Related papers: A New Approach to Numerical Quantum Field Theory
We present a novel Galerkin method for solving partial differential equations on the sphere. The problem is discretized by a highly localized basis which is easily constructed. The stiffness matrix entries are computed by a recently…
The light-cone approach is reviewed. This method allows to find the underlying quantum field theory for any integrable lattice model in its gapless regime. The relativistic spectrum and S-matrix follows straightforwardly in this way through…
Problems in lattice gauge models with fermions are discussed. A new bosonic Hermitean effective action for lattice QCD with dynamical quarks is presented. In distinction of the previous version, it does not include constraints and is better…
We present a new approach to some four-fermion lattice field theories which we call the generalized fermion bag approach. The basic idea is to identify unpaired fermionic degrees of freedom that cause sign problems and collect them in a…
A nonlocal method to obtain discrete classical fields is presented. This technique relies on well-behaved matrix representations of the derivatives constructed on a non--equispaced lattice. The drawbacks of lattice theory like the fermion…
Quantum Monte Carlo method is applied to fractional quantum Hall systems. The use of the linear programming method enables us to avoid the negative-sign problem in the Quantum Monte Carlo calculations. The formulation of this method and the…
Neural networks are increasingly recognized as a powerful numerical solution technique for partial differential equations (PDEs) arising in diverse scientific computing domains, including quantum many-body physics. In the context of…
In Monte Carlo calculations of expectation values in lattice quantum field theories, the stochastic variance of the sampling procedure that is used defines the precision of the calculation for a fixed number of samples. If the variance of…
We introduce a classical computational method for quantum dynamics that relies on a global-in-time variational principle. Unlike conventional time-stepping approaches, our scheme computes the entire state trajectory over a finite time…
The functional Schrodinger picture formulation of quantum field theory and the variational Gaussian approximation method based on the formulation are briefly reviewed. After presenting recent attempts to improve the variational…
By putting a confined inter source, we construct a model which can give us convergent solution from free field equation. On the other hand, the solution of new field equation can be separated into two parts, one part is just same as the one…
We propose a numerical method of estimating various physical quantities in lattice (supersymmetric) quantum mechanics. The method consists only of deterministic processes such as computing a product of transfer matrix, and has no…
We define a natural coarse-graining procedure which can be applied to any closed equilibrium quantum system described by a density matrix ensemble and we show how the coarse-graining leads to the Gaussian and canonical ensembles. After this…
In the last years, chiral effective field theory has been successfully developed for and applied to systems with few nucleons. Here, I present a new approach for ab initio calculations of nuclei that combines these precise and systematic…
In this work we introduce a worldline based fermion Monte Carlo algorithm for studying few body quantum mechanics of self-interacting fermions in the Hamiltonian lattice formulation. Our motivation to construct the method comes from our…
In this paper, numerical solutions of singularly perturbed boundary value problems are given by using variants of finite element method. Both Galerkin and subdomain Galerkin method based on quadratic B-spline functions are applied over the…
In this paper, we discover a new quantum Monte Carlo (QMC) method to solve the fermion sign problem in interacting fermion models by employing Majorana representation of complex fermions. We call it "Majorana QMC" (MQMC). Especially, MQMC…
Quantum Toda lattice may solved by means of the Representation Theory of semisimple Lie groups, or alternatively by using the technique of the Quantum Inverse Scattering Method. A comparison of the two approaches, which is the purpose of…
We study uncertainty quantification for a Boltzmann-Poisson system that models electron transport in semiconductors and the physical collision mechanisms over the charges. We use the stochastic Galerkin method in order to handle the…
Aiming at evading the notorious sign problem in classical Monte-Carlo approaches to lattice quantum chromodynamics, we present an approach for quantum computing finite-temperature lattice gauge theories at non-zero density. Based on the…