Related papers: Smooth Boundary Conditions For Quantum Lattice Sys…

An efficient new method is presented to calculate the quantum transports using periodic boundary conditions. This new method is based on a method we developed previously, but with an essential change in solving the Schrodinger's equation.…

Hybrid Monte Carlo (HMC) simulations of lattice gauge theories with fermionic matter rely on the invertibility of the lattice Dirac operator. Near-zero modes of the latter can therefore significantly slow down the update algorithm and cause…

We discuss the role of boundary conditions in determining the physical content of the solutions of the Schrodinger equation. We study the standing-wave, the ``in,'' the ``out,'' and the purely outgoing boundary conditions. As well, we…

Two-particle lattice states are important for physics of magnetism, superconducting oxides, and cold quantum gases. The quantum-mechanical lattice problem is exactly solvable for finite-range interaction potentials. A two-body Schroedinder…

We present an approach for the semiclassical treatment of open quantum systems. An expansion into localized states allows restriction of a simulation to a fraction of the environment that is located within a predefined vicinity of the…

Recently, Murthy et al. [2017] and Escande et al. [2020] adopted the Lattice Boltzmann Method (LBM) to model the linear elastodynamic behaviour of isotropic solids. The LBM is attractive as an elastodynamic solver because it can be…

This paper explores the feasibility of quantum simulation for partial differential equations (PDEs) with physical boundary or interface conditions. Semi-discretisation of such problems does not necessarily yield Hamiltonian dynamics and…

Lees Edwards boundary conditions (LEbc) for Molecular Dynamics simulations are an extension of the well known periodic boundary conditions and allow the simulation of bulk systems in a simple shear flow. We show how the idea of LEbc can be…

Lattice quantum chromodynamics calculations of multi-baryon systems with physical quark masses would start a new age of ab initio predictions in nuclear physics. Performed on a finite grid, such calculations demand extrapolation of their…

We discuss designer Hamiltonians---lattice models tailored to be free from sign problems ("de-signed") when simulated with quantum Monte Carlo methods but which still host complex many-body states and quantum phase transitions of interest…

The problem of choice of boundary conditions are discussed for the case of numerical integration of the shallow water equations on a substantially irregular relief. In modeling of unsteady surface water flows has a dynamic boundary…

Bandlimited approaches to quantum field theory offer the tantalizing possibility of working with fields that are simultaneously both continuous and discrete via the Shannon Sampling Theorem from signal processing. Conflicting assumptions in…

We discuss conditions for the absence of spontaneous breakdown of continuous symmetries in quantum lattice systems at $T=0$. Our analysis is based on Pitaevskii and Stringari's idea that the uncertainty relation can be employed to show…

Phase transitions in a non-perturbative regime can be studied by ab initio Lattice Field Theory methods. The status and future research directions for LFT investigations of Quantum Chromo-Dynamics under extreme conditions are reviewed,…

Specifying boundary conditions continues to be a challenge in numerical relativity in order to obtain a long time convergent numerical simulation of Einstein's equations in domains with artificial boundaries. In this paper, we address this…

Quantum computing holds great promise to accelerate scientific computations in fluid dynamics and other classical physical systems. While various quantum algorithms have been proposed for linear flows, developing quantum algorithms for…

We consider many-body quantum systems on a finite lattice, where the Hilbert space is the tensor product of finite-dimensional Hilbert spaces associated with each site, and where the Hamiltonian of the system is a sum of local terms. We are…

Non-Hermitian systems exhibit unique spectral properties, including the non-Hermitian skin effect and exceptional points, often influenced by boundary conditions. The modulation of these phenomena by generalized boundary conditions remains…

This dissertation describes the effect of quenched randomness on first order phase transitions in lattice systems, classical and quantum. It is proven that a large class of quantum lattice systems in low dimension (d <= 2 or, with suitable…

We investigate the long-time behavior of solutions of quasilinear hyperbolic systems with transparent boundary conditions when small source terms are incorporated in the system. Even if the finite-time stability of the system is not…