CEA
CNRS
Univ. Paris-Saclay

Service de Physique de l'Etat Condensé

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Jean-Louis PICHARD

Service de Physique de l'Etat Condensé (SPEC)

Groupe Modélisation et Théorie (GMT)

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Fonction

Ingénieur Supelec, Docteur es Sciences Physiques (Université Paris-Sud).

Theorist at CEA-Saclay since 1977. 

Professor PAST at Université de Cergy-Pontoise (2002-2005)

Deputy Head of SPEC (2006-2010).

CEA Research Director

Head of GMT group.

Sujets de recherche

  1. 1977-1986:  Electron localization in disordered systems. Numerical studies of the inverse localization length in 2d strips and 3d bars. Electrical conductance in terms of the radial parameters of the multiplicative transfer matrix. Finite size scaling and extrapolations to the 2d limit (power law localization in weakly disordered 2d systems) and to the 3d limit (metal-insulator transition). Calculation of the critical exponent using phenomenological renormalization. Scaling theory of the disordered chain.
  2. 1987-1994: Mesoscopic conductance fluctuations in disordered metals (universal conductance fluctuations) and in disordered insulators (log-normal fluctuations). Random Matrix Theory of Quantum Transport. Maximum Entropy Approach to Conductance Fluctuations. Universal changes of the localization length upon breaking time reversal symmetry and spin rotation symmetry.Theory of random multiplicative transfer-matrices and its implications for quantum transport.
  3. 1994-1998:  Universal signatures of quantum chaos in ballistic transport, Quantum interference and the spin orbit interaction in mesoscopic normal-superconducting junctions, Brownian-motion ensembles and parametric correlations of the transmission eigenvalues. Delocalization of certain two-particle states by short range interactions in Anderson insulators. Level statistics and localization for two interacting particles in a random potential. From the Fermi glass towards the Mott insulator in one dimension: Delocalization and strongly enhanced persistent currents.
  4. 1998-2004: New quantum phase between the Fermi glass and the Wigner crystal in two dimensions.  Andreev-Lifshitz supersolid for a few electrons on small periodic square lattices. Effect of a lattice upon an interacting system of electrons in two dimensions: Breakdown of scaling and decay of persistent currents. Residual conductance of correlated one-dimensional nanosystems. Critical quantum chaos and the one-dimensional Harper model.
  5. 2004-2010: Interacting electron systems between Fermi leads: effective one-body transmissions and correlation clouds, Effect of measurement probes upon the conductance of an interacting nanosystem, Scanning gate microscopy of a nanostructure where electrons interact,  Scattering approach to quantum transport and many body effects, Universal scaling of the quantum conductance of an inversion-symmetric interacting model.
  6. 2010-2015: Thermal Enhancement of Interference Effects in Quantum Point Contacts, The embedding method beyond the single-channel case. Thermoelectric transport in mesoscopic systems, Delay-time and thermopower distributions at the spectrum edges of a chaotic scatterer, Gate-modulated thermopower in disordered nanowires, Using activated transport in arrays of parallel disordered nanowires for energy harvesting and hot spot cooling.

 

