Related papers: On conservative difference schemes for the many-bo…
For the calculation of the partition function $\mathcal{Z}$ of small, isolated and interacting many body systems an improvement with respect to previous formulations is presented. By including anharmonicities and employing a variational…
We review our results for the dynamics of isolated many-body quantum systems described by one-dimensional spin-1/2 models. We explain how the evolution of these systems depends on the initial state and the strength of the perturbation that…
In this paper, a class of arbitrarily high-order linear momentum-preserving and energy-preserving schemes are proposed, respectively, for solving the regularized long-wave equation. For the momentum-preserving scheme, the key idea is based…
In this work, we propose multicontinuum splitting schemes for the wave equation with a high-contrast coefficient, extending our previous research on multiscale flow problems. The proposed approach consists of two main parts: decomposing the…
The method of equivariant moving frames on multi-space is used to construct symmetry preserving finite difference schemes of partial differential equations invariant under finite-dimensional symmetry groups. Invariant numerical schemes for…
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum…
Understanding and characterising quantum many-body dynamics remains a significant challenge due to both the exponential complexity required to represent quantum many-body Hamiltonians, and the need to accurately track states in time under…
A novel class of high-order linearly implicit energy-preserving integrating factor Runge-Kutta methods are proposed for the nonlinear Schr\"odinger equation. Based on the idea of the scalar auxiliary variable approach, the original equation…
This paper proposes a new class of arbitrarily high-order conservative numerical schemes for the generalized Korteweg-de Vries (KdV) equation. This approach is based on the scalar auxiliary variable (SAV) method. The equation is…
Recently a new class of numerical integration methods -- ``mixed variable symplectic integrators'' -- has been introduced for studying long-term evolution in the conservative gravitational few-body problem. These integrators are an order of…
In recent years, the efficient numerical solution of Hamiltonian problems has led to the definition of a class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). Such methods admit an interesting…
We discuss here some aspects related to the symmetries of a quantum many-body problem when trying to treat it on a quantum computer. Several features related to symmetry conservation, symmetry breaking, and possible symmetry restoration are…
In ordinary turbulence research it has been a long standing tradition to solve the equations in spectral space giving the best possible accuracy. This is indeed a natural choice for incompressible problems with periodic boundaries, but it…
We introduce a second-order, central-upwind finite volume method for the discretization of nonlinear hyperbolic conservation laws posed on the two-dimensional sphere. The semi-discrete version of the proposed method is based on a technique…
Understanding the many-body dynamics of isolated quantum systems is one of the central challenges in modern physics. To this end, the direct experimental realization of strongly correlated quantum systems allows one to gain insights into…
A novel modular modeling and control framework based on Lagrangian mechanics is proposed for multibody systems, motivated by the challenges of modular control of systems with closed kinematic chains and by the need for a modeling framework…
A solution of the n-body problem in R^d is a relative equilibrium if all of the mutual distance between the bodies are constant. In other words, the bodies undergo a rigid motion. Here we investigate the possibility of partially rigid…
In this paper, based on the weak form of the Hamiltonian formulation of the regularized long-wave equation and a novel approach of transforming the original Hamiltonian energy into a quadratic functional, a fully implicit and three…
Finite element methods provide accurate and efficient methods for the numerical solution of partial differential equations by means of restricting variational problems to finite-dimensional approximating spaces. However, they do not…
The elliptic restricted three body problem has been well studied. However, the previous formulations of the problem have used a rotating coordinate system to keep the positions of the primary and secondary on the x-axis. This requires the…