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Renormalized phonons in nonlinear lattices: A variational approach.
Phys Rev E Stat Nonlin Soft Matter Phys
April 2015
State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China.
We propose a variational approach to study renormalized phonons in momentum-conserving nonlinear lattices with either symmetric or asymmetric potentials. To investigate the influence of pressure for phonon properties, we derive an inequality which provides both the lower and upper bound of the Gibbs free energy as the associated variational principle. This inequality is a direct extension to the Gibbs-Bogoliubov inequality.
View Article and Find Full Text PDFDevelopment of a new variational approach for thermal density matrices.
J Chem Phys
June 2011
School of Chemistry, University of Hyderabad, Hyderabad 500 046, India.
A McLachlan-type variational principle is derived for thermal density matrices. In this approach, the trace of the mean square of the differences between the derivatives of the exact and model density matrices is minimized with respect to the parameters in the model Hamiltonian. Applications to model anharmonic systems in the independent particle model show that the method can provide thermodynamic state functions accurately (within 5% of the converged basis set results) and at the same level of accuracy as the results using Feynman-Gibbs-Bogoliubov variational principle at this level of approximation.
View Article and Find Full Text PDFAnharmonic stabilization of the high-pressure simple cubic phase of calcium.
Phys Rev Lett
April 2011
Materia Kondentsatuaren Fisika Saila, Zientzia eta Teknologia Fakultatea, Euskal Herriko Unibertsitatea, Bilbao, Basque Country, Spain.
The phonon spectrum of the high-pressure simple cubic phase of calcium, in the harmonic approximation, shows imaginary branches that make it mechanically unstable. In this Letter, the phonon spectrum is recalculated by using density-functional theory ab initio methods fully including anharmonic effects up to fourth order at 50 GPa. Considering that the perturbation theory cannot be employed with imaginary harmonic frequencies, a variational procedure based on the Gibbs-Bogoliubov inequality is used to estimate the renormalized phonon frequencies.
View Article and Find Full Text PDFJensen-Feynman approach to the statistics of interacting electrons.
Phys Rev E Stat Nonlin Soft Matter Phys
August 2009
CEA, DAM, DIF, F-91297 Arpajon, France.
Faussurier [Phys. Rev. E 65, 016403 (2001)] proposed to use a variational principle relying on Jensen-Feynman (or Gibbs-Bogoliubov) inequality in order to optimize the accounting for two-particle interactions in the calculation of canonical partition functions.
View Article and Find Full Text PDFVariational formula for the free energy based on incomplete sampling in a molecular simulation.
Phys Rev E Stat Nonlin Soft Matter Phys
August 2003
Department of Chemical Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, USA.
Finite sampling in free-energy perturbation (FEP) calculations by molecular simulation leads to reproducible systematic errors, with sign shown to depend (in a known way) only on which system governs sampling in the simulation. Thus the result of a FEP calculation can be used as a bound on the true free energy. This inequality is of a wholly different nature from established forms such as the Gibbs-Bogoliubov inequality or the second law, in that its origins relate to the performance of a molecular simulation.
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