upward

Random walks

Zeitouni O, Random walks in random environments, JPA 39, R433 (2006)

den Hollander F, Steif J E, Random walk in random scenery: A survey of some recent results, IMS Lecture Notes 48, 53 (2006)

Zeitouni O, Random walks in random environment, LNM 1837, 189 (2004)

Kehr K W, Wichmann T, Diffusion coefficients of single and many particles in lattices with different forms of disorder, cond-mat/9602121

Revesz P, Random walk in random and non-random environments (WSPC, 1990)

Kirkpatrick S, Percolation and conduction, RMP 45, 574 (1973)

General models

Mussawisade K, Wichmann T, Kehr K W, Combination of random-barrier and random-trap models, JPC 9, 1181 (1997)

Denteneer P J H, Ernst M H, Diffusion in systems with static disorder, PRB 29, 1755 (1984)

Derrida B, Luck J M, Diffusion on a random lattice: Weak-disorder expansion in arbitrary dimension, PRB 28, 7183 (1983)

Movaghar B, Grunewald M, Pohlmann B, Wurtz D, Schirmacher W, Theory of hopping and multiple-trapping transport in disordered systems, JSP 30, 315 (1983)

B Movaghart, B Pohlmann, D Wurtz, The Hall mobility in hopping conduction, JPC 14, 5127 (1981)

Movaghar B, Schirmacher W, On the theory of hopping conductivity in disordered systems, JPC 14, 859 (1981)

Movaghar B, Pohlmann B, Sauer G W, Theory of AC and DC conductivity in disordered hopping systems, PSSB 97, 533 (1980) – two-site theory, EMA

Movaghar B, Pohlmann B, Schirmacher W, Theory of electronic hopping transport in disordered materials, Philos Mag B 41, 49 (1980) – RPE

Tunneling hopping

Hartenstein B, Bassler H, Jakobs A, Kehr K W, Comparison between multiple trapping and multiple hopping transport in a random medium, PRB 54, 8574 (1996)

Movaghar B, Ries B, Grunewald M, Diffusion and relaxation of energy in disordered systems: Departure from mean-field theories, PRB 34, 5574 (1986)

Movaghar B, Grunewald M, Ries B, Bassler H, Wurtz D, Diffusion and relaxation of energy in disordered organic and inorganic materials, PRB 33, 5545 (1986)

Grunewald M, Movaghar B, Pohlmann B, Wurtz D, Hopping theory of band-tail relaxation in disordered semiconductors, PRB 32, 8191 (1985)

Grunewald M, Movaghar B, Pohlmann B, Wurtz D, Theory of non-equilibrium diffusive transport in disordered materials, Philos Mag B 49, 341 (1984)

Silver M, Schoenherr, Baessler H, Dispersive hopping transport from an exponential energy distribution of sites, PRL 48, 352 (1982)

RBM

Byshkin M S, Turkin A A, A new method for the calculation of the conductivity of inhomogeneous systems, JPA 38, 5057 (2005)

Wu F Y, Theory of resistor networks: the two-point resistance, JPA 37, 6653 (2004)

Braga G A, Proccaci A, Sanchis R, Analyticity of the d-dimensional bond percolation probability around p=1, JSP 107, 1267 (2002)

Saadatfar M, Sahimi M, Diffusion in disordered media with long-range correlations: Anomalous, Fickian, and superdiffusive transport and log-periodic oscillations, PRE 65, 036116 (2002)

Dyre J C, Schroeder T B, Hopping models and ac universality, PSSB 230, 5 (2002) – questionable results

Ganter C, Schirmacher W, Generalization of the effective-medium approximation for hopping transport in amorphous materials, PSSB 218, 71 (2000) – enhanced version of Gochanour79

P Argyrakis, A Milchev, V Pereyra, K W Kehr, Dependence of the diffusion coefficient on the energy distribution of random barriers, PRE 52, 3623 (1995)

Horner A, Milchev A, Argyrakis P, Role of percolation in diffusion on random lattices, PRE 52, 3570 (1995)

Ambaye H, Kehr K W, Asymptotic diffusion coefficient of particles in a random medium, PRE 51, 5101 (1995)

Avramov I, Milchev A, Argyrakis P, Diffusion in a random medium: A Monte Carlo study, PRE 47, 2303 (1993)

Parris P E, Site-diagonal T-matrix expansion for anisotropic transport and percolation on bond-disordered lattices, PRB 36, 5437 (1987)

Kariotis R, Diffusion coefficient for two- and three-dimensional disordered lattices, JPA 17, 2889 (1984) – via genfun

Sahimi M, Hughes B D, Scriven L E, Davis H D, Real-space renormalization and effective-medium approximation to the percolation conduction problem, PRB 28, 307 (1983)

Sahimi M, Hughes B D, Scriven L E, Davis H T, Stochastic transport in disordered systems, JCP 78, 6849 (1983) – EMA, CTRW

Odagaki T, Lax M, Coherent-medium approximation in the stochastic transport theory of random media, PRB 24, 5284 (1981) – time-dependent EMA

Webman I, Effective-medium approximation for diffusion on a random lattice, PRL 47, 1496 (1981) – time-dependent EMA

Gochanour C R, Andersen H C, Fayer M D, Electronic excited state transport in solution, JCP 70, 4254 (1979) – diagram expan

