Quantum Stabilization in Anharmonic Crystals

Sergio Albeverio, Yuri Kondratiev, Yuri Kozitsky, and Michael Röckner
Phys. Rev. Lett. 90, 170603 – Published 29 April 2003

Abstract

For a model of interacting quantum particles of mass m oscillating in a double-well crystalline field, a mechanism of its stabilization by quantum effects is described. In particular, a stability condition involving m, the interaction intensity, and the parameters of the crystalline field is given. It is independent of the temperature and is satisfied if m is small enough and/or the tunneling frequency is big enough. It is shown that under this condition the infinite-volume free energy density is an analytic function of the external field and the displacement-displacement correlation function decays exponentially; hence, no phase transitions can arise at all temperatures. This gives a complete and rigorous answer to the question about the influence of quantum effects on structural phase transitions, the discussion of which was initiated in [T. Schneider, H. Beck, and E. Stoll, Phys. Rev. B 13, 1123 (1976)].

  • Received 12 December 2002

DOI:https://doi.org/10.1103/PhysRevLett.90.170603

©2003 American Physical Society

Authors & Affiliations

Sergio Albeverio1,2,3,4,*, Yuri Kondratiev2,5,6,†, Yuri Kozitsky7,‡, and Michael Röckner2,5,§

  • 1Abteilung für Stochastic, Universität Bonn, D 53115 Bonn, Germany
  • 2BiBoS Research Centre, Bielefeld, Germany
  • 3CERFIM, Locarno and Academia di Architettura, Università della Svizzera Italiana, Switzerland
  • 4Dipartimento di Matematica, Università degli Studi di Trento, Trento, Italy
  • 5Fakultät für Mathematik, Universität Bielefeld, D 33615 Bielefeld, Germany
  • 6Institute of Mathematics, Kiev, Ukraine
  • 7Instytut Matematyki, Uniwersytet Marii Curie-Sklodowskiej, 20-031 Lublin, Poland

  • *Electronic address: albeverio@uni-bonn.de
  • Electronic address: kondrat@mathematik.uni-bielefeld.de
  • Electronic address: jkozi@golem.umcs.lublin.pl
  • §Electronic address: roeckner@mathematik.uni-bielefeld.de

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Issue

Vol. 90, Iss. 17 — 2 May 2003

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