Related papers: Uncertainty relations and applications in spectral…
Lecture notes for one of the courses at the OPSFA Summerschool 6, July 11-15, 2016. All the results in these notes have appeared in the literature. Many special functions are eigenfunctions to explicit operators, such as difference and…
Extending density functional theory (DFT) to an {\it ab initio} orbital functional theory (OFT) requires new methodology for nonlocal exchange and correlation potentials. This paper describes such modifications to a standard Dirac-Slater…
In open-domain dialogues, predictive uncertainties are mainly evaluated in a domain shift setting to cope with out-of-distribution inputs. However, in real-world conversations, there could be more extensive distributional shifted inputs…
These are notes to accompany my lectures at the $2024$ "Current Developments in Mathematics" conference hosted by Harvard/MIT. The lectures were about some recent progress in our understanding of two and three dimensional dynamical systems,…
Obtaining Compton Form Factors (CFFs) and Transverse Momentum Dependent parton distribution functions (TMDs) from experimental data using neural network-based information extraction requires the precise propagation of experimental errors.…
Uncertainty relations involving complementary observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum…
The spectral properties of a class of non-selfadjoint second order elliptic operators with indefinite weight functions on unbounded domains $\Omega$ are investigated. It is shown that under an abstract regularity assumption the nonreal…
We revise the extended uncertainty relations for the Rindler and Friedmann spacetimes recently discussed by Dabrowski and Wagner in [9]. We reveal these results to be coordinate dependent expressions of the invariant uncertainty relations…
Uncertainty relations for Hermitian operators have been confirmed through many experiments. However, previous experiments have only tested the special case of non-Hermitian operators, i.e., uncertainty relations for unitary operators. In…
These are the proceedings of the workshop "HadAtom01", held at the Institut fuer Theoretische Physik, Universitaet Bern, October 11 - 12, 2001. The main topics discussed at the workshop were the physics of hadronic atoms and in this context…
This volume contains the proceedings of the Sixth International Workshop on Computing with Terms and Graphs (TERMGRAPH 2011). The workshop took place in Saarbruecken, Germany, on April 2nd, 2011, as part of the fourteenth edition of the…
In this work we study integral equations defined on the whole real line. Using a suitable Banach space, we look for solutions which satisfy some certain kind of asymptotic behavior. We will consider spectral theory in order to find fixed…
The differential-geometric and topological structure of Delsarte transmutation operators and associated with them Gelfand-Levitan-Marchenko type eqautions are studied making use of the De Rham-Hodge-Skrypnik differential complex. The…
Recently, Zheng constructs a quantum-control-assisted multipartite variance-based uncertainty relation, which successfully extends the conditional uncertainty relation to the multipartite case [Annalen der physik, 533, 2100014 (2021)]. We…
Spectral problems governed by differential operators underpin a wide range of physical systems, yet remain computationally challenging because their spectra depend sensitively on continuous parameters and often demand repeated evaluations…
This survey of recent developments in cloaking and transformation optics is an expanded version of the lecture by Gunther Uhlmann at the 2008 Annual Meeting of the American Mathematical Society.
This work presents an online learning-based control method for improved trajectory tracking of unmanned aerial vehicles using both deep learning and expert knowledge. The proposed method does not require the exact model of the system to be…
This is a lecture note prepared for the SFT 9 workshop in Augsburg, Germany. The text describes a polyfold approach to the construction of symplectic field theory and focuses on the perturbation and transversality theory.
A concise review of various mathematical formulations of the uncertainty relations in quantum mechanics discovered since 1927 is given. Besides the traditional Heisenberg inequality, the modifications made by Schr\"odinger and Robertson, as…
As a foundation of modern physics, uncertainty relations describe an ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertain relations are formulated by mathematical bounds for a specific state.…