skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Violation of the zero-force theorem in the time-dependent Krieger-Li-Iafrate approximation

Abstract

We demonstrate that the time-dependent Krieger-Li-Iafrate approximation in combination with the exchange-only functional violates the zero-force theorem. By analyzing the time-dependent dipole moment of Na{sub 5} and Na{sub 9}{sup +}, we furthermore show that this can lead to an unphysical self-excitation of the system depending on the system properties and the excitation strength. Analytical aspects, especially the connection between the zero-force theorem and the generalized-translation invariance of the potential, are discussed.

Authors:
; ; ;  [1];  [2];  [3]
  1. Physikalisches Institut, Universitaet Bayreuth, D-95440 Bayreuth (Germany)
  2. (Netherlands)
  3. (Germany)
Publication Date:
OSTI Identifier:
20982438
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.75.050501; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; APPROXIMATIONS; CATIONS; DENSITY FUNCTIONAL METHOD; DIPOLE MOMENTS; EXCITATION; HEAVY IONS; POTENTIALS; SODIUM; TIME DEPENDENCE

Citation Formats

Mundt, Michael, Kuemmel, Stephan, Leeuwen, Robert van, Reinhard, Paul-Gerhard, University of Groningen, Theoretical Chemistry, Zernike Institute for Advanced Materials, 9747AG, Nijenborgh 4, Groningen, and Institut fuer Theoretische Physik II, Universitaet Erlangen-Nuernberg, Staudtstrasse 7, D-91058 Erlangen. Violation of the zero-force theorem in the time-dependent Krieger-Li-Iafrate approximation. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.050501.
Mundt, Michael, Kuemmel, Stephan, Leeuwen, Robert van, Reinhard, Paul-Gerhard, University of Groningen, Theoretical Chemistry, Zernike Institute for Advanced Materials, 9747AG, Nijenborgh 4, Groningen, & Institut fuer Theoretische Physik II, Universitaet Erlangen-Nuernberg, Staudtstrasse 7, D-91058 Erlangen. Violation of the zero-force theorem in the time-dependent Krieger-Li-Iafrate approximation. United States. doi:10.1103/PHYSREVA.75.050501.
Mundt, Michael, Kuemmel, Stephan, Leeuwen, Robert van, Reinhard, Paul-Gerhard, University of Groningen, Theoretical Chemistry, Zernike Institute for Advanced Materials, 9747AG, Nijenborgh 4, Groningen, and Institut fuer Theoretische Physik II, Universitaet Erlangen-Nuernberg, Staudtstrasse 7, D-91058 Erlangen. Tue . "Violation of the zero-force theorem in the time-dependent Krieger-Li-Iafrate approximation". United States. doi:10.1103/PHYSREVA.75.050501.
@article{osti_20982438,
title = {Violation of the zero-force theorem in the time-dependent Krieger-Li-Iafrate approximation},
author = {Mundt, Michael and Kuemmel, Stephan and Leeuwen, Robert van and Reinhard, Paul-Gerhard and University of Groningen, Theoretical Chemistry, Zernike Institute for Advanced Materials, 9747AG, Nijenborgh 4, Groningen and Institut fuer Theoretische Physik II, Universitaet Erlangen-Nuernberg, Staudtstrasse 7, D-91058 Erlangen},
abstractNote = {We demonstrate that the time-dependent Krieger-Li-Iafrate approximation in combination with the exchange-only functional violates the zero-force theorem. By analyzing the time-dependent dipole moment of Na{sub 5} and Na{sub 9}{sup +}, we furthermore show that this can lead to an unphysical self-excitation of the system depending on the system properties and the excitation strength. Analytical aspects, especially the connection between the zero-force theorem and the generalized-translation invariance of the potential, are discussed.},
doi = {10.1103/PHYSREVA.75.050501},
journal = {Physical Review. A},
number = 5,
volume = 75,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}
  • From joint meeting of the American Nuclear Soeiety and the Atomic Industrial forum and Nuclear Energy Exhibition; San Francisco, California, USA (11 Nov 1973). See CONF-731101-.
  • We give a rigorous analytical derivation of low-temperature behavior of the Casimir entropy in the framework of the Lifshitz formula combined with the Drude dielectric function. An earlier result that the Casimir entropy at zero temperature is not equal to zero and depends on the parameters of the system is confirmed, i.e., the third law of thermodynamics (the Nernst heat theorem) is violated. We illustrate the resolution of this thermodynamical puzzle in the context of the surface impedance approach by several calculations of the thermal Casimir force and entropy for both real metals and dielectrics. Different representations for the impedances,more » which are equivalent for real photons, are discussed. Finally, we argue in favor of the Leontovich boundary condition which leads to results for the thermal Casimir force that are consistent with thermodynamics.« less
  • Let L be an entire function of exponential type in C with indicator function h{sub L}; let {lambda}={l_brace}{lambda}{sub n}{r_brace}, n=1,2,..., be a subsequence of zeros of the entire function of exponential type L{ne}0; let {gamma}={l_brace}{gamma}{sub n}{r_brace} be a complex number sequence and assume that {sigma}{sub n}|1/{lambda}{sub n} - 1/{gamma}{sub n}|<{infinity}. A simple construction of a sequence of entire functions of exponential type {l_brace}L{sub n}{r_brace} transforming {lambda} into a subsequence {gamma} of zeros of an entire function of exponential type G{ne}0 such that h{sub G}=h{sub L} is put forward (an approximation theorem). This result is applied to stability problems of zeromore » sequences and non-uniqueness sequences for spaces of entire functions of exponential type with constraints on the indicators and to the problem of the stability of the completeness property of exponential systems in the space of germs of analytic functions on a compact convex set.« less
  • The vibrational predissociation dynamics of a collinear model of the I2(v)He cluster is studied by numerically exact time-dependent quantum mechanics, and by the time-dependent self-consistent field (TDSCF) approximation. The time evolution for the initial excitation levels v = 5, 11, 22 is explored. Excellent agreement is found between the TDSCF and the exact evolution of the wave packet; in particular the approximation reproduces well the dephasing events in the dynamics, and the measurable predissociation lifetimes. The results are very encouraging as to the applicability of quantum TDSCF as a quantitative tool in the study of van der Waals predissociation dynamics.