Related papers: MCTDH-X: The multiconfigurational time-dependent H…
Quantum systems of indistinguishable particles are commonly described using the formalism of second quantisation, which relies on the assumption that any admissible quantum state must be either symmetric or anti-symmetric under particle…
We introduce the time-dependent restricted active space Configuration Interaction method to solve the time-dependent Schr\"odinger equation for many-electron atoms, and particularly apply it to the treatment of photoionization processes in…
In two previous papers (Price & Monaghan 2004a,b) (papers I,II) we have described an algorithm for solving the equations of Magnetohydrodynamics (MHD) using the Smoothed Particle Hydrodynamics (SPH) method. The algorithm uses dissipative…
This paper presents the first implementation of a coupling between advanced wave function theories and molecular density functional theory (MDFT). This method enables the modeling of solvent effect into quantum mechanical (QM) calculations…
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…
A system of $N$ particles in a chemical medium in $\mathbb{R}^{d}$ is studied in a discrete time setting. Underlying interacting particle system in continuous time can be expressed as \begin{eqnarray} dX_{i}(t) &=&[-(I-A)X_{i}(t) +…
We present a systematic method for dealing with time dependent quantum dynamics, based on the quantum brachistochrone and matrix mechanics. We derive the explicit time dependence of the Hamiltonian operator for a number of constrained…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…
The molecular dynamics following the electronic $B\ ^3\Pi_u\left(0^+\right) \longleftarrow X\ ^1\Sigma_g^+$ photoexcitation of the iodine molecule embedded in solid krypton are studied quantum mechanically using the Gaussian variant of the…
We present unrestricted Hartree Fock method coupled with configuration interaction (CI) method (URHF-CI) suitable for the calculation of ground and excited states of large number of electrons localized by complex gate potentials in…
{Many-body quantum states at thermal equilibrium are ubiquitous in nature. Investigating their dynamical properties is a formidable task due to the complexity of the Hilbert space they live in. Quantum computers may have the potential to…
Simulating and predicting dynamics of quantum many-body systems is extremely challenging, even for state-of-the-art computational methods, due to the spread of entanglement across the system. However, in the long-wavelength limit, quantum…
Hamiltonian and Schrodinger evolution equations on finite-dimensional projective space are analyzed in detail. Hartree-Fock (HF) manifold is introduced as a submanifold of many electron projective space of states. Evolution equations, exact…
A dynamical formulation of coupled cluster theory is derived using a variational principle. By allowing time-dependent single-particle functions, a high degree of adaptivity is introduced, allowing complex systems to be simulated with high…
We present a formulation and numerical algorithm to extend the scheme for grey radiation magneto-hydrodynamics (MHD) developed by Jiang (2021) to include the frequency dependence via the multi-group approach. The entire frequency space can…
In quantum physics the free particle and the harmonically trapped particle are arguably the most important systems a physicist needs to know about. It is little known that, mathematically, they are one and the same. This knowledge helps us…
We present the AM$^3$ ("Astrophysical Multi-Messenger Modeling") software. AM$^3$ is a documented open source software that efficiently solves the coupled integro-differential equations describing the temporal evolution of the spectral…
Recent progress in the realm of noisy, intermediate scale quantum (NISQ) devices represents an exciting opportunity for many-body physics, by introducing new laboratory platforms with unprecedented control and measurement capabilities. We…
We consider a general class of discrete unitary dynamical models on the lattice. We show that generically such models give rise to a wavefunction satisfying a Schroedinger equation in the continuum limit, in any number of dimensions. There…
We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can…