Ahmed G, Blackman J A, On theories of transport in disordered media, JPC 12, 837 (1979) – 3D version of Blackman76

Turban L, On the effective-medium approximation for bond-percolation conductivity, JPC 11, 449 (1978) – cluster EMA

Haan S W, Zwanzig R, Forster migration of electronic excitation between randomly distributed molecules, JCP 68, 1879 (1978) – 2-nd order some density expan

Bernasconi J, Real-space renormalization of bond-disordered conductance lattices, PRB 18, 2185 (1978)

Bernasconi J, Schneider W R, Wiesmann H J, Some rigorous results for random planar conductance networks, PRB 16, 5250 (1977)

Blackman J A, A theory of conductivity in disordered resistor networks, JPC 9, 2049 (1976) – perturbation, cluster EMA

RSM

Фатеев М П, Метод когерентного потенциала для задачи диффузии на случайной решетке замещения, ТМФ 149, 252 (2006)

Bernasconi J, Wiesmann H J, Effective-medium theories for site-disordered resistance networks, PRB 13, 1131 (1976)

RTM

den Hollander F, Naudts J, Redig F, Dynamic structure factor in a random diffusion model, JSP 76, 1267 (1994)

den Hollander F, Naudts J, Redig F, Long-time tails in a random diffusion model, JSP 69, 731 (1992)

Tamor M A, Random walk in an exponential band, PRB 35, 5729 (1987)

Kundu K, Phillips P, Hopping transport on site-disordered d-dimensional lattices, PRA 35, 857 (1987)

Silver M, Cohen L, Monte Carlo simulation of anomalous transit-time dispersion of amorphous solids, PRB 15, 3276 (1977)

Biased random walk

Bustingorry S, Manuel O, Caceres M O, Reyes E R, Effective-medium approximation with asymmetric transition rates, PRE 65, 165205 (2002)

Rinn B, Braunschweig U, Maass P, Schirmacher W, Effective-medium approximation for energy-dependent hopping on a lattice, PSSB 218, 93 (2000)

Stauffer D, Sornette D, Log-periodic oscillations for biased diffusion on random lattice, PA 252, 271 (1998)

Avramov I, Milchev A, Arapaki E, Argyrakis P, Biased random walk in energetically disordered lattices, PRE 58, 2788 (1998)

Weeks E R, Swinney H L, Anomalous diffusion resulting from strongly asymmetric random walks, PRE 57, 4915 (1998)

Arapaki E, Argyrakis P, Avramov I, Milchev A, Effect of temperature on biased random walks in disordered media, PRE 56, R29 (1997)

Finitely distorted

Batchelor M T, Henry B I, Exact solution for random walks on the triangular lattice with absorbing boundaries, JPA 35, 5951 (2002)

Martzel N, Aslangul C, Effect of a forbidden site on a d-dimensional lattice random walk, JPA 34, 391 (2001)

Dynamical environment

К Болдригини, Р А Минлос, А Пеллегринотти, Случайные блуждания в случайной (флуктуирующей) среде, УМН 62, 4.27 (2007) – confusing: quenched=dynamic

Mandal S, Dasgupta R, Ballabh T K, Middya T R, Tarafdar S, Diffusion with rearranging traps, PRE 63, 026205 (2001)

Vocka R, Transport on an annealed disordered lattice, PRE 60, 3516 (1999)

Milchev A, Brankov J, Pereyra V D, Tracer diffusion in a random barrier model: The crossover from static to dynamic disorder, PRE 58, 4299 (1998)

A Nitzan, M A Ratner, Conduction in Polymers: Dynamic Disorder Transport, JPC 98, 1765 (1994)

Other random walk models

Henry B I, Batchelor M T, Random walks on finite lattice tubes, PRE 68, 016112 (2003)

Mussawisade K, Wichmann T, Kehr K W, Single-particle diffusion coefficient on surfaces with Ehrlich-Schwoebel barriers, Surf Sci 412, 55 (1998)

Bulnes F etal, Simulation of tracer diffusion on heteregeneous energy surfaces, JPC 5, A223 (1993)

Lawler G F, Low-density expansion for a two-state random walk in a random environment, JMP 30, 145 (1989) – similar to slab

Kundu K, Parris P E, Phillips P, Transport anisotropy and percolation in the two-dimensional random-hopping model, PRB 35, 3468 (1987)

Kehr K W, Richter D, Incoherent scattering law for diffusion in crystals with random impurities, Solid State Comm 20, 477 (1976) – average T-matrix approx (ATA)

Spin waves

Matsubara T, An application of CPA to a random spin system, PTPS 53, 202 (1973)

Edwards S F, Jones R C, A Green function theory of spin waves in randomly disordered magnetic systems. I. The ferromagnet, JPC 4, 2109 (1971)

Izyumov Yu, Spin-wave theory of ferromagnetic crystals containing impurities, Proc Phys Soc 87, 505 (1966)

Miscellaneous

Giacometti A, Nakanishi H, A new finite-size scaling approach to random walks, JPA 27, 2277 (2004)

Acedo L, Ernst M H, Lyapunov exponent of random walkers on a bond-disordered lattice, PA 247, 91 (1997)

Козлов С М, Метод усреднения и блуждания в неоднородных средах, УМН 40, 2.61 (1985)