Related papers: From Vlasov-Poisson to Schr\"odinger-Poisson: dark…
Self-gravitating quantum matter may exist in a wide range of cosmological and astrophysical settings from the very early universe through to present-day boson stars. Such quantum matter arises in a number of different theories, including…
Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. This approach typically relies on deep circuits and is therefore hampered by the substantial…
We obtain solutions to the coupled Schr\"odinger-Poisson equations. The solutions describe the evolution of cold dark matter density perturbations in an otherwise homogeneous expanding Friedmann universe. We discuss the relationships…
We study existence and uniqueness of the solution to the Vlasov-Poisson system describing a plasma constituted by different species evolving in $\mathbb{R}^3$, whose particles interact via the Coulomb potential. The species can have both…
Semi-analytical methods, based on Eulerian perturbation theory, are a promising tool to follow the time evolution of cosmological perturbations at small redshifts and at mildly nonlinear scales. All these schemes are based on two…
The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation…
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…
In this paper we discuss a Schwinger-Dyson [SD] approach for determining the time evolution of the unequal time correlation functions of a non-equilibrium classical field theory, where the classical system is described by an initial density…
We describe a new hybrid N-body/hydrodynamical code based on the particle-mesh (PM) method and the piecewise-parabolic method (PPM) for use in solving problems related to the evolution of large-scale structure, galaxy clusters, and…
Quantum simulation is a prominent application of quantum computers. While there is extensive previous work on simulating finite-dimensional systems, less is known about quantum algorithms for real-space dynamics. We conduct a systematic…
Modern cosmological observations allow us to study in great detail the evolution and history of the large scale structure hierarchy. The fundamental problem of accurate constraints on the cosmological parameters, within a given cosmological…
Engineering simulations are usually based on complex, grid-based, or mesh-free methods for solving partial differential equations. The results of these methods cover large fields of physical quantities at very many discrete spatial…
Quantum simulation is known to be capable of simulating certain dynamical systems in continuous time -- Schrodinger's equations being the most direct and well-known -- more efficiently than classical simulation. Any linear dynamical system…
In this paper, a novel high order semi-Lagrangian (SL) spectral volume (SV) method is proposed and studied for nonlinear Vlasov-Poisson (VP) simulations via operator splitting. The proposed algorithm combines both advantages of…
The Vlasov equation for the collisionless evolution of the single-particle probability distribution function (PDF) is a well-known Lie-Poisson Hamiltonian system. Remarkably, the operation of taking the moments of the Vlasov PDF preserves…
A collisionless plasma is modeled by the Vlasov-Poisson system in three space dimensions. A fixed background of positive charge, which is independent of time and space, is assumed. The situation in which mobile negative ions balance the…
A numerical method of calculating the non-Markovian evolution of a driven atom radiating into a structured continuum is developed. The formal solution for the atomic reduced density matrix is written as a Markovian algorithm by introducing…
In this paper, we consider a finite difference grid-based semi-Lagrangian approach in solving the Vlasov-Poisson (VP) system. Many of existing methods are based on dimensional splitting, which decouples the problem into solving linear…
We develop new numerical schemes for Vlasov--Poisson equations with high-order accuracy. Our methods are based on a spatially monotonicity-preserving (MP) scheme and are modified suitably so that positivity of the distribution function is…
The Vlasov-Poisson equation is a classical example of an effective equation which shall describe the coarse-grained time evolution of a system consisting of a large number of particles which interact by Coulomb or Newton's gravitational…