Field-Theoretical Approach to Complex Networks

Lead Research Organisation: University of Birmingham
Department Name: School of Physics and Astronomy


We propose to create new tools for describing complex network systems by extending and modifying techniques used in theoretical physics for the description of disordered mesoscopic systems. We intend to provide a framework for a universal description of stochastic propagation through complex network systems belonging to different classes. Taking into account both dynamical disorder (due to the inevitable stochasticity of the input) and quenched disorder (that models complex networks of different topologies), we will formulate a set of relevant Langevin equations defined on discrete manifolds (networks). To achieve the universal description, we are going to cast these equations into the form of an effective field theory. This would allow us first to classify the networks (crucially, allowing both for the character of random signal and / simultaneously / for the network topology) and thus present new universality classes that emerge as the result of this complexity, and then to use powerful field theoretical methods for determining and calculating relevant observable quantities on the complex network.


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Altshuler BL (2009) Jumps in current-voltage characteristics in disordered films. in Physical review letters

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Chudnovskiy AL (2012) Doublon relaxation in the Bose-Hubbard model. in Physical review letters

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Gangardt DM (2010) Quantum decay of dark solitons. in Physical review letters

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Gangardt DM (2009) Bloch oscillations in a one-dimensional spinor gas. in Physical review letters

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Kagalovsky V (2017) Local impurity in a multichannel Luttinger liquid in Physical Review B

Description We have developed a set of field-theoretical models based on the Fokker-Planck description of `data random walks' in complex systems, in particular packet-switch networks like the Internet. We have modeled the onset of network congestion and the protocol-driven network reaction to it - a sharp reduction of the input traffic rate through congested routes. We have shown that traffic losses at the onset of congestion can be described as a phase transition characterized by strong non-Gaussian loss fluctuations at a mesoscopic time scale. The fluctuations, caused by noise in input traffic, are exacerbated by the heterogeneous nature of the network manifested in a scale-free load distribution and result in the network strongly overreacting to the first signs of congestion. We have also used the Fokker-Planck description of the Sinai model with random drifts to obtain the exact probability distribution of random walks there. We have used similar methods for other complex systems. In total, we acknowledged EPSRC support in 9 publications (three in PRL, one more submitted there), including two by the visiting research fellow (Prof A Kamenev, University of Minnesota) in the collaboration, initiated due to the support of this grant, with another member of the Birmingham team (Dr D Gangardt).
Exploitation Route Our suggestions on improving protocols for network communications with the aim to reduce networks delay due to protocol over-reaction on nascent congestion can be useful for communication technology.
Sectors Digital/Communication/Information Technologies (including Software),Other

Description University of Minnesota 
Organisation University of Minnesota
Country United States 
Sector Academic/University 
PI Contribution We have collaborated with Professor A Kamenev, and collaboration initiated by this grant has resulted in several joint publications with a member of Birmingham team (Dr D Gangardt).
Collaborator Contribution Prof Kamenev has suggested some new methods that have been implemented in our research.
Impact Several publications including a couple in Physical Review Letters.
Start Year 2009