Publications scientifiques

  • Thermoelectric effects in nanowire-based MOSFETs
    R. Bosisio, G. Fleury, C. Gorini, and J.-L. Pichard
    Advances in Physics: X 2, 344 (2017)
  • Mesoscopic thermoelectric phenomena
    Special issue in Comptes Rendus Physique
    Edited by Jean-Louis Pichard and Robert S. Whitney
    Comptes Rendus Physique 17, 1039-1174 (2016)
  • Absorbing/emitting phonons with one dimensional MOSFETs
    R. Bosisio, C. Gorini, G. Fleury and J.-L. Pichard
    Physica E 74, 340 (2015)
  • Scanning gate microscopy of quantum contacts under parallel magnetic field: Beating patterns between spin-split transmission peaks or channel openings
    A. Kleshchonok, G. Fleury, J.-L. Pichard, and G. Lemarié
    Phys. Rev. B 91, 125416 (2015)
  • Using activated transport in parallel nanowires for energy harvesting and hot spot cooling
    R. Bosisio, C. Gorini, G. Fleury and J.-L. Pichard
    Phys. Rev. Applied 3, 054002 (2015)
  • Gate-modulated thermopower of disordered nanowires: II. Variable-Range Hopping Regime
    R. Bosisio, C. Gorini, G. Fleury and J.-L. Pichard
    New J. of Phys. 16, 095005 (2014)
  • Gate-modulated thermopower in disordered nanowires: I. Low temperature coherent regime
    Bosisio, R.; Fleury, G. and Pichard, J.-L.
    New J. of Phys. 16, 035004 (2014)
  • Delay-time and thermopower distributions at the spectrum edges of a chaotic scatterer
    Abbout, A.; Fleury, G.; Pichard, J.-L. and Muttalib, K.
    Phys. Rev. B 87, 115147(2013)
  • Thermal Enhancement of Interference Effects in Quantum Point Contacts
    Abbout, A.; Lemarie, G. and Pichard, J.-L.
    Phys. Rev. Lett. 106, 156810 (2011)
  • The embedding method beyond the single-channel case Two-mode and Hubbard chains
    Freyn, A.; Vasseur, G.; Schmitteckert, P..; Weinmann, D..; Ingold, G.-L.; Jalabert, R. A. and Pichard, J.-L.
    Eur. Phys. J. B 75, 253 (2010)
  • Universal scaling of the quantum conductance of an inversion-symmetric interacting model
    Freyn, A. and Pichard, J.-L.
    Phys. Rev. B 81, 085108 (2010)
  • Scattering approach to quantum transport and many body effects
    Pichard, J.-L. and Freyn, A.
    AIP Conf. Proc. 1319, 17 (2010)
    4th Mexican Meeting on Mathematical and Experimental Physics; July 19-23, 2010; Mexico City, MEXICO
  • Interaction induced non-locality of the quantum conductance
    Freyn, A. and Pichard, J.-L.
    Physica B - Condensed Matter 404, 407 (2009)
    5th International Workshop on Electronic Crystals; Aug. 24-30, 2008; Cargese, FRANCE
  • Detection of interaction-induced nonlocal effects using perfectly transmitting nanostructures
    Weinmann, D..; Jalabert, R. A.; Freyn, A.; Ingold, G.-L. and Pichard, J.-L.
    Eur. Phys. J. B 66, 239 (2008)
  • Scanning gate microscopy of a nanostructure where electrons interact
    Freyn, A.; Kleftogiannis, I. and Pichard, J.-L.
    Phys. Rev. Lett. 100, 226802 (2008)
  • Effect of flux-dependent Friedel oscillations upon the effective transmission of an interacting nano-system
    Freyn, A. and Pichard, J.-L.
    Eur. Phys. J. B 58, 279 (2007)
  • Effect of measurement probes upon the conductance of an interacting nanosystem: Detection of an attached ring by nonlocal many body effects
    Freyn, A. and Pichard, J.-L.
    Phys. Rev. Lett. 98, 186401 (2007)
  • Conductance of nano-systems with interactions coupled via conduction electrons: effect of indirect exchange interactions
    Asada, Y.; Freyn, A. and Pichard, J.-L.
    Eur. Phys. J. B 53, 109 (2006)
  • Interplay between electronic correlations and quantum fluctuations in disordered square lattices
    Pichard, J.-L. and Nemeth, Z.A.
    Journal de Physique IV 131, 155 (2005)
    International Worskhop on Electronic Crystals; Aug. 21-27, 2005; Cargese, FRANCE
  • Interacting electron systems between Fermi leads: effective one-body transmissions and correlation clouds
