Results 61 to 70 of about 1,393 (155)

An approach to calculate Franck-Condon factors involving anharmonic potentials using harmonic oscillator bases

Journal of Physics Communications
In this contribution a discrete variable representation (DVR) approach to calculate Franck-Condon factors (FCFs) is presented. The method is illustrated using a harmonic oscillator basis. The advantage of this approach is that it is possible to calculate
E Suárez, R Lemus
doaj   +1 more source

Elucidating the Physical and Mathematical Properties of the Prouhet‐Thue‐Morse Sequence in Quantum Computing

Annalen der Physik, Volume 538, Issue 4, April 2026.
The Prouhet‐Thue‐Morse (PTM) sequence emerges as a unifying thread across quantum error correction, noise‐resistant memories, spin‐chain dynamics, quantum chaos, and Dirichlet links to the Riemann zeta function. Mapping PTM‐encoded logical states onto qubit and qudit architectures uncovers symmetry‐protected resilience and multifractal signatures ...
Denis Janković, Rémi Pasquier, Jean‐Gabriel Hartmann, Paul‐Antoine Hervieux   +3 more
wiley   +1 more source

Persistence in discrete Morse theory [PDF]

, 2022
Bauer, Ulrich, University of Göttingen
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Smoothing discrete Morse theory [PDF]

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2016
After surveying classical notions of PL topology of the Seventies, we clarify the relation between Morse theory and its discretization by Forman. We show that PL handles theory and discrete Morse theory are equivalent, in the sense that every discrete Morse vector on some PL triangulation is also a PL handle vector, and conversely, every PL handle ...
openaire   +2 more sources

Rigidity and Toledo Invariant for Spin*(8)-Higgs Bundles

Mathematics
In this paper, we study Spin*(8)-Higgs bundles over compact Riemann surfaces, extending the work of Bradlow, García-Prada, and Gothen on SO*(8). The group Spin*(8) is exceptional among classical real forms, as its complexification Spin(8,C) admits ...
Álvaro Antón-Sancho
doaj   +1 more source

Discrete Morse Theory Is At Least As Perfect As Morse Theory

, 2010
In bounding the homology of a manifold, Forman's Discrete Morse theory recovers the full precision of classical Morse theory: Given a PL triangulation of a manifold that admits a Morse function with c_i critical points of index i, we show that some subdivision of the triangulation admits a boundary-critical discrete Morse function with c_i interior ...
openaire   +2 more sources

Counting and Discrete Morse Theory

UF Journal of Undergraduate Research, 2019
We examine enumerating discrete Morse functions on graphs up to equivalence by gradient vector fields and by restrictions on the codomain.  We give formulae for the number of discrete Morse functions on specific classes of graphs (line, cycle, and bouquet of circles).
openaire   +2 more sources

Discrete Morse theory on graphs

Topology and its Applications, 2009
Discrete Morse theory is originally introduced by R. Forman as a discrete analogue of classical Morse theory to study homotopy properties of finite CW-complexes. In [\textit{R. Ayala}, \textit{L. M. Fernández}, and \textit{J. A. Vilches}, ``Discrete Morse inequalities on infinite graphs'', Electron. J. Comb. 16, No. 1, Research Paper R38, 11p.
Ayala, R., Fernández, L.M., Fernández-Ternero, D., Vilches, J.A.   +3 more
openaire   +2 more sources

Discrete Morse theory and localization [PDF]

Journal of Pure and Applied Algebra, 2019
30 pages, 6 figures.
openaire   +4 more sources

Discrete Morse theory for the collapsibility of supremum sections

CoRR, 2018
The Dushnik-Miller dimension of a poset $\le$ is the minimal number $d$ of linear extensions $\le_1, \ldots , \le_d$ of $\le$ such that $\le$ is the intersection of $\le_1, \ldots , \le_d$. Supremum sections are simplicial complexes introduced by Scarf and are linked to the Dushnik-Miller as follows: the inclusion poset of a simplicial complex is of ...
Bauer, Balthazar, Isenmann, Lucas
openaire   +3 more sources