5,472 research outputs found
Quantum many-body dynamics in a Lagrangian frame: II. Geometric formulation of time-dependent density functional theory
We formulate equations of time-dependent density functional theory (TDDFT) in
the co-moving Lagrangian reference frame. The main advantage of the Lagrangian
description of many-body dynamics is that in the co-moving frame the current
density vanishes, while the density of particles becomes independent of time.
Therefore a co-moving observer will see the picture which is very similar to
that seen in the equilibrium system from the laboratory frame. It is shown that
the most natural set of basic variables in TDDFT includes the Lagrangian
coordinate, , a symmetric deformation tensor , and a
skew-symmetric vorticity tensor, . These three quantities,
respectively, describe the translation, deformation, and the rotation of an
infinitesimal fluid element. Reformulation of TDDFT in terms of new basic
variables resolves the problem of nonlocality and thus allows to regularly
derive a local nonadiabatic approximation for exchange correlation (xc)
potential. Stationarity of the density in the co-moving frame makes the
derivation to a large extent similar to the derivation of the standard static
local density approximation. We present a few explicit examples of nonlinear
nonadiabatic xc functionals in a form convenient for practical applications.Comment: RevTeX4, 18 pages, Corrected final version. The first part of this
work is cond-mat/040835
Anti-adiabatic limit of the exchange-correlation kernels of an inhomogeneous electron gas
We express the high-frequency (anti-adiabatic) limit of the
exchange-correlation kernels of an inhomogeneous electron gas in terms of the
following equilibrium properties: the ground-state density, the kinetic stress
tensor, the pair-correlation function, and the ground-state
exchange-correlation potential. Of these quantities, the first three are
amenable to exact evaluation by Quantum Monte Carlo methods, while the last can
be obtained from the inversion of the Kohn-Sham equation for the ground-state
orbitals. The exact scalar kernel, in this limit, is found to be of very long
range in space, at variance with the kernel that is used in the standard local
density approximation. The anti-adiabatic xc kernels should be useful in
calculations of excitation energies by time-dependent DFT in atoms, molecules,
and solids, and provides a solid basis for interpolation between the low- and
high-frequency limits of the xc kernels.Comment: 9 pages, 3 figures, to be submitted to PR
Continuum Mechanics for Quantum Many-Body Systems: The Linear Response Regime
We derive a closed equation of motion for the current density of an
inhomogeneous quantum many-body system under the assumption that the
time-dependent wave function can be described as a geometric deformation of the
ground-state wave function. By describing the many-body system in terms of a
single collective field we provide an alternative to traditional approaches,
which emphasize one-particle orbitals. We refer to our approach as continuum
mechanics for quantum many-body systems. In the linear response regime, the
equation of motion for the displacement field becomes a linear fourth-order
integro-differential equation, whose only inputs are the one-particle density
matrix and the pair correlation function of the ground-state. The complexity of
this equation remains essentially unchanged as the number of particles
increases. We show that our equation of motion is a hermitian eigenvalue
problem, which admits a complete set of orthonormal eigenfunctions under a
scalar product that involves the ground-state density. Further, we show that
the excitation energies derived from this approach satisfy a sum rule which
guarantees the exactness of the integrated spectral strength. Our formulation
becomes exact for systems consisting of a single particle, and for any
many-body system in the high-frequency limit. The theory is illustrated by
explicit calculations for simple one- and two-particle systems.Comment: 23 pages, 4 figures, 1 table, 6 Appendices This paper is a follow-up
to PRL 103, 086401 (2009
A Geometric Formulation of Quantum Stress Fields
We present a derivation of the stress field for an interacting quantum system
within the framework of local density functional theory. The formulation is
geometric in nature and exploits the relationship between the strain tensor
field and Riemannian metric tensor field. Within this formulation, we
demonstrate that the stress field is unique up to a single ambiguous parameter.
The ambiguity is due to the non-unique dependence of the kinetic energy on the
metric tensor. To illustrate this formalism, we compute the pressure field for
two phases of solid molecular hydrogen. Furthermore, we demonstrate that
qualitative results obtained by interpreting the hydrogen pressure field are
not influenced by the presence of the kinetic ambiguity.Comment: 22 pages, 2 figures. Submitted to Physical Review B. This paper
supersedes cond-mat/000627
Time-dependent density functional theory: Derivation of gradient-corrected dynamical exchange-correlational potentials
URL:http://link.aps.org/doi/10.1103/PhysRevB.76.195126
DOI:10.1103/PhysRevB.76.195126We have recently proposed an approximation for the dynamical exchange-correlation (XC) potentials of time-dependent current-density functional theory beyond the local density approximation [Phys. Rev. Lett. 97, 036403 (2006)]. The novel feature of the approximation is that the dependence of the dynamical XC potentials upon the density gradient and other inhomogeneity parameters (e.g., the Laplacian of the density and the kinetic energy density) is introduced by applying the generalized gradient approximation (GGA) and meta-GGA to the calculation of the XC stress tensor. The scheme may allow a more accurate treatment of the dynamical properties of an inhomogeneous system, while reducing to the exact form for slowly varying densities and slowly varying external potentials. In this work, we present in detail the derivation of this XC potential, spell out the underlying assumptions, and explain their physical basis.This work was supported by the DOE under Grant No. DE-FG02-05ER46203
Ward Identities for Transport in 2+1 Dimensions
We use the Ward identities corresponding to general linear transformations,
and derive relations between transport coefficients of -dimensional
systems. Our analysis includes relativistic and Galilean invariant systems, as
well as systems without boost invariance such as Lifshitz theories. We consider
translation invariant, as well as broken translation invariant cases, and
include an external magnetic field. Our results agree with effective theory
relations of incompressible Hall fluid, and with holographic calculations in a
magnetically charged black hole background.Comment: 17 pages, references and conclusions added. Published versio
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