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We isolate a geometric mechanism that complements the dynamical suppression of macroscopic interference: In a high-dimensional Hilbert space, almost all state vectors are nearly orthogonal, accommodating an exponentially large reservoir of…
We generalize the concept of quasiparticle for one-dimensional (1D) interacting electronic systems. The $\uparrow $ and $\downarrow $ quasiparticles recombine the pseudoparticle colors $c$ and $s$ (charge and spin at zero magnetic field)…
We consider the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic…
Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which the…
Coordinate atypical representation of the orthosymplectic superalgebra osp(2/2) in a Hilbert superspace of square integrable functions constructed in a special way is given. The quantum nonrelativistic free particle Hamiltonian is an…
We present a unified geometric and dynamical framework for a physical system consisting of $n$ spin-$1/2$ particles with all-range Ising interaction. Using the Fubini-Study formalism, we derive the metric tensor of the associated quantum…
This paper posits the existence of, and finds a candidate for, a variable change that allows quantum mechanics to be interpreted as quantum geometry. The Bohr model of the Hydrogen atom is thought of in terms of an indeterministic electron…
In the field of quantum information science and technology, the representation and visualization of quantum states and related processes are essential for both research and education. In this context, a focus especially lies on ensembles of…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
Electronic coupling and hence hybridization of atoms serve as the basis for the rich properties of the endless library of naturally occurring molecules. Colloidal quantum dots (CQDs) manifesting quantum strong confinement, possess atomic…
We introduce a machine learning method in which energy solutions from the Schrodinger equation are predicted using symmetry adapted atomic orbitals features and a graph neural-network architecture. \textsc{OrbNet} is shown to outperform…
We discuss the problem of spin-orbit interaction in a 2D chaotic or diffusive quantum dot in the presence of exchange correlations. Spin-orbit scattering breaks spin rotation invariance, and in the crossover regime between different…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
Dynamic Hubbard models have been proposed as extensions of the conventional Hubbard model to describe the orbital relaxation that occurs upon double occupancy of an atomic orbital. These models give rise to pairing of holes and…
Despite rapid advances in molecular and materials machine learning, most models still lack physical transferability: they fit correlations across whole molecules or crystals rather than learning the quantum interactions between atomic…
Multipole degrees of freedom describe the mutual interplay among the charge, spin, and orbital degrees of freedom in electrons, which provides a microscopic understanding of unconventional electronic orderings and their associated physical…
Motivated by relating the representation theory of the split real and $p$-adic forms of a connected reductive algebraic group $G$, we describe a subset of $2^r$ orbits on the complex flag variety for a certain symmetric subgroup. (Here $r$…
Background: Quasi dynamical symmetries (QDS) and partial dynamical symmetries (PDS) play an important role in the understanding of complex systems. Up to now these symmetry concepts have been considered to be unrelated. Purpose: Establish a…
In the well-known Nilsson diagrams, depicting the dependence of the nuclear single-particle energy levels on quadrupole deformation, a spin paradox appears {as the deformation sets in, leading from spherical shapes to prolate deformed…
Quantum entanglement is a central concept of quantum theory for multiple particles. Entanglement played an important role in the development of the foundations of the theory and makes possible modern applications in quantum information…