    Molina, R.A.; Weinmann, D.. and Pichard, J.-L.
    Eur. Phys. J. B 48, 243 (2005)
  • Persistent currents in two dimensions: New regimes induced by the interplay between electronic correlations and disorder
    Nemeth, Z.A. and Pichard, J.-L.
    Eur. Phys. J. B 45, 111 (2005)
  • Length-dependent oscillations of the conductance through atomic chains: The importance of electronic correlations
    Molina, R.A.; Weinmann, D. and Pichard, J.-L.
    Europhys. Lett. 67, 96 (2004)
  • Effect of a lattice upon an interacting system of electrons in two dimensions: Breakdown of scaling and decay of persistent currents
    Falakshahi, H.; Nemeth, Z.A. and Pichard, J.-L.
    Eur. Phys. J. B 39, 93 (2004)
  • Residual conductance of correlated one-dimensional nanosystems: A numerical approach
    Molina, R.A.; Schmitteckert, P.; Weinmann, D.; Jalabert, R.A.; Ingold, G.L. and Pichard, J.-L.
    Eur. Phys. J. B 39, 107 (2004)
  • Conductance through a one-dimensional correlated system: Relation to persistent currents and the role of the contacts
    Molina, R.A.; Weinmann, D.; Jalabert, R.A.; Ingold, G.L. and Pichard, J.-L.
    Phys. Rev. B 67, 235306 (2003)
  • Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice. I
    Katomeris, G.; Selva, F. and Pichard, J.-L.
    Eur. Phys. J. B 31, 401 (2003)
  • Andreev-Lifshitz supersolid for a few electrons on small periodic square lattices
    in Anderson localization and its ramifications: disorder, phase coherence and electron correlations
    Pichard, J.-L. and Nemeth, Z.A.
    Lecture notes in physics 630, 275 (2003)
    283rd International WE Heraeus Seminar on Localization, Quantum Coherence and Interactions; Sep. 04-06, 2002; Hamburg, Germany
  • Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice II
    Nemeth, Z.A. and Pichard, J.-L.
    Eur. Phys. J. B 33, 87 (2003)
  • From the Fermi liquid towards the Wigner solid in two dimensions
    Book chapter in Exotic states in quantum nanostructures
    Pichard, J.-L.; Benenti, G.; Katomeris, G.; Selva, R. and Waintal, X.
    PY Available as hal-00120574 (2003)
  • Correlated electrons on square lattices
    Pichard, J.-L.
    Progress Of Theoretical Physics Supplement 150, 188 (2003)
    5th International Summer School and Conference on Lets Face Chaos through Nonlinear Dynamics; Jun. 30-Jul. 14, 2002; Maribor, Slovenia
  • From independent particle towards collective motion for two polarized electrons on a square lattice
    Martinez, M. and Pichard, J.-L.
    Eur. Phys. J. B 30, 93 (2002)
  • Ground state of a partially melted Wigner molecule
    Nemeth, Z.A. and Pichard, J.-L.
    Europhys. Lett. 58, 744 (2002)
  • Two-dimensional mesoscopic Wigner crystallization and related issues
    Pichard, J.-L.
    Pramana - Journal of Physics 58, 259 (2002)
    International Discussion Meeting on Mesoscopic and Disordered Systems; Dec. 18-20, 2000; Bangalore, India
  • Role of a parallel magnetic field upon a few correlated electrons trapped in 2d mesoscopic disordered clusters
    Selva, F. and Pichard, J.-L.
    Europhys. Lett. 55, 518 (2001)
  • Coulomb repulsion versus Hubbard repulsion in a disordered chain
    Selva, F. and Pichard, J.-L.
    Eur. Phys. J. B 20, 441 (2001)
  • Partial delocalization of the ground state by repulsive interactions in a disordered chain
    Jalabert, R.A.; Weinmann, D. and Pichard, J.-L.
    Physica E 9, 347 (2001)
    International Workshop and Seminar on Dynamics of Complex Systems; Mar.31 - Jun.15, 1999; Dresden, Germany
  • Mesoscopic Wigner crystallization in two dimensional lattice models
    in Electronic Correlations: From Meso- to Nano-Physics
    Pichard, J.-L.; Katomeris, G. and Selva, F.
    Proceedings of the 36th Rencontres de Moriond on Electronic Correlations; Jan. 20-27, 2001; Savoie, France
    Available as cond-mat/0107500 (2001)
  • Delocalization effects and charge reorganizations induced by repulsive interactions in strongly disordered chains
