E. W. Montroll and G. H. Weiss, Random Walks on Lattices. II, J. Math. Phys, vol.6, pp.167-181, 1965.

B. Balagurov, . Ya, and V. G. Vaks, Random walk of a particle in a lattice with traps, J.E.T.P, vol.38, pp.968-971, 1974.

M. Donsker and S. R. Varadhan, Asymptotics for the Wiener sausage, Commun. Pure Appl. Math, vol.28, pp.525-565, 1975.

M. Donsker and S. R. Varadhan, On the number of distinct sites visited by a random walk, Commun. Pure Appl. Math, vol.32, pp.721-747, 1979.

P. Grassberger and I. Procaccia, The long time properties of diffusion in a medium with static traps, J. Chem. Phys, vol.77, pp.6281-6284, 1982.

D. Toussaint and F. Wilczek, Particle-antiparticle annihilation in diffusive motion, J. Chem. Phys, vol.78, pp.2642-2647, 1983.

J. Klafter, G. Zumofen, and A. Blumen, Long-time properties of trapping on fractals, J. Phys, vol.45, pp.49-56, 1984.
URL : https://hal.archives-ouvertes.fr/jpa-00232307

M. Bramson and J. L. Lebowitz, Asymptotic behavior of densities in diffusion-dominated annihilation reactions, Phys. Rev. Lett, vol.61, pp.2397-2400, 1988.

M. Bramson and J. L. Lebowitz, Asymptotic behavior of densities in diffusion-dominated annihilation reactions (erratum), Phys. Rev. Lett, vol.62, pp.694-694, 1989.

E. Ben-naim, S. Redner, and G. H. Weiss, Partial absorption and 'virtual' traps, J. Stat. Phys, vol.71, pp.75-85, 1993.

J. W. Haus and K. W. Kehr, Diffusion in regular and disordered lattices, Phys. Rep, vol.150, pp.263-406, 1987.

S. Havlin and D. Ben-avraham, Diffusion in disordered media, Adv. Phys, vol.36, pp.695-798, 1987.

P. L. Krapivsky, S. Redner, and E. Ben-naim, A Kinetic View of Statistical Physics, 2010.

I. M. Lifshitz, The energy spectrum of disordered systems, Adv. Phys, vol.13, pp.483-536, 1964.

I. M. Lifshitz, S. A. Gredeskul, and L. A. Pastur, Introduction to the Theory of Disordered Systems, 1988.

L. Pastur and A. Figotin, Spectra of Random and Almost-Periodic Operators, 1992.

H. B. Rosenstock, Random walks on lattices with traps, J. Math. Phys, vol.11, pp.487-490, 1970.

G. T. Barkema, P. Biswas, and H. Van-beijeren, Diffusion with random distribution of static traps, Phys. Rev. Lett, vol.87, p.170601, 2001.

R. Friedberg and J. M. Luttinger, Density of electronic energy levels in disordered systems, Phys. Rev. B, vol.12, pp.4460-4474, 1975.

J. L. Cardy, Electron localisation in disordered systems and classical solutions in Ginzburg-Landau field theory, J. Phys. C, vol.11, pp.321-327, 1978.

J. M. Luttinger and R. Tao, Electronic density of levels in a disordered system, Ann. Phys, vol.145, pp.185-203, 1983.

T. C. Lubensky, Fluctuations in random walks with random traps, Phys. Rev. A, vol.30, pp.2657-2665, 1984.

T. M. Nieuwenhuizen and J. M. Luck, Singularities in spectra of disordered systems: an instanton approach for arbitrary dimension and randomness, Europhys. Lett, vol.9, pp.407-413, 1989.

T. M. Nieuwenhuizen, Trapping and Lifshitz tails in random media, self-attracting polymers, and the number of distinct sites visited: a renormalized instanton approach in three dimensions, Phys. Rev. Lett, vol.62, pp.357-360, 1989.

A. Zee and I. Affleck, Hopping between random locations: spectrum and instanton, J. Phys. Cond. Matt, vol.12, pp.8863-8873, 2000.

P. E. Parris, One-dimensional trapping kinetics at zero temperature, Phys. Rev. Lett, vol.62, pp.1392-1395, 1989.

P. E. Parris, One-dimensional quantum transport in the presence of traps, Phys. Rev. B, vol.40, pp.4928-4937, 1989.

J. W. Edwards and P. E. Parris, Quantum transport in the presence of random traps, Phys. Rev. B, vol.40, pp.8045-8048, 1989.

P. E. Parris, Quantum and stochastic aspects of low-temperature trapping and reaction dynamics, J. Stat. Phys, vol.65, pp.1161-1172, 1991.

R. M. Pearlstein, Impurity quenching of molecular excitons. I. Kinetic comparison of FörsterDexter and slowly quenched Frenkel excitons in linear chains, J. Chem. Phys, vol.56, pp.2431-2442, 1972.

R. P. Hemenger, K. Lakatos-lindenberg, and R. M. Pearlstein, Impurity quenching of molecular excitons. III. Partially coherent excitons in linear chains, J. Chem. Phys, vol.60, pp.3271-3277, 1974.

D. L. Huber, Decay of the k=0 exciton mode at a finite trap concentration, Phys. Rev. B, vol.24, pp.1083-1086, 1981.

H. Benk and R. Silbey, Exciton-phonon scattering and exciton trapping in one-dimensional exciton systems, J. Chem. Phys, vol.79, pp.3487-3495, 1983.

