Random walks on random lattices
Study of
diffusion on random lattices started as the topic of my postdoc work in the
group of M. Ernst in Utrecht.
- The anomalous diffusion in strongly disordered chains was a rather rich
and elegant subject, [P6].
- A general theory for diffusion on two-dimensional lattices was worked out
for the case of small concentrations of impurities, [L5],[P15],[P16],[P17],[P25],[P26].
- This topic has some connections with long time survival probabilities in
random walks on lattices with traps, [L10] and [P29].
- With master student H. Brandt the problem with imperfect traps in one dimension
was considered, [P27].
[L10] Th.M. N., 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. 62 (1989) 357-360
[L5] Th.M. N., P.F.J. van Velthoven, and M.H. Ernst, Diffusion and long time tails in a two-dimensional site percolation model, Phys. Rev. Lett. 57 (1986) 2477-2480
[P29] Th.M. N., Singularies in spectra of disordered systems, Physica A 167 (1990) 43-65
[P27] Th.M. N. and H. Brandt, Diffusion and survival in a medium with imperfect traps, J. Stat. Phys. 59 (1990) 53-72
[P26] M.H.
Ernst and Th.M. N., Biased random walks on lattices with diluted disorder,
J.
Phys. A 22 (1989) 5231-5248
[P25] Th.M.
N., Dynamical properties of 2-d systems with site disorder,
Physica
A 157 (1989) 1101-1138
[P17] M.H. Ernst, Th.M. N., and P.F.J. van Velthoven, Density expansion on a 2-D site disordered lattice II, J. Phys. A 20 (1987) 5335-5350
[P16] Th.M.
N., P.F.J. van Velthoven, and M.H. Ernst, Density expansion of transport
properties on 2-D site disordered lattices: I, General Theory, J.
Phys. A 20 (1987) 4001-4015
[P15] M.H. Ernst, P.F.J. van Velthoven, and Th.M. N., Systematic density expansion for random resistor networks, J. Phys. A 20 (1987) 949-959
[P6] Th.M. N. and M.H. Ernst, Transport and spectral properties of strongly disordered chains, Phys. Rev. B 31 (1985) 3518-3533