Inverz szóráselméleti kutatások = Problems of inverse scattering theory

Kifejlesztettünk egy új fix-energiás inverz kvantum szórás módszert. Szórási adatok invertálására alkalmassá tettük a Cox-Thompson inverz kvantum szórás eljárást. Bose-kondenzátumok ütközéséből származó fázistolás adatokból határoztunk meg effektív Rb-Rb atomi potenciálokat. Kétkomponensű Bose-Einstein kondenzátumok stabilitását vizsgáltuk. Megbecsültük a különző specimenek közti szóráshosszak azon tartományát, amely esetében szoliton gerjesztések létrejöhetnek a kondenzátumban. Kifejelesztettünk és numerikusan teszteltünk egy csatolt Gross-Pitaevskii egyenlet megoldó programot. A kutatási munkatervben vállalt 7 publikáció és 4 konferencia előadást jelentősen túl teljestettük, amennyiben 3 disszertáció, 3 konferenciakiadvány és 25 publiáció született az egy évvel meghosszabbított, 5 éves 4 résztvevős kutatás alatt. Ezen kívül egy nemzetközi inverz kvantum szórás konferenciát is rendeztünk (www.math.bme.hu/~hirvath/iqs). | New fix-energy inverse quantum scattering method has been developed. The Cox-Thompson inverse quantum scattering procedure has been made appropriate to invert scattering data. We have determined Rb-Rb atomic scattering potential from data extracted from Bose condensate collisions. Stability of two-component Bose-Einstein condensates has been inversigated. Assessments have been given to values of interspecies scattering length at which soliton excitations are to be expected to exist inside the condensate. We have developed and numerically tested an evolution code which simulate the time evolution of a two-component Bose-Einstein condensate accoring to the Gross-Pitaevskii equation. The original undertaking has been well overcompleted in that 3 theses (1 Phd and 2 DSc), 3 conference contribution and 25 publications in journals of high international reputation have been delivered ba the 4 participants during the 5 years research. Besides also an international inverse quantum scattering conference has been held (www.math.bme.hu/~hirvath/iqs)

On isometries of Wasserstein spaces (Research on preserver problems on Banach algebras and related topics)

It is known that if p ≥ 1, then the isometry group of the metric space (X, ϱ) embeds into the isometry group of the Wasserstein space Wp(X, ϱ). Those isometries that belong to the image of this embedding are called trivial. In many concrete cases, all isometries are trivial, however, this is not always the case. The aim of this survey paper is to provide a structured overview of recent results concerning trivial and different types of nontrivial isometries

Isometric study of Wasserstein spaces - the real line

Recently Kloeckner described the structure of the isometry group of the quadratic Wasserstein space $\mathcal {W}_2(\mathbb{R}^n)$. It turned out that the case of the real line is exceptional in the sense that there exists an exotic isometry flow. Following this line of investigation, we compute $\mathrm {Isom}(\mathcal {W}_p(\mathbb{R}))$, the isometry group of the Wasserstein space $\mathcal {W}_p(\mathbb{R})$ for all $p \in [1, \infty )\setminus \{2\}$. We show that $\mathcal {W}_2(\mathbb{R})$ is also exceptional regarding the parameter $p$: $\mathcal {W}_p(\mathbb{R})$ is isometrically rigid if and only if $p\neq 2$. Regarding the underlying space, we prove that the exceptionality of $p=2$ disappears if we replace $\mathbb{R}$ by the compact interval $[0,1]$. Surprisingly, in that case, $\mathcal {W}_p([0,1])$ is isometrically rigid if and only if $p\neq 1$. Moreover, $\mathcal {W}_1([0,1])$ admits isometries that split mass, and $\mathrm {Isom}(\mathcal {W}_1([0,1]))$ cannot be embedded into $\mathrm {Isom}(\mathcal {W}_1(\mathbb{R}))$

Supporting Digital Supply Chains by IoT Frameworks: Collaboration, Control, Combination

The purpose of this paper is to introduce a technology-oriented SCM (Supply Chain Management) development methodology, which can be used in the design of IoT (Internet of Things) frameworks especially characterized by supply chain processes. In order to meet DSC (Digital Supply Chain) expectations, two areas are examined in detail during the literature review. Firstly, the current SCM models are studied. Secondly, Industry 4.0 requirements had to be surveyed. As a consequence, challenges and gaps are identified for which we seek the solution during our research. Based on the results, it can be stated that digitization has definitely required an improved technological solution that IoT frameworks can provide. The result is a technology-driven, IoT-based SCM development methodology that serves as a basis for the design of such platforms, which will manage supply chains. To prove the feasibility of the proposed development methodology, the Arrowhead industrial IoT framework is used for validation

Quantum Wasserstein isometries on the qubit state space

We describe Wasserstein isometries of the quantum bit state space with respect to distinguished cost operators. We derive a Wigner-type result for the cost operator involving all the Pauli matrices: in this case, the isometry group consists of unitary or anti-unitary conjugations. In the Bloch sphere model, this means that the isometry group coincides with the classical symmetry group $\mathbf{O}(3).$ On the other hand, for the cost generated by the qubit "clock" and "shift" operators, we discovered non-surjective and non-injective isometries as well, beyond the regular ones. This phenomenon mirrors certain surprising properties of the quantum Wasserstein distance.Comment: 18 pages, 3 figures. v2: new references added, v3: minor change