Dr. Christoph Rahmede

Responsible of the quantum gravity and networks research field 


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Research Interests:

Network analysis, statistical physics, particle physics, quantum gravity, cosmology


see google scholar 



Research Positions


10/2015 – 09/2016    Rome International Center for Materials Science Superstripes, Rome (ITA)

 Research Affiliate


10/2012 – 09/2015Karlsruhe Institute of Technology (GER), Institute for Theoretical Physics

Postdoctoral Research Associate


10/2011 – 09/2012Technical University Dortmund (GER), Institute for Theoretical Physics

Postdoctoral Research Associate


06/2009 – 09/2011University of Sussex, Brighton (UK), Institute for Theoretical Particle Physics

Postdoctoral Research Associate


01/2009 – 02/2009University of Mainz (GER), Institute for Theoretical High Energy Physics

Postdoctoral Research Associate


11/2004 – 12/2008International School for Advanced Studies (SISSA), Trieste (Italy)

PhD-scholarship in theoretical astroparticle physics

Degree: PhD


04/1999 – 06/2004Goethe-University, Frankfurt/Main (Germany)

Undergraduate studies in physics

Degree: Diplom-Physicist



1. Network geometry with flavor: from complexity to quantum geometry

Ginestra Bianconi, Christoph Rahmede 

Phys. Rev. E 93, 032315 (2016)

doi;  10.1103/PhysRevE.93.032315 arXiv:1511.04539

Abstract: Here we introduce the Network Geometry with Flavor s=−1,0,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a non-equilibrium dynamics. The NGF can generate discrete geometries of different nature, ranging from chains and higher dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution and non-trivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási model for complex networks the stochastic Apollonian network, and the recently introduced model for Complex Quantum Network Manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states are evolving by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t. Interestingly the NGF remains fully classical but its statistical properties reveal the relation to its quantum mechanical description. In fact the δ-dimensional faces of the NGF have generalized degrees that follow either the Fermi-Dirac, Boltzmann or Bose-Einstein statistics depending on the flavor s and the dimensions d and δ.      

2. Functional Multiplex PageRank

Jacopo Iacovacci, Christoph Rahmede, Alex Arenas, Ginestra Bianconi 

EPL (Europhysics Letters), 116 (2016) 28004

doi: 10.1209/0295-5075/116/28004

preprint: arXiv:1608.06328

Abstract: Recently it has been recognized that many complex social, technological and biological networks have a multilayer nature and can be described by multiplex networks. Multiplex networks are formed by a set of nodes connected by links having different connotations forming the different layers of the multiplex. Characterizing the centrality of the nodes in a multiplex network is a challenging task since the centrality of the node naturally depends on the importance associated to links of a certain type. Here we propose to assign to each node of a multiplex network a centrality called Functional Multiplex PageRank that is a function of the weights given to every different pattern of connections (multilinks) existent in the multiplex network between any two nodes. Since multilinks distinguish all the possible ways in which the links in different layers can overlap, the Functional Multiplex PageRank can describe important non-linear effects when large relevance or small relevance is assigned to multilinks with overlap. Here we apply the Functional Page Rank to the multiplex airport networks, to the neuronal network of the nematode c.elegans, and to social collaboration and citation networks between scientists. This analysis reveals important differences existing between the most central nodes of these networks, and the correlations between their so called "pattern to success”.


3. Centralities of Nodes and Influences of Layers in Large Multiplex Networks

Christoph Rahmede, Jacopo Iacovacci, Alex Arenas, Ginestra Bianconi

Journal of Complex Networks, cnx050 (2017)

doi: 10.1093/comnet/cnx050                                                               

preprint : arXiv:1703.05833

 Abstract: We formulate and propose an algorithm (MultiRank) for the ranking of nodes and layers in large multiplex networks. MultiRank takes into account the full multiplex network structure of the data and exploits the dual nature of the network in terms of nodes and layers. The proposed centrality of the layers (influences) and the centrality of the nodes are determined by a coupled set of equations. The basic idea consists in assigning more centrality to nodes that receive links from highly influential layers and from already central nodes. The layers are more influential if highly central nodes are active in them. The algorithm applies to directed/undirected as well as to weighted/unweighted multiplex networks. We discuss the application of MultiRank to three major examples of multiplex network datasets: the European Air Transportation Multiplex Network, the Pierre Auger Multiplex Collaboration Network and the FAO Multiplex Trade Network.                                                                                                       


4. Emergent Hyperbolic Network Geometry

Ginestra Bianconi, Christoph Rahmede 

Scientific Reports 7, 41974 (2017)

doi. 10.1038/srep41974 

preprint: arXiv:1607.05710

Abstract: A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a discretization of spacetime. Here, by extending our knowledge of growing complex networks to growing simplicial complexes we investigate the nature of the emergent geometry of complex networks and explore whether this geometry is hyperbolic. Specifically we show that an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes that are purely combinatorial. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free degree distribution, small-world and communities) at the same time. Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by relevant changes in the network geometry. 


 5. Asymptotic safety of quantum gravity beyond Ricci scalars

Kevin G. Falls, Callum R. King, Daniel F. Litim, Kostas Nikolakopoulos, Christoph Rahmede 

Physical Review D 97, 086006 (2018) 

doi:  10.1103/PhysRevD.97.086006

preprint : arXiv:1801.00162

Abstract: We investigate the asymptotic safety conjecture for quantum gravity including curvature invariants beyond Ricci scalars. Our strategy is put to work for families of gravitational actions which depend on functions of the Ricci scalar, the Ricci tensor, and products thereof. Combining functional renormalisation with high order polynomial approximations and full numerical integration we derive the renormalisation group flow for all couplings and analyze their fixed points, scaling exponents, and the fixed point effective action as a function of the background Ricci curvature. The theory is characterised by three relevant couplings. Higher-dimensional couplings show near-Gaussian scaling with increasing canonical mass dimension. We find that Ricci tensor invariants stabilise the UV fixed point and lead to a rapid convergence of polynomial approximations. We apply our results to models for cosmology and establish that the gravitational fixed point admits inflationary solutions. We also compare findings with those from f(R)-type theories in the same approximation and pin-point the key new effects due to Ricci tensor interactions. Implications for the asymptotic safety conjecture of gravity are indicated.

6. On de Sitter solutions in asymptotically safe f(R)

 Kevin Falls, Daniel F. Litim, Kostas Nikolakopoulos, Christoph Rahmede 

Classical and Quantum Gravity, 35(13), 135006 (2018) 

DOI: https://doi.org/10.1088/1361-6382/aac440


Preprint arXiv:1607.04962

Abstract: The availability of scaling solutions in renormalisation group improved versions of cosmology are investigated in the high-energy limit. We adopt f(R)-type models of quantum gravity which display an interacting ultraviolet fixed point at shortest distances. Expanding the gravitational fixed point action to very high order in the curvature scalar, we detect a convergence-limiting singularity in the complex field plane. Resummation techniques including Padé approximants as well as infinite order approximations of the effective action are used to maximise the domain of validity. We find that the theory displays near de Sitter solutions as well as an anti-de Sitter solution in the UV whereas real de Sitter solutions, for small curvature, appear to be absent. The significance of our results for inflation, and implications for more general models of quantum gravity are discussed.