    Weinmann, D.; Schmitteckert, P.; Jalabert, R.A. and Pichard, J.-L.
    Eur. Phys. J. B 19, 139 (2001)
  • Compressibility crossover and quantum opening of a gap for two-dimensional disordered clusters with Coulomb repulsion
    Benenti, G.; Waintal, X.; Pichard, J.-L. and Shepelyansky, D.L.
    Eur. Phys. J. B 17, 515 (2000)
  • Signatures of an intermediate 2d Coulomb phase at low temperatures
    Benenti, G; Waintal, X. and Pichard, J.-L.
    Europhys. Lett. 51, 89 (2000)
  • Critical quantum chaos and the one-dimensional Harper model
    Evangelou, S.N. and Pichard, J.-L.
    Phys. Rev. Lett. 84, 1643 (2000)
  • Delocalized Coulomb phase in two dimensions
    Waintal, X.; Benenti, G. and Pichard, J.-L.
    Europhys. Lett. 49, 466 (2000)
  • New quantum phase between the Fermi glass and the Wigner crystal in two dimensions
    Benenti, G; Waintal, X. and Pichard, J.-L.
    Phys. Rev. Lett. 83, 1826 (1999)
  • Two interacting particles in a disordered chain. III. Dynamical aspects of the interplay disorder-interaction
    De Toro Arias, S.; Waintal, X. and Pichard, J.-L.
    Eur. Phys. J. B 10, 149 (1999)
  • Two interacting particles in a disordered chain II: Critical statistics and maximum mixing of the one body states
    Waintal, X.; Weinmann, D. and Pichard, J.-L.
    Eur. Phys. J. B 7, 451 (1999)
  • Metallic phase between the Fermi glass and the Wigner crystal in two dimensions
    Waintal, X.; Benenti, G. and Pichard, J.-L.
    Annalen der Physik 8, 691 (1999)
    International Conference on Disorder and Interaction in Transport Phenomena (LOCALIZATION 1999); Jul.30 - Aug.03, 1999; Hamburg, Germany
  • Two interacting particles in a disordered chain I: Multifractality of the interaction matrix elements
    Waintal, X. and Pichard, J.-L.
    Eur. Phys. J. B 6, 117 (1998)
  • From the Fermi glass towards the Mott insulator in one dimension: Delocalization and strongly enhanced persistent currents
    Schmitteckert, P.; Jalabert, R.A.; Weinmann, D. and Pichard, J.-L.
    Phys. Rev. Lett. 81, 2308 (1998)
  • Interplay disorder-interaction in one-dimensional quantum models
    Pichard, J.-L.; Weinmann, D.; Arias, S.D.; Jalabert, R.A.; Schmitteckert, P.; Waintal, X. and Wobst, A.
    Annalen der Physik 7, 462 (1998)
    Proceedings of the 210th WE-Heraeus-Seminar on Percolation, Interaction, Localization - Simulations of Transport in Disordered Systems; Oct., 1998; Berlin, Germany
  • Level curvatures, spectral statistics and scaling for interacting particles
    Akkermans, E. and Pichard, J.-L.
    Eur. Phys. J. B 1, 223 (1998)
  • Thouless numbers for few-particle systems with disorder and interactions
    Weinmann, D.; Pichard, J.-L. and Imry, Y.
    Journal de Physique I 7, 1559 (1997)
  • Parametric statistics of the scattering matrix: From metallic to insulating quasi-unidimensional disordered systems
    Mucciolo, E.R.; Jalabert, R.A. and Pichard, J.-L.
    Journal de Physique I 7, 1267 (1997)
  • Comment on "No enhancement of the localization length for two interacting particles in a random potential"
    Frahm, K.; Muller-Groeling, A.; Pichard, J.-L. and Weinmann, D.
    Phys. Rev. Lett. 78, 4889 (1997)
  • Two interacting particles in a random potential: Mapping onto one parameter localization theories without interaction
    Frahm, K.; Muller-Groeling, A. and Pichard, J.-L.
    Z. Phys. B Condens. Matt. 102, 261 (1997)
  • Level statistics and localization for two interacting particles in a random potential
    Weinmann, D. and Pichard, J.-L.
    Phys. Rev. Lett. 77, 1556 (1996)
  • Quantum interference and the spin orbit interaction in mesoscopic normal-superconducting junctions
    Slevin, K.; Pichard, J.-L. and Mello, P.A.
    Journal de Physique I 6, 529 (1996)
  • Effective sigma model formulation for two interacting electrons in a disordered metal
