Related papers: Discrete Variable Representation method in the stu…
We consider a variational problem for the two-dimensional (2D) Heisenberg and XY models, using a trial state which is constructed as a 2D product of local weights. Variational energy is calculated by use of the the corner transfer matrix…
The two-electron reduced density matrix (2RDM) carries enough information to evaluate the electronic energy of a many-electron system. The variational 2RDM (v2RDM) approach seeks to determine the 2RDM directly, without knowledge of the wave…
Besides perturbation theory (which clearly requires the knowledge of the exact unperturbed solution), variational techniques represent the main tool for any investigation of the eigenvalue problem of some semibounded operator H in quantum…
We develop a nondirect product discrete variable representation (npDVR) for treating quantum dynamical problems which involve nonseparable angular variables. The npDVR basis is constructed on spherical functions orthogonalized on the grids…
Variational representations of quantum states abound and have successfully been used to guess ground-state properties of quantum many-body systems. Some are based on partial physical insight (Jastrow, Gutzwiller projected, and fractional…
This paper presents a fortran program to solve diverse few-body problems with the stochastic variational method. Depending on the available computational resources the program is applicable for $N=2-3-4-5-6-...$-body systems with $L=0$…
We examine the procedure to construct the variables of use for the momentum representation in quantum mechanics. The momentum variables must be chosen properly conjugate to the corresponding position space variables, such that valid…
In this thesis the variational optimisation of the density matrix is discussed as a method in many-body quantum mechanics. This is a relatively unknown technique in which one tries to obtain the two-particle reduced density matrix directly…
Methods of quantum nuclear wave-function dynamics have become very efficient in simulating large isolated systems using the time-dependent variational principle (TDVP). However, a straightforward extension of the TDVP to the density matrix…
We present a numerical implementation of the density matrix renormalization group (DMRG) using the discrete variable representation (DVR) basis set. One main advantage of using the local DVR basis sets is that the computations of…
The variational two-electron reduced density matrix (v2RDM) method is generalized for the description of total angular momentum ($J$) and projection of total angular momentum ($M_{J}$) states in atomic systems described by non-relativistic…
In this work, we present a stochastic variational calculation (SVM) of energies and wave functions of few particle systems coupled to quantum fields in cavity QED. The light-matter coupled system is described by the Pauli-Fierz Hamiltonian.…
For a wide class of Hamiltonians, a novel method to obtain lower and upper bounds for the lowest energy is presented. Unlike perturbative or variational techniques, this method does not involve the computation of any integral (a…
We analyze the method for calculation of properties of non-relativistic quantum systems based on exact diagonalization of space-discretized short-time evolution operators. In this paper we present a detailed analysis of the errors…
Energy distributions of high frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics,…
Solving non-Hermitian quantum many-body systems on a quantum computer by minimizing the variational energy is challenging as the energy can be complex. Here, based on energy variance, we propose a variational method for solving the…
Here we present a many-body theory based on a solution of the $N$-representability problem in which the ground-state two-particle reduced density matrix (2-RDM) is determined directly without the many-particle wave function. We derive an…
Relativistic treatments of quantum mechanical systems are important for understanding hadronic structure and dynamics at sub-nucleon distance scales. Hadronic states in different inertial reference frames are needed to compute current…
Slater determinants have underpinned quantum chemistry for nearly a century, yet their full potential has remained challenging to exploit. In this work, we show that a variational wavefunction composed of a few hundred optimized…
We develop a computationally and numerically efficient method to calculate binding energies and corresponding wave functions of quantum mechanical three-body problems in low dimensions. Our approach exploits the tensor structure of the…