Related papers: Quantum Dynamics in Phase Space using Projected vo…
The von Neumann lattice refers to a discrete basis of Gaussians located on a lattice in phase space. It provides an attractive approach for solving quantum mechanical problems, allowing the pruning of tensor-product basis sets using phase…
We present an efficient implementation of dynamically pruned quantum dynamics, both in coordinate space and in phase space. We combine the ideas behind the biorthogonal von Neumann basis (PvB) with the orthogonalized momentum-symmetrized…
Quantum computers can be used to simulate nonlinear non-Hamiltonian classical dynamics on phase space by using the generalized Koopman-von Neumann formulation of classical mechanics. The Koopman-von Neumann formulation implies that the…
We report recent progress on the phase space formulation of quantum mechanics with coordinate-momentum variables, focusing more on new theory of (weighted) constraint coordinate-momentum phase space for discrete-variable quantum systems.…
The Koopman-von Neumann (KvN) formalism recasts classical mechanics in a Hilbert space framework using complex wavefunctions and linear operators, akin to quantum mechanics. Instead of evolving probability densities in phase space (as in…
We propose a phase space method to propagate a quantum wavepacket driven by a strong external field. The method employs the so-called biorthogonal von Neumann basis recently introduced for the calculation of the energy eigenstates of…
The Projection Postulate from Standard Quantum Mechanics relies fundamentally on measurements. But measurements implicitly suggest the existence of anthropocentric notions like measuring devices, which should rather emerge from the theory.…
We review recent developments in the theory of quantum dynamics in ultra-cold atomic physics, including exact techniques, but focusing on methods based on phase-space mappings that are appli- cable when the complexity becomes exponentially…
We introduce a numerical method to simulate nonlinear open quantum dynamics of a particle in situations where its state undergoes significant expansion in phase space while generating small quantum features at the phase-space Planck scale.…
We present a phase space formulation of quantum mechanics in the Schr\"odinger representation and derive the associated Weyl pseudo-differential calculus. We prove that the resulting theory is unitarily equivalent to the standard…
The physical phase space in gauge systems is studied. Effects caused by a non-Euclidean geometry of the physical phase space in quantum gauge models are described in the operator and path integral formalisms. The projection on the Dirac…
We introduce matrix quantum phase-space distributions. These extend the idea of a quantum phase-space representation via projections onto a density matrix of global symmetry variables. The method is applied to verification of low-loss…
A phase-space representation of nuclear interactions, which depends on the distance $\vec{r}$ and relative momentum $\vec{p}$ of the nucleons, is presented. A method is developed that permits to extract the interaction $V(\vec{r},\vec{p})$…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
Quantum computing offers a promising platform to address the computational challenges inherent in quantum chemistry, and particularly in valence bond (VB) methods, which are chemically appealing but suffer from high computational cost due…
Phase-space representations are of increasing importance as a viable and successful means to study exponentially complex quantum many-body systems from first principles. This review traces the background of these methods, starting from the…
We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
We present an efficient quantum algorithm for beyond-Born-Oppenheimer molecular energy computations. Our approach combines the quantum full configuration interaction method with the nuclear orbital plus molecular orbital (NOMO) method. We…
In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schr\"odinger framework from this perspective and provide a description of the Weyl-Wigner construction. Finally,…