    Frahm, K.; Muller-Groeling, A. and Pichard, J.-L.
    Phys. Rev. Lett. 76, 1509 (1996)
  • Delocalization of certain two-particle states by short range interactions in Anderson insulators
    Book chapter in Quantum transport in semiconductor submicron structures
    Frahm, K.; Muller-Groeling, A.; Pichard, J.-L. and Weinmann, D.
    NATO ASI Series, Series E, Applied Sciences 326, 173 (1996)
    NATO Advanced Study Institute on Quantum Transport in Semiconductor Submicron Structures; Aug. 20-31, 1995; Bad Lauterberg, Germany
  • h/2e oscillations for correlated electron pairs in disordered mesoscopic rings
    Weinmann, D.; Muller-Groeling, A.; Pichard, J.-L. and Frahm, K.
    Phys. Rev. Lett. 75, 1598 (1995)
  • Scaling in interaction-assisted coherent transport
    Frahm, K.; Muller-Groeling, A.; Pichard, J.-L. and Weinmann, D.
    Europhys. Lett. 31, 169 (1995)
  • Magnetoconductance of ballistic chaotic quantum dots - a brownian-motion approach for the s-matrix
    Frahm, K. and Pichard, J.-L.
    Journal de Physique I 5, 847 (1995)
  • Brownian-motion ensembles and parametric correlations of the transmission eigenvalues - application to coupled quantum billiards and to disordered wires
    Frahm, K. and Pichard, J.-L.
    Journal de Physique I 5, 877 (1995)
  • Quantum mesoscopic scattering: disordered-systems and Dyson circular ensembles
    Jalabert, R.A. and Pichard, J.-L.
    Journal de Physique I 5, 287 (1995)
  • Universal quantum signatures of chaos in ballistic transport
    Jalabert, R.A.; Pichard, J.-L. and Beenakker, C. W. J.
    Europhys. Lett. 27, 255 (1994)
  • A matrix ensemble with a preferential basis and its application to disordered metals and insulators
    Pichard, J.-L. and Shapiro, B.
    Journal de Physique I 4, 623 (1994)
  • From chaotic scattering to localization: A brief review of random matrix approaches
    Book chapter in Coulomb and interference effects in small electronic structures
    Pichard, J.-L.
    Editions Frontieres, Gif-sur-Yvette, 1994 Series: Moriond Condensed Matter Physics, 80, 231
    Proceedings of the XXIXth Rencontre de Moriond; Jan. 22-29, 1994; Villars Sur Ollon, Switzerland
  • Quantum transmission in disordered insulators: random-matrix theory and transverse localization
    Avishai, Y.; Pichard, J.-L. and Muttalib, K.A.
    Journal de Physique I 3, 2343 (1993)
  • Long-range energy-level interaction in small metallic particles
    Jalabert, R.A.; Pichard, J.-L. and Beenakker, C. W. J.
    Europhys. Lett. 24, 1 (1993)
  • Conductance fluctuations due to motion of a single impurity in the localized regime
    Feng, S.; Pichard, J.-L. and Zeng, F.
    Phys. Rev. B 48, 2529 (1993)
  • Maximum-entropy ansatz for transmission in quantum conductors: a quantitative study in 2 and 3 dimensions
    Slevin, K.; Pichard, J.-L. and Muttalib, K.A.
    Journal de Physique I 3, 1387 (1993)
  • Validity of a maximum-entropy: description for 2-dimensional disordered quantum conductors
    Slevin, K.; Pichard, J.-L. and Mello, P.
    Europhys. Lett. 16, 649 (1991)
  • Reproducible conductance fluctuations in macroscopic Anderson insulators
    Feng, S. and Pichard, J.-L.
    Phys. Rev. Lett. 67, 753 (1991)
  • Reproducible conductance fluctuations in macroscopic Anderson insulators
    Feng, S. and Pichard, J.-L.
    Phys. Rev. Lett. 67, 753 (1991)
  • Symmetries and parametrization of the transfer-matrix in electronic quantum transport theory
    Mello, P.A. and Pichard, J.-L.
    Journal de Physique I 1, 493 (1991)
  • Symmetry-breaking in Anderson insulators
    Slevin, K.; Pichard, J.-L. and Sanquer, M.
    Physica B 169, 491 (1991)
    Proceedings of the 19th International Conference On Low Temperature Physics; Aug. 16-22, 1990; Brighton, England
  • Symmetry-breaking effects and magnetoconductance fluctuations in the Mott hopping regime
    Pichard, J.-L.
    Institute Of Physics Conference Series 108, 77 (1991)
