time dynamics and finite-density regimes. A novel dressed-site formalism is introduced, enabling…
An alternative approach to lattice gauge theory has been under development for the past decade. It is based on discretizing the operator Heisenberg equations of motion in such a way as to preserve the canonical commutation relations at each…
The fermion bag approach is a new method to tackle fermion sign problems in lattice field theories. Using this approach it is possible to solve a class of sign problems that seem unsolvable by traditional methods. The new solutions emerge…
Tensor network methods are a class of numerical tools and algorithms to study many-body quantum systems in and out of equilibrium, based on tailored variational wave functions. They have found significant applications in simulating lattice…
Intrusive Uncertainty Quantification methods such as stochastic Galerkin are gaining popularity, whereas the classical stochastic Galerkin approach is not ensured to preserve hyperbolicity of the underlying hyperbolic system. We apply a…
We couple the L1 discretization for Caputo derivative in time with spectral Galerkin method in space to devise a scheme that solves quasilinear subdiffusion equations. Both the diffusivity and the source are allowed to be nonlinear…
This paper presents a new and unified approach to the derivation and analysis of many existing, as well as new discontinuous Galerkin methods for linear elasticity problems. The analysis is based on a unified discrete formulation for the…
In this review we study quantum field theories and conformal field theories with global symmetries in the limit of large charge for some of the generators of the symmetry group. At low energy the sectors of the theory with large charge are…
In this paper, we describe a numerical technique for the solution of macroscopic traffic flow models on networks of roads. On individual roads, we consider the standard Lighthill-Whitham-Richards model which is discretized using the…
Efficient control of qubits plays a key role in quantum information processing. In the current work, an alternative set of differential equations are derived for an optimal quantum control of single or multiple qubits with or without…
We develop a new method that allows us to map models of interacting fermions onto bosonic models describing collective excitations in an arbitrary dimension. This mapping becomes exact in the thermodynamic continuous time limit. The boson…
High-dimensional transport equations frequently occur in science and engineering. Computing their numerical solution, however, is challenging due to its high dimensionality. In this work we develop an algorithm to efficiently solve the…