Results 61 to 70 of about 53,900 (153)

Analysis of density matrix embedding theory around the non‐interacting limit

Communications on Pure and Applied Mathematics, Volume 78, Issue 8, Page 1359-1410, August 2025.
Abstract This article provides the first mathematical analysis of the Density Matrix Embedding Theory (DMET) method. We prove that, under certain assumptions, (i) the exact ground‐state density matrix is a fixed‐point of the DMET map for non‐interacting systems, (ii) there exists a unique physical solution in the weakly‐interacting regime, and (iii ...
Eric Cancès, Fabian M. Faulstich, Alfred Kirsch, Eloïse Letournel, Antoine Levitt   +4 more
wiley   +1 more source

Heisenberg‐smooth operators from the phase‐space perspective

Mathematische Nachrichten, Volume 298, Issue 8, Page 2845-2866, August 2025.
Abstract Cordes' characterization of Heisenberg‐smooth operators bridges a gap between the theory of pseudo‐differential operators and quantum harmonic analysis (QHA). We give a new proof of the result by using the phase‐space formalism of QHA. Our argument is flexible enough to generalize Cordes' result in several directions: (1) we can admit general ...
Robert Fulsche, Lauritz van Luijk
wiley   +1 more source

Analysis of the Generalized Ostrovsky Equation in the Propagation of Surface and Internal Waves in Rotating Fluids

Mathematical Methods in the Applied Sciences, Volume 48, Issue 12, Page 12427-12439, August 2025.
ABSTRACT The Ostrovsky equation models long, weakly nonlinear waves, explaining the propagation of surface and internal waves in a rotating fluid. The study focuses on the generalized Ostrovsky equation. Introduced by Levandosky and Liu, this equation demonstrates the existence of solitary waves through variational methods.
Sol Sáez
wiley   +1 more source

Categorifying the $sl(2,C)$ Knizhnik-Zamolodchikov Connection via an Infinitesimal 2-Yang-Baxter Operator in the String Lie-2-Algebra

, 2012
We construct a flat (and fake-flat) 2-connection in the configuration space of $n$ indistinguishable particles in the complex plane, which categorifies the $sl(2,C)$-Knizhnik-Zamolodchikov connection obtained from the adjoint representation of $sl(2,C)$.
Cirio, Lucio S., Martins, João Faria
core  

On some modules of covariants for a reflection group

, 2017
Let $\mathfrak g$ be a simple Lie algebra with Cartan subalgebra $\mathfrak h$ and Weyl group $W$. We build up a graded map $(\mathcal H\otimes \bigwedge\mathfrak h\otimes \mathfrak h)^W\to (\bigwedge \mathfrak g\otimes \mathfrak g)^\mathfrak g$ of ...
De Concini, Corrado, Papi, Paolo
core   +1 more source

Global bases for Bosonic extensions of quantum unipotent coordinate rings

Proceedings of the London Mathematical Society, Volume 131, Issue 2, August 2025.
Abstract In the paper, we establish the global basis theory for the bosonic extension Â$\widehat{\mathcal {A}}$ associated with an arbitrary symmetrizable generalized Cartan matrix. When Â$\widehat{\mathcal {A}}$ is of simply laced finite type, Â$\widehat{\mathcal {A}}$ is isomorphic to the quantum Grothendieck ring Kq(Cg0)$\mathcal {K}_q(\mathcal ...
Masaki Kashiwara, Myungho Kim, Se‐jin Oh, Euiyong Park   +3 more
wiley   +1 more source

Product of Exponentials (POE) Splines on Lie‐Groups: Limitations, Extensions, and Application to SO(3)$$ SO(3) $$ and SE(3)$$ SE(3) $$

International Journal for Numerical Methods in Engineering, Volume 126, Issue 14, 30 July 2025.
ABSTRACT Existing methods for constructing splines and Bézier curves on a Lie group G$$ G $$ involve repeated products of exponentials deduced from local geodesics, w.r.t. a Riemannian metric, or rely on general polynomials. Moreover, each of these local curves is supposed to start at the identity of G$$ G $$.
Andreas Müller
wiley   +1 more source

Representations up to homotopy of Lie algebroids [PDF]

, 2017
We introduce and study the notion of representation up to homotopy of a Lie algebroid, paying special attention to examples. We use representations up to homotopy to define the adjoint representation of a Lie algebroid and show that the resulting ...
Abad, Camilo Arias, Crainic, Marius
core  

Flat Connections and Quantum Groups

, 2002
We review the Kohno-Drinfeld theorem as well as a conjectural analogue relating quantum Weyl groups to the monodromy of a flat connection D on the Cartan subalgebra of a complex, semi-simple Lie algebra g with poles on the root hyperplanes and values in ...
Toledano-Laredo, Valerio
core  

Optimal system and dynamics of optical soliton solutions for the Schamel KdV equation. [PDF]

Sci Rep, 2023
Hussain A, Chahlaoui Y, Usman M, Zaman FD, Park C.   +4 more
europepmc   +1 more source