Y. Aharonov, L. Davidovich, and N. Zagury, Quantum random walks, Phys. Rev. A, vol.48, pp.1687-1690, 1993.

E. Farhi and S. Gutmann, Quantum computation and decision trees, Phys. Rev. A, vol.58, pp.915-928, 1998.

A. M. Childs and J. Goldstone, Spatial search by quantum walk, Phys. Rev. A, vol.70, p.22314, 2004.

A. M. Childs, Universal computation by quantum walk, Phys. Rev. Lett, vol.102, p.180501, 2009.

A. M. Childs, On the relationship between continuous-and discrete-time quantum walk, Commun. Math. Phys, vol.294, pp.581-603, 2010.

J. Kempe, Quantum random walks: an introductory overview, Contemp. Phys, vol.44, pp.307-327, 2003.

A. Ambainis, Quantum walks and their algorithmic applications, Int. J. Quant. Inf, vol.1, pp.507-518, 2003.

H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti et al., Realization of quantum walks with negligible decoherence in waveguide lattices, Phys. Rev. Lett, vol.100, p.170506, 2008.

A. Peruzzo, M. Lobino, J. C. Matthews, N. Matsuda, A. Politi et al., Quantum walks of correlated photons, vol.329, pp.1500-1503, 2010.

N. Konno, Quantum random walks in one dimension, Quant. Inf. Processing, vol.1, pp.345-354, 2002.

T. D. Mackay, S. D. Bartlett, L. T. Stephenson, and B. C. Sanders, Quantum walks in higher dimensions, J. Phys. A, vol.35, pp.2745-2753, 2002.

B. Tregenna, W. Flanagan, R. Maile, and V. Kendon, Controlling discrete quantum walks: coins and initial states, New J. Phys, vol.5, p.83, 2003.

S. De-toro-arias and J. M. Luck, Anomalous dynamical scaling and bifractality in the one-dimensional Anderson model, J. Phys. A, vol.31, pp.7699-7717, 1998.

D. Ben-avraham, E. M. Bollt, and C. Tamon, One-dimensional continuous-time quantum walks, Quant. Inf. Processing, vol.3, pp.295-308, 2004.

E. Akkermans, A. Comtet, J. Desbois, G. Montambaux, and C. Texier, Spectral determinant on quantum graphs, Ann. Phys, vol.284, pp.10-51, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00003196

F. W. Strauch, Connecting the discrete-and continuous-time quantum walks, Phys. Rev. A, vol.74, p.30301, 2006.

S. E. Venegas-andraca, Quantum walks: a comprehensive review, Quant. Inf. Processing, vol.11, pp.1015-1106, 2012.

S. Haroche and J. M. Raimond, Exploring the Quantum: Atoms, Cavities, and Photons, 2006.

N. Konno, T. Namiki, T. Soshi, and A. Sudbury, Absorption problems for quantum walks in one dimension, J. Phys. A, vol.36, pp.241-253, 2003.

O. Mülken, A. Blumen, T. Amthor, C. Giese, M. Reetz-lamour et al., Survival probabilities in coherent exciton transfer with trapping, Phys. Rev. Lett, vol.99, p.90601, 2007.

O. Mülken, V. Pernice, and A. Blumen, Slow excitation trapping in quantum transport with long-range interactions, Phys. Rev. E, vol.78, p.21115, 2008.

E. Agliari, O. Mülken, and A. Blumen, Continuous-time quantum walks and trapping, Int. J. Bif. Chaos, vol.20, pp.271-279, 2010.

E. Agliari, Trapping of continuous-time quantum walks on Erdös-Rényi graphs, Physica A, vol.390, pp.1853-1860, 2011.

O. Mülken and A. Blumen, Continuous-time quantum walks: models for coherent transport on complex networks, Phys. Rep, vol.502, pp.37-87, 2011.

M. Gönülol, E. Aydiner, Y. Shikano, and Ö. E. Müstecaplioglu, Survival probability in a one-dimensional quantum walk on a trapped lattice, New J. Phys, vol.13, p.33037, 2011.

C. Ampadu, M. Gönülol, and E. Aydiner, Survival probability of the quantum walk with phase parameters on the two-dimensional trapped lattice, J. Quant. Inf. Sc, vol.3, pp.51-56, 2013.

A. Anishchenko, A. Blumen, and O. Mülken, Geometrical aspects of quantum walks on random two-dimensional structures, Phys. Rev. E, vol.88, p.62126, 2013.

T. M. Nieuwenhuizen and J. M. Luck, Lifshitz singularities in random harmonic chains: periodic amplitudes near the band edge and near special frequencies, J. Stat. Phys, vol.48, pp.393-424, 1987.

J. M. Luck, Systèmes désordonnés unidimensionnels. Collection Aléa Saclay, 1992.

S. Selstø, Formulae for partial widths derived from the Lindblad equation, Phys. Rev. A, vol.85, p.62518, 2012.

S. Selstø and S. Kvaal, Absorbing boundary conditions for dynamical many-body quantum systems, J. Phys. B, vol.43, p.65004, 2010.

A. Diaz-torres, Absence of decoherence in the complex-potential approach to nuclear scattering, Phys. Rev. C, vol.81, p.41603, 2010.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 1965.

D. E. Holz, H. Orland, and A. Zee, On the remarkable spectrum of a non-Hermitian random matrix model, J. Phys. A, vol.36, pp.3385-3400, 2003.