    Proceedings of the International Conference on Localisation; Aug. 13-15, 1990; London, England
  • Random transfer-matrix theory and conductance fluctuations
    Book chapter in Quantum coherence in mesoscopic system
    Pichard, J.-L.
    Nato ASI Series B 254, 369 (1991)
  • Broken symmetries and localization lengths in anderson insulators - theory and experiment
    Pichard, J.-L.; Sanquer, M.; Slevin, K. and Debray, P.
    Phys. Rev. Lett. 65, 1812 (1990)
  • Quantum conductance fluctuations and maximum-entropy ensembles for the transfer-matrix
    Pichard, J.-L. and Sanquer, M.
    Physica A 167, 66 (1990)
    Workshop On Anderson Transition And Mesoscopic Fluctuations; Jan. 09-12, 1990; Brunswick, Germany
  • Theory of random multiplicative transfer-matrices and its implications for quantum transport
    Pichard, J.-L.; Zanon, N.; Imry, Y. and Stone, A.D.
    Journal de Physique 51, 587 (1990)
  • Maximum-entropy approaches to quantum transport
    Pichard, J.-L.; Mello, P.A.; Stone, A.D. and Zanon, N.
    Surface Science 229, 101 (1990)
    8th International Conference On The Electronic Properties Of Two-Dimensional Systems; Sep. 04-08, 1989; Grenoble, FRANCE
  • Reduction of mesoscopic conductance fluctuations due to Zeeman splitting in a disordered conductor without spin-orbit scattering
    Debray, P.; Pichard, J.-L.; Vicente, J. and Tung, P.N.
    Phys. Rev. Lett. 63, 2264 (1989)
  • Maximum-entropy approaches to quantum electronic transport
    Mello, P.A. and Pichard, J.-L.
    Phys. Rev. B 40, 5276 (1989)
  • Reduction of quantum noise in a GaAlAs/GaAs heterojunction by a magnetic-field: an orthogonal-to-unitary Wigner statistics transition
    Mailly, D.; Sanquer, M.; Pichard, J.-L. and Pari, P.
    Europhys. Lett. 8, 471 (1989)
  • Random matrix-theory and universal statistics for disordered quantum conductors with spin-dependent hopping
    Zanon, N. and Pichard, J.-L.
    Journal de Physique 49, 907 (1988)
  • Universal conductance fluctuations, random matrix theory and the scaling theory of localization
    Book chapter in Anderson localisation
    Stone, A.D.; Muttalib, K.A. and Pichard, J.-L.
    Springer Proceedings in Physics, 28 (1988)
    Proceedings of the International Symposium on Anderson Localization; Aug. 16-18, 1987; Tokyo, Japan
  • Random-matrix theory and universal statistics for disordered quantum conductors
    Muttalib, K.A.; Pichard, J.-L. and Stone, A.D.
    Phys. Rev. Lett. 59, 2475 (1987)
  • Lyapounov exponents of products of random matrices: weak disorder expansion. Application to localization
    Derrida, B.; Mecheri, K. and Pichard, J.-L.
    Journal de Physique 48, 733 (1987)
  • Many-channel transmission: Large volume limit of the distribution of localization lengths and one-parameter scaling
    Pichard, J.-L. and Andre, G.
    Europhys. Lett. 2, 477 (1986)
  • Many-channel conductance of d-dimensional pure and randomly layered materials
    Carton, J.-P.; Pichard, J.-L. and Zanon, N.
    J. Phys. C: Solid State Phys. 19, 4041 (1986)
  • The one-dimensional Anderson model: scaling and resonances revisited
    Pichard, J.-L.
    J. Phys. C: Solid State Phys. 19, 1519 (1986)
  • Power-law decay and fractal character of eigenstates in two-dimensional disordered-systems
    Pichard, J.-L. and Sarma, G.
    J. Phys. C: Solid State Phys. 18, 3457 (1985)
  • Finite size scaling approach to Anderson localization
    Pichard, J.-L. and Sarma, G.
    Journal de Physique 42, 37 (1981)
  • Finite size scaling approach to Anderson localization
    Pichard, J.-L. and Sarma, G.
    J. Phys. C: Solid State Phys. 14, L127 (1981)
  • Finite-size scaling approach to Anderson localization. 2. Quantitative-analysis and new results
    Pichard, J.-L. and Sarma, G.
    J. Phys. C: Solid State Phys. 14, L617 (1981)

 

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