Related papers: Compact submanifolds supporting singular interacti…
We study a quantum mechanical system consisting of up to three identical dipoles confined to move along a helical shaped trap. The long-range interactions between particles confined to move in this one dimension leads to an interesting…
The paper is devoted to the Hamiltonian treatment of classical and quantum properties of Liouville field theory on a timelike strip in 2d Minkowski space. We give a complete description of classical solutions regular in the interior of the…
Local unitary operations allow for a unifying approach to the quantification of quantum correlations among the constituents of a bipartite quantum system. For pure states, the distance between a given state and its image under…
We solve the single particle Dirac bound state equation with a particular confining potential and comment its significance from the point of view of the quantum field theory. We show that the solutions describe a complex physical system…
The paper gives a comprehensive study of Inertial Manifolds for hyperbolic relaxations of an abstract semilinear parabolic equation in a Hilbert space. A new scheme of constructing Inertial Manifolds for such type of problems is suggested…
We consider, in a first instance, the class of boundaries of sets with locally finite perimeter whose (weakly defined) mean curvature is $g \nu$, for a given continuous positive ambient function $g$, and where $\nu$ denotes the inner…
We investigate the entanglement structure of a bipartite quantum system through the lens of quantum thermodynamics in the absence of conformal symmetry. Specifically, we consider the long-range Kitaev model, where the pairing interaction…
Interactions in atomic and molecular systems are dominated by electromagnetic forces and the theoretical framework must be in the quantum regime. The physical theory for the combination of quantum mechanics and electromagnetism, quantum…
We investigate spectral properties of a quantum particle confined to an infinite straight planar strip by imposing Robin boundary conditions with variable coupling. Assuming that the coupling function tends to a constant at infinity, we…
We show that two properly embedded compact surfaces in an orientable 4-manifold are cobordant if and only if they are $\mathbb{Z}/2$-homologous and either the 4-manifold has boundary or the surfaces have the same normal Euler number. If the…
For an oriented surface $S$, the singular set of a fold map $f:S\rightarrow \mathbb{R}^2$ is a collection of smooth curves, also known as fold singularities. We construct a sharp lower bound on the number of self-intersections of such fold…
Several protocols are proposed to build continuous energy surfaces of many-body quantum systems, regarding both energy and states. The standard variational principle is augmented with constraints on state overlap, ensuring arbitrary…
We cast the quantum chemistry problem of computing bound states as that of solving a set of auxiliary eigenvalue problems for a family of parameterized compact integral operators. The compactness of operators assures that their spectrum is…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
In [8] the authors introduced a pair of new de Rham complexes on a compact oriented Riemannian manifold with boundary by using a pair of new boundary conditions to discuss the refined analytic torsion on a compact manifold with boundary. In…
The Bethe-Salpeter equation provides the most widely used technique to extract bound states and resonances in a relativistic Quantum Field Theory. Nevertheless a thorough discussion how to identify its solutions with physical states is…
We investigate how to include bound states in a thermal gas in the context of quantum field theory (QFT). To this end, we use for definiteness a scalar QFT with a $\varphi^{4}$ interaction, where the field $\varphi$ represents a particle…
We consider the problem of a quantum particle interacting with $N$ attractive point $\delta$-interactions in two and three dimensional Riemannian manifolds and discuss its some spectral properties. The main aim of this paper is to give a…
We investigate how entangled states can be created by considering collections of point-particles arranged at different spatial configurations, i.e., Fock states with spatial constraints. This type of states can be realized in Hubbard chains…
We solve the bound state problem for the Hamiltonian with the spin-orbit and the Raman coupling included. The Hamiltonian is perturbed by a one-dimensional short-range potential V which describes the impurity scattering. In addition to the…