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As argued in our previous papers, it would be more natural to modify the standard approach to quantum theory by requiring that i) one unitary irreducible representation (UIR) of the symmetry algebra should describe a particle and its…
Gausslets are one of the few basis constructions for electronic structure that combine locality, orthonormality, variable resolution, and an accurate diagonal approximation for the electron-electron interaction, but the original…
The concept of physical twin observables (PTO) for bipartite quantum states,introduced and proved relevant for quantum information theory in recent work, is substantially simplified. The relation of observable and state is studied in detail…
We introduce a simple spherical model whose structural properties are similar to the ones generated by models with directional interactions, by employing a binary mixture of large and small hard spheres, with a square-well attraction acting…
We present a complete classification of the geometry of the mutually complementary sets of entangled and separable states in three-dimensional Hilbert subspaces of bipartite and multipartite quantum systems. Our analysis begins by finding…
Our main concern in this work is to show how higher shell admixtures affect the spectrum of a Q.Q interaction. We first review how, in the valence space, the familiar SU(3) result for the energy spectrum can be obtained using a coordinate…
We study theoretically the electron states in a system of two vertically stacked quantum dots. We investigate the influence of the geometrical symmetry breaking (caused by the displacement as well as the ellipticity of the dots) on the…
Summary. A simple derivation of finite Schmidt decomposition of pure states describing finite dimensional systems interacting with the infinite dimensional ones is presented. In particular, maximally entangled pure states in such systems…
We study the spin- 1/2 two and three dimensional Orbital Compass Models relevant to the problem of orbital ordering in transition metal oxides. We show that these systems display self-dualities and novel (gauge-like) discrete sliding…
We present the characterizations of symbol correspondences for mechanical systems that are symmetric by $SU(3)$, which we refer to as \emph{quark systems}. The quantum quark systems are the unitary irreducible representations of $SU(3)$ of…
An arrangement of pseudocircles is a finite set of oriented closed Jordan curves each two of which cross each other in exactly two points. To describe the combinatorial structure of arrangements on closed orientable surfaces, in (Linhart,…
Studying the geometry of sets appearing in various problems of quantum information helps in understanding different parts of the theory. It is thus worthwhile to approach quantum mechanics from the angle of geometry -- this has already…
Within the framework of Relativistic Schroedinger Theory (an alternative form of quantum mechanics for relativistic many-particle systems) it is shown that a general N-particle system must occur in one of two forms: either as a ``positive''…
Hallmarks of quantum mechanics include superposition and entanglement. In the context of large complex systems, these features should lead to situations like Schrodinger's cat, which exists in a superposition of alive and dead states…
Using a single spin-1 object as an example, we discuss a recent approach to quantum entanglement. The key idea of the approach consists in presetting of basic observables in the very definition of quantum system. Specification of basic…
We outline a program for interpreting the higher-spin dS/CFT model in terms of physics in the causal patch of a dS observer. The proposal is formulated in "elliptic" de Sitter space dS_4/Z_2, obtained by identifying antipodal points in…
We study quantum many-body mixed states with a symmetry from the perspective of separability, i.e., whether a mixed state can be expressed as an ensemble of short-range entangled (SRE) symmetric pure states. We provide evidence for…
Correspondence between classical periodic orbits and quantum shell structure is investigated for a reflection-asymmetric deformed oscillator model as a function of quadrupole and octupole deformation parameters. Periodic orbit theory…
Real-to-complex spectral transitions and the associated spontaneous symmetry breaking of eigenstates are central to non-Hermitian physics, yet a comprehensive and universal theory that precisely describes the underlying physical mechanisms…
We study the dimension of the manifold of quantum states (called orbit) that a given quantum state of light can reach under the dynamics of linear or Gaussian quantum optics. That is, we investigate how many directions in the Hilbert space…