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Transient stability is crucial to the reliable operation of power systems. Existing theories rely on the simplified electromechanical models, substituting the detailed electromagnetic dynamics of inductor and capacitor with their impedance…
For electron-phonon Hamiltonians with the couplings linear in the phonon operators we construct a class of unitary transformations that separate the normal modes into two groups. The modes in the first group interact with the electronic…
We develop a density matrix formalism to describe coupled electron-nuclear dynamics. To this end we introduce an effective Hamiltonian formalism that describes electronic transitions and small (quantum) nuclear fluctuations along a…
In electronic structure theory, variational methods offer a valuable paradigm for approximating electronic ground states. However, for historical reasons, this principle is mostly restricted to model chemistries in pre-defined fixed basis…
Computationally efficient and accurate quantum mechanical approximations to solve the many-electron Schr\"odinger equation are at the heart of computational materials science. In that respect the coupled cluster hierarchy of methods plays a…
Despite the successes of machine learning methods in physical sciences, prediction of the Hamiltonian, and thus electronic properties, is still unsatisfactory. Here, based on graph neural network architecture, we present an extendable…
Explicit symplectic integrators have been important tools for accurate and efficient approximations of mechanical systems with separable Hamiltonians. For the first time, the article proposes for arbitrary Hamiltonians similar integrators,…
The exact solution of the Schrodinger equation for atoms, molecules and extended systems continues to be a "Holy Grail" problem for the field of atomic and molecular physics since inception. Recently, breakthroughs have been made in the…
A highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to…
Electronic Structure Theory (EST) describes the behavior of electrons in matter and is used to predict material properties. Conventionally, this involves forming a Hamiltonian and solving the Schr\"odinger equation through discrete…
We demonstrate how electric fields with arbitrary time profile can be used to control the time-dependent parameters of spin and orbital exchange Hamiltonians. Analytic expressions for the exchange constants are derived from a time-dependent…
We prove that, contrary to the common belief, the classical Maxwell electrodynamics of a point-like particle may be formulated as an infinite-dimensional Hamiltonian system. We derive well defined quasi-Hamiltonian which possesses direct…
This work presents an exactly soluble scheme to address the problem of optimal transfer of quantum states through a set of $s$ harmonic oscillators composing a network with connected ends as a closed quantum circuit. For this purpose we…
We present a quantum electronic embedding method derived from the exact factorization approach to calculate static properties of a many-electron system. The method is exact in principle but the practical power lies in utilizing input from a…
An approximate relativistic two-component Hamiltonian for use in molecular electronic structure calculations is derived in the form of a sum of fixed atom-centered kinetic and spin-orbit operators added to the non-relativistic Hamiltonian.…
The quantum mechanical motion of the atomic nuclei is considered over a single- or a multi-dimensional subspace of electronic states which is separated by a gap from the rest of the electronic spectrum over the relevant range of nuclear…
By expressing the electronic wavefunction in an explicitly-correlated (Jastrow-factorised) form, a similarity-transformed effective Hamiltonian can be derived. The effective Hamiltonian is non-Hermitian and contains three-body interactions.…
Mathematical descriptions of the interplay between strong electron correlations and lattice degrees of freedom are of enormous importance in the development of new devices based on metal oxides such as VO$_{2}$ and the Cuprate…
For many-particle systems defined on lattices we investigate the global structure of effective Hamiltonians and observables obtained by means of a suitable basis transformation. We study transformations which lead to effective Hamiltonians…
A canonical Hamiltonian formalism is derived for a class of Ermakov systems specified by several different frequency functions. This class of systems comprises all known cases of Hamiltonian Ermakov systems and can always be reduced to…