Trapping of continuous-time quantum walks on Erdös–Rényi graphs

We consider the coherent exciton transport, modeled by continuous-time quantum walks, on Erdos–Reny graphs in the presence of a random distribution of traps. The role of trap concentration and of the substrate dilution is deepened showing that, at long times and for intermediate degree of dilution, the survival probability typically decays exponentially with a (average) decay rate which depends non-monotonically on the graph connectivity; when the degree of dilution is either very low or very high, stationary states, not affected by traps, get more likely giving rise to a survival probability decaying to a finite value. Both these features constitute a qualitative difference with respect to the behavior found for classical walks.

[1]  R. Wagner,et al.  Molecular Optoelectronic Gates , 1996 .

[2]  E. Farhi,et al.  Quantum computation and decision trees , 1997, quant-ph/9706062.

[3]  J. Leydold,et al.  Laplacian eigenvectors of graphs : Perron-Frobenius and Faber-Krahn type theorems , 2007 .

[4]  R. Merris.  Laplacian matrices of graphs: a survey , 1994 .

[5]  E. Montroll,et al.  Random Walks on Lattices. II , 1965 .

[6]  Peter F. Stadler,et al.  Laplacian Eigenvectors of Graphs , 2007 .

[7]  M J Therien,et al.  Highly conjugated, acetylenyl bridged porphyrins: new models for light-harvesting antenna systems. , 1994, Science.

[8]  Riccardo Zecchina,et al.  Exact solutions for diluted spin glasses and optimization problems , 2001, Physical review letters.

[9]  Elena Agliari,et al.  Quantum-walk approach to searching on fractal structures , 2010, 1002.1274.

[10]  Elena Agliari,et al.  Continuous-Time Quantum Walks and Trapping , 2009, Int. J. Bifurc. Chaos.

[11]  Julia Kempe,et al.  Quantum random walks: An introductory overview , 2003, quant-ph/0303081.

[12]  Andris Ambainis,et al.  Quantum search algorithms , 2004, SIGA.

[13]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[14]  S. Lloyd,et al.  Environment-assisted quantum walks in photosynthetic energy transfer. , 2008, The Journal of chemical physics.

[15]  Xin-Ping Xu,et al.  Continuous-time quantum walks on one-dimensional regular networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Klaus Schulten,et al.  Comparison of the light-harvesting networks of plant and cyanobacterial photosystem I. , 2005, Biophysical journal.

[17]  Frank Harary,et al.  Graph Theory , 2016 .

[18]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[19]  Masoud Mohseni,et al.  Environment-assisted quantum transport , 2008, 0807.0929.

[20]  R. Merris.  Laplacian graph eigenvectors , 1998 .

[21]  X. P. Xu,et al.  Continuous-time quantum walks on ErdsRnyi networks , 2008 .

[22]  Volkhard May,et al.  Charge and Energy Transfer Dynamics in Molecular Systems, 2nd, Revised and Enlarged Edition , 2004 .

[23]  Animesh Datta,et al.  Highly efficient energy excitation transfer in light-harvesting complexes: The fundamental role of n , 2009, 0901.4454.

[24]  S. Datta.  Quantum Transport: Atom to Transistor , 2004 .

[25]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[26]  Volker Pernice,et al.  Quantum transport on small-world networks: a continuous-time quantum walk approach. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  M. Fiedler.  A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory , 1975 .

[28]  E. Agliari,et al.  Dynamics of continuous-time quantum walks in restricted geometries , 2008, 0810.1184.

[29]  M. Weidemüller,et al.  Survival probabilities in coherent exciton transfer with trapping. , 2007, Physical review letters.

[30]  Bruce A. Reed,et al.  A Critical Point for Random Graphs with a Given Degree Sequence , 1995, Random Struct. Algorithms.