26 citations · 102 across the 11 of their papers we have counts for
13 papers
Quantizations of Lie bialgebras, duality involution and oriented graph complexes
Sergei Merkulov, Marko Živković
We prove that the action of the Grothendieck-Teichmüller group on the genus completed properad of (homotopy) Lie bialgebras commutes with the reversing directions involution of the…
Oriented hairy graphs and moduli spaces of curves
Assar Andersson, Thomas Willwacher, Marko Zivkovic
We discuss a graph complex formed by directed acyclic graphs with external legs. This complex comes in particular with a map to the ribbon graph complex computing the (compactly su…
Multi-directed graph complexes and quasi-isomorphisms between them II: Sourced graphs
Marko Živković
We prove that the inclusion from oriented graph complex into graph complex with at least one source is a quasi-isomorphism, showing that homology of the "sourced" graph complex is…
Differentials on graph complexes II - hairy graphs
Anton Khoroshkin, Thomas Willwacher, Marko Živković
We study the cohomology of the hairy graph complexes which compute the rational homotopy of embedding spaces, generalizing the Vassiliev invariants of knot theory. We provide spect…
Differentials on graph complexes
Anton Khoroshkin, Thomas Willwacher, Marko Živković
We study the cohomology of complexes of ordinary (non-decorated) graphs, introduced by M. Kontsevich. We construct spectral sequences converging to zero whose first page contains t…
Trace decategorification of categorified quantum sl(3)
Marko Živković
We prove that the trace of categorified quantum sl(3) introduced by M. Khovanov and A. Lauda can also be identified with quantum sl(3), thus providing an alternative way of decateg…
Trace decategorification of categorified quantum sl(2)
Anna Beliakova, Kazuo Habiro, Aaron D. Lauda +1
The trace or the th Hochschild--Mitchell homology of a linear category may be regarded as a kind of decategorification of . We compute traces of the t…
The dimensions and Euler characteristics of M. Kontsevich's graph complexes
Thomas Willwacher, Marko Živković
We provide a generating function for the (graded) dimensions of M. Kontsevich's graph complexes of ordinary graphs. This generating function can be used to compute the Euler charac…
Quantum Transport in Graphene Nanoribbons with Realistic Edges
Patrick Hawkins, Milan Begliarbekov, Marko Zivkovic +2
Due to their unique electrical properties, graphene nanoribbons (GNRs) show great promise as the building blocks of novel electronic devices. However, these properties are strongly…
Quantum dynamics of cavity assisted photoassociation of Bose-Einstein condensed atoms
Christopher P. Search, J. Mauricio Campuzano, Marko Zivkovic
We explore the quantum dynamics of photoassociation of Bose-Einstein condensed atoms into molecules using an optical cavity field. Inside of an optical resonator, photoassociation…
Sagnac effect in a chain of mesoscopic quantum rings
Chris P. Search, John R. E. Toland, Marko Zivkovic
The ability to interferometrically detect inertial rotations via the Sagnac effect has been a strong stimulus for the development of atom interferometry because of the potential 10…
Quantum bistability and spin current shot noise of a single quantum dot coupled to an optical microcavity
Ivana Djuric, Marko Zivkovic, Chris P. Search +1
Here we explore spin dependent quantum transport through a single quantum dot coupled to an optical microcavity. The spin current is generated by electron tunneling between a singl…
Sagnac Rotational Phase Shifts in a Mesoscopic Electron Interferometer with Spin-Orbit Interactions
Marko Zivkovic, Markku Jaaskelainen, Christopher P. Search +1
The Sagnac effect is an important phase coherent effect in optical and atom interferometers where rotations of the interferometer with respect to an inertial reference frame result…