L. A. Pastur, “On the Schrödinger equation with a random potential”, TMF, 6:3 (1971), 415–424; Theoret. and Math. Phys., 6:3 (1971), 299

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Teoreticheskaya i Matematicheskaya Fizika, 1971, Volume 6, Number 3, Pages 415–424 (Mi tmf3650)

This article is cited in 11 scientific papers (total in 11 papers)

On the Schrödinger equation with a random potential

L. A. Pastur

Full-text PDF (900 kB) Citations (11)

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Abstract: A study is made of the ergodic properties of various quantities connected with a Schrödinger equation with a random potential. For the case when the potential is a metrically transitive (ergodic) random field with realizations that are bounded below it is shown that these quantities tend to nonrandom limits with probability 1 when the volume in which the equation is considered tends to infinity. It is shown that these limiting values are independent of the boundary conditions.

Received: 12.06.1970

English version:
Theoretical and Mathematical Physics, 1971, Volume 6, Issue 3, Pages 299–306
DOI: https://doi.org/10.1007/BF01030111

Bibliographic databases:

Language: Russian

Citation: L. A. Pastur, “On the Schrödinger equation with a random potential”, TMF, 6:3 (1971), 415–424; Theoret. and Math. Phys., 6:3 (1971), 299–306

Citation in format AMSBIB

\Bibitem{Pas71}

\by L.~A.~Pastur

\paper On~the~Schr\"{o}dinger equation with a~random potential

\jour TMF

\yr 1971

\vol 6

\issue 3

\pages 415--424

\mathnet{http://mi.mathnet.ru/tmf3650}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=473499}

\zmath{https://zbmath.org/?q=an:0208.12903}

\transl

\jour Theoret. and Math. Phys.

\yr 1971

\vol 6

\issue 3

\pages 299--306

\crossref{https://doi.org/10.1007/BF01030111}

Linking options:

https://www.mathnet.ru/eng/tmf3650

https://www.mathnet.ru/eng/tmf/v6/i3/p415

This publication is cited in the following 11 articles:

Abel Klein, Peter Müller, “The conductivity measure for the Anderson model”, Zhurn. matem. fiz., anal., geom., 4:1 (2008), 128–150
Hajo Leschke, Peter Müller, Simone Warzel, Interacting Stochastic Systems, 2005, 119
Dirk Hundertmark, Barry Simon, “A diamagnetic inequality for semigroup differences”, Journal für die reine und angewandte Mathematik (Crelles Journal), 2004:571 (2004)
Olivier Lenoble, Leonid A. Pastur, Valentin A. Zagrebnov, “Bose–Einstein condensation in random potentials”, Comptes Rendus. Physique, 5:1 (2004), 129
THOMAS HUPFER, HAJO LESCHKE, PETER MÜLLER, SIMONE WARZEL, “EXISTENCE AND UNIQUENESS OF THE INTEGRATED DENSITY OF STATES FOR SCHRÖDINGER OPERATORS WITH MAGNETIC FIELDS AND UNBOUNDED RANDOM POTENTIALS”, Rev. Math. Phys., 13:12 (2001), 1547
VADIM KOSTRYKIN, ROBERT SCHRADER, “THE DENSITY OF STATES AND THE SPECTRAL SHIFT DENSITY OF RANDOM SCHRÖDINGER OPERATORS”, Rev. Math. Phys., 12:06 (2000), 807
L. A. Pastur, “Spectral theory of random self-adjoint operators”, J. Soviet Math., 46:4 (1989), 1979–2021
J.M Luttinger, Roger Waxler, “Low energy density of states in several disordered systems”, Annals of Physics, 175:2 (1987), 319
N. V. Laskin, S. V. Peletminskii, V. I. Prikhod'ko, “Kinetic theory of systems in random fields”, Theoret. and Math. Phys., 34:2 (1978), 154–162
L. A. Pastur, “Behavior of some Wiener integrals as $t\to\infty$ and the density of states of Schrödinger equations with random potential”, Theoret. and Math. Phys., 32:1 (1977), 615–620
L. A. Pastur, “On the distribution of the eigenvalues of the Schrödinger equation with a random potential”, Funct. Anal. Appl., 6:2 (1972), 163–165

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	92
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