08 Fakultät Mathematik und Physik

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Institute: search.filters.UBSInstitut.Fakultät Mathematik und Physik (Institutsübergreifend)Publication Type: search.filters.UBSTyp.Zeitschriftenartikel

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Now showing 1 - 6 of 6
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    A note on the Fröhlich dynamics in the strong coupling limit
    (2021) Mitrouskas, David
    We revise a previous result about the Fröhlich dynamics in the strong coupling limit obtained in Griesemer (Rev Math Phys 29(10):1750030, 2017). In the latter it was shown that the Fröhlich time evolution applied to the initial state ϕ0 ⊗ξα, where ϕ0 is the electron ground state of the Pekar energy functional and ξα the associated coherent state of the phonons, can be approximated by a global phase for times small compared to α2. In the present note we prove that a similar approximation holds for t = O(α2) if one includes a nontrivial effective dynamics for the phonons that is generated by an operator proportional to α-2 and quadratic in creation and annihilation operators. Our result implies that the electron ground state remains close to its initial state for times of order α2, while the phonon fluctuations around the coherent state ξα can be described by a time-dependent Bogoliubov transformation.
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    Entropy by neighbor distance as a new measure for characterizing spatiotemporal orders in microscopic collective systems
    (2023) Fu, Yulei; Wu, Zongyuan; Zhan, Sirui; Yang, Jiacheng; Gardi, Gaurav; Kishore, Vimal; Malgaretti, Paolo; Wang, Wendong
    Collective systems self-organize to form globally ordered spatiotemporal patterns. Finding appropriate measures to characterize the order in these patterns will contribute to our understanding of the principles of self-organization in all collective systems. Here we examine a new measure based on the entropy of the neighbor distance distributions in the characterization of collective patterns. We study three types of systems: a simulated self-propelled boid system, two active colloidal systems, and one centimeter-scale robotic swarm system. In all these systems, the new measure proves sensitive in revealing active phase transitions and in distinguishing steady states. We envision that the entropy by neighbor distance could be useful for characterizing biological swarms such as bird flocks and for designing robotic swarms.
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    On the weakness of short-range interactions in Fermi gases
    (2022) Griesemer, Marcel; Hofacker, Michael
    Ultracold quantum gases of equal-spin fermions with short-range interactions are often considered free even in the presence of strongly binding spin-up-spin-down pairs. We describe a large class of many-particle Schrödinger operators with short-range pair interactions, where this approximation can be justified rigorously.
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    Unitals with many involutory translations
    (2023) Grundhöfer, Theo; Stroppel, Markus J.; Maldeghem, Hendrik van
    If every point of a unital is fixed by a non-trivial translation and at least one translation has order two then the unital is classical (i.e., hermitian).
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    Finite subunitals of the hermitian unitals
    (2022) Grundhöfer, Theo; Stroppel, Markus J.; Maldeghem, Hendrik van
    Every finite subunital of any generalized hermitian unital is itself a hermitian unital; the embedding is given by an embedding of quadratic field extensions. In particular, a generalized hermitian unital with a finite subunital is a hermitian one (i.e., it originates from a separable field extension).
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    Fractional calculus for distributions
    (2024) Hilfer, Rudolf; Kleiner, Tillmann
    Fractional derivatives and integrals for measures and distributions are reviewed. The focus is on domains and co-domains for translation invariant fractional operators. Fractional derivatives and integrals interpreted as -convolution operators with power law kernels are found to have the largest domains of definition. As a result, extending domains from functions to distributions via convolution operators contributes to far reaching unifications of many previously existing definitions of fractional integrals and derivatives. Weyl fractional operators are thereby extended to distributions using the method of adjoints. In addition, discretized fractional calculus and fractional calculus of periodic distributions can both be formulated and understood in terms of -convolution.