In the last ten years application of complex networks for the study of many diverse problems have appeared, but I cannot recall any study on quantum systems.
Is there any work around that you are aware of?
Thanks for the reply.
But this is not what I meant. I am looking for applications on real systems involving quantum effects, eg entanglement, electronic structure etc. where a network approach helped to describe the system, eventually giving new insights into the underlying physics.
Your idea is very interesting and probably networks (graphs) can be used in the respect that you are thinking. I am not aware of any such research being conducted so far (maybe due to the fact that these are different communities who do not use each other's ideas... ) Well, go on, start it.
We have done something in the direction of applying the networks to study quantum tunneling conduction in nano-particle assemblies,
(you can have a look at our review article in http://iopscience.iop.org/0953-8984/22/16/163201/ )
where we use graph theory to quantify the effects of the topology of the assembly onto its conduction properties.
if "a network is a graph" for your studies then it might be worthwhile to checking these out:
Classical dynamics on graphs,
F. Barra and P. Gaspard,
Physical Review E 63 (2001) 066215 (22 pages); preprint nlin.CD/0011045. (pdf)
On the Level Spacing Distribution in Quantum Graphs,
F. Barra and P. Gaspard,
Journal of Statistical Physics 101 (2000) 283-319; preprint quant-ph/0011099. (pdf)
good luck!
Hi Francesco, I had done some work on this in the past. In particular, I looked at quantum walks on networks, and tried to understand what sort of insights can the quantum dynamics give us about the network structure (in terms of community detection), stability, etc. Details can be found here: http://arxiv.org/abs/1012.2405
"Quantum walks on complex networks with connection instabilities and community structure", Phys. Rev. A 83, 052315 (2011).
Best wishes
Dimitris
Hi,
take a look to our recent paper on a related topic:
http://iopscience.iop.org/1742-5468/2013/04/P04019?fromSearchPage=true
Hi Francesco,
Sorry for the delay, I just saw your question.
I've been working on this topic for the last few years, also a workshop was recently held at IQC (Canada). Check out the following two articles of mine as examples:
In the first
http://www.nature.com/srep/2013/130806/srep02361/full/srep02361.html
we show that transport on networks can be directed, enhanced and suppressed through local phase changes in the Hamiltonian, and the result depends on the topology of the network.
In the second
http://arxiv.org/abs/1305.6078
we relate the probability distribution to the degree of the nodes as in the classical case.
Cheers,
Mauro
Hi Francesco,
Interesting question, and I guess it depends on what one calls a complex network, I am not sure whether I am an expert on that subject (albeit they invited me recently to make an invited talk at an Intern. conference on those networks, albeit it could've happened by mistake, who knows:-), but just in case here are a few pointers to our (mine and S. Volkov's) research:
http://psi.ece.jhu.edu/~kaplan/PUBL/AEK.pubs/124.pdf
http://psi.ece.jhu.edu/~kaplan/PUBL/AEK.pubs/127E.pdf
http://psi.ece.jhu.edu/~kaplan/PUBL/AEK.pubs/128.pdf
http://psi.ece.jhu.edu/~kaplan/PUBL/AEK.pubs/130.pdf
Hope it comes close, but I still suspect that complex networks are something else...:-)
Francesco,
the notion of a "quantum graph" or "quantum network" was invented in the early years of QM by Pauling [J. Chem. Phys. 4, 673 (1936)] as a model of naphthalene, where he imagined the molecule as a graphs with atoms as nodes and bonds as edges. Electrons then travel along the edges and scatter at nodes. The matter was revived recently [Smilansky, PRL 79, 4794 (1997)] in the context of quantum chaos, because is a non-trivial system that is classically chaotic and has exact quantum solution.
It's a fascinating problem ...
As far as I know, David Bohm's conception of quantum systems as a deep structure of wholeness is very similar to Christopher Alexander's wholeness. The wholeness is defined mathematically as a recursive structure, and exists physically in space and matter, and reflects psychologically in human minds and cognition. In other words, the wholeness is not merely intuition or cognition, but something of physics. I developed a complex-network perspective on Alexander's wholeness:
Article A Complex-Network Perspective on Alexander's Wholeness
And further developed a topological representation for extracting geographic space or the Earth's surface as a coherent whole.
Article A Topological Representation for Taking Cities as a Coherent Whole
However, I must make it clear that complex network perspective is essentially under Descartes' mechanistic framework, largely for understanding complexity, BUT (BIG BUT) the wholeness is under Alexander's organic world view, not only for understanding complexity, but also for making complex or living structures: buildings, cities, gardens etc.. Herewith one related talk:
Presentation Geospatial Big Data and Living Structure For better Understa...
Presentation Scaling Law and Tobler's Law for Characterizing Asymmetry in Geography
- Badges
- Science topic