Related papers: On Some Open Problems in Many-Electron Theory
We consider the quantum dynamics of a many-fermion system in $\mathbb R^d$ with an ultraviolet regularized pair interaction as previously studied in [M. Gebert, B. Nachtergaele, J. Reschke, and R. Sims, Ann. Henri Poincar\'e 21.11 (2020)].…
We look over recent developments on our understanding about relativistic matter under external electromagnetic fields and mechanical rotation. I review various calculational approaches for concrete physics problems, putting my special…
Quantum physics has intrigued scientists and philosophers alike, because it challenges our notions of reality and locality--concepts that we have grown to rely on in our macroscopic world. It is an intriguing open question whether the…
We summarize recent work to develop an effective theory of muon-to-electron conversion, based on a complete set of low-energy effective operators that are developed from a systematic expansion in velocities and momenta. The expansion…
The object of this contribution is twofold. On one hand, it rises some general questions concerning the definition of the electromagnetic field and its intrinsic properties, and it proposes concepts and ways to answer them. On the other…
Open effective field theories provide a systematic framework for describing systems coupled to an environment, where dissipation, noise, and modified conservation laws naturally arise. Working within the Schwinger-Keldysh formalism, we…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
In the study of the electronic structure of heavy atoms, relativistic effects cannot be neglected and the Dirac operator naturally appears in place of the Schr\"odinger operator, raising a number of additional difficulties. The complexity…
The tunneling process in a many-body system is a phenomenon which lies at the very heart of quantum mechanics. It appears in nature in the form of alpha-decay, fusion and fission in nuclear physics, photoassociation and photodissociation in…
Four level quantum systems, known as quartits, and their relation to two- qubit systems are investigated group theoretically. Following the spirit of Klein's lectures on the icosahedron and their relation to Hopf sphere bra- tions,…
We consider a general one-dimensional tight-binding electron model which has a period $P$. For any filling factor $\nu$ such that $P\nu$ is non-integral, we prove that the model in the infinite volume limit has either a symmetry breaking or…
We describe here the coherent formulation of electromagnetism in the non-relativistic quantum-mechanical many-body theory of interacting charged particles. We use the mathematical frame of the field theory and its quantization in the spirit…
A supersymmetric generalization of the Lieb-Liniger-Yang dynamics governing $N$ massive bosons moving on a line with delta interactions among them at coinciding points is developed. The analysis of the delicate balance between integrability…
Open quantum systems can be approximately described by non-Hermitian Hamiltonians (NHHs) and Liouvillian superoperators. The two approaches differ by quantum jump terms corresponding to a measurement of the system by its environment. We…
We present a formal derivation of the many-body perturbation theory for a system of electrons and bosons subject to a nonlinear electron-boson coupling. The interaction is treated at an arbitrary high order of bosons scattered. The…
Strongly interacting quantum many-body systems are fundamentally compelling and ubiquitous in science. However, their complexity generally prevents exact solutions of their dynamics. Precisely engineered ultracold atomic gases are emerging…
Complete and joint mixability has raised considerable interest in recent few years, in both the theory of distributions with given margins, and applications in discrete optimization and quantitative risk management. We list various open…
We consider many-body quantum systems on a finite lattice, where the Hilbert space is the tensor product of finite-dimensional Hilbert spaces associated with each site, and where the Hamiltonian of the system is a sum of local terms. We are…
We review methods that allow one to detect and characterise quantum correlations in many-body systems, with a special focus on approaches which are scalable. Namely, those applicable to systems with many degrees of freedom, without…
More and more applications require early decisions, i.e. taken as soon as possible from partially observed data. However, the later a decision is made, the more its accuracy tends to improve, since the description of the problem to hand is…