The spectral shape of the displacement correlation function of a quantum chain of atoms interacting through a nearest-neighbor potential is approached at all temperatures and wave vectors by the evaluation of the related frequency moments. The latter ones have been obtained, until the sixth one, by using an effective potential derived by a variational approach to the path-integral formulation of the quantum statistical mechanics. This method allows us to reduce the computation of quantum averages of time-independent functions to classical-like space integrals, so that all the tools developed for classical calculations can be again applied. Explicit results for the Lennard-Jones potential are presented and tested against extensive quantum path-integral Monte Carlo simulations, where an improved Trotter extrapolation procedure is also used. The good agreement between the two calculations confirms the apparent strong simplification introduced by the variational method in the evaluation of the quantum averages when the quantum coupling can be treated semiclassically. The reconstruction of the dynamical behavior of the system through the knowledge of a sufficient number of moments appears realistic. Explicit spectral shapes of Lennard-Jones chains are given, showing the relevance of the quantum effects.

Frequency Moments and Spectral Shape of Quantum Chains / A. CUCCOLI; V. TOGNETTI; A.A. MARADUDIN; A.R. MC GURN; R. VAIA. - In: PHYSICAL REVIEW. B, CONDENSED MATTER. - ISSN 0163-1829. - STAMPA. - 46:(1992), pp. 8839-8857. [10.1103/PhysRevB.46.8839]

Frequency Moments and Spectral Shape of Quantum Chains

CUCCOLI, ALESSANDRO;TOGNETTI, VALERIO;
1992

Abstract

The spectral shape of the displacement correlation function of a quantum chain of atoms interacting through a nearest-neighbor potential is approached at all temperatures and wave vectors by the evaluation of the related frequency moments. The latter ones have been obtained, until the sixth one, by using an effective potential derived by a variational approach to the path-integral formulation of the quantum statistical mechanics. This method allows us to reduce the computation of quantum averages of time-independent functions to classical-like space integrals, so that all the tools developed for classical calculations can be again applied. Explicit results for the Lennard-Jones potential are presented and tested against extensive quantum path-integral Monte Carlo simulations, where an improved Trotter extrapolation procedure is also used. The good agreement between the two calculations confirms the apparent strong simplification introduced by the variational method in the evaluation of the quantum averages when the quantum coupling can be treated semiclassically. The reconstruction of the dynamical behavior of the system through the knowledge of a sufficient number of moments appears realistic. Explicit spectral shapes of Lennard-Jones chains are given, showing the relevance of the quantum effects.
1992
46
8839
8857
A. CUCCOLI; V. TOGNETTI; A.A. MARADUDIN; A.R. MC GURN; R. VAIA
File in questo prodotto:
File Dimensione Formato  
CTMMV92.pdf

Accesso chiuso

Tipologia: Versione finale referata (Postprint, Accepted manuscript)
Licenza: Tutti i diritti riservati
Dimensione 814.59 kB
Formato Adobe PDF
814.59 kB Adobe PDF   Richiedi una copia

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/250881
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 34
  • ???jsp.display-item.citation.isi??? 29
social impact