Biomedical subjects

C A Ullrich

Publications and source records attributed to C A Ullrich.

6 recordsLinked to original sources

PubMed2006

Time-dependent density-functional theory beyond the adiabatic approximation: insights from a two-electron model system.

Most applications of time-dependent density-functional theory (TDDFT) use the adiabatic local-density approximation (ALDA) for the dynamical exchange-correlation potential V(xc)(r,t). An exact (i.e., nonadiabatic) extension of the ground-state LDA into the dynamical regime leads to a V(xc)(r,t) with a memory, which causes the electron dynamics to become dissipative. To illustrate and explain this nonadiabatic behavior, this paper studies the dynamics of two interacting electrons on a two-dimensional quantum strip of finite size, comparing TDDFT within and beyond the ALDA with numerical solutions of the two-electron time-dependent Schrodinger equation. It is shown explicitly how dissipation arises through multiple particle-hole excitations, and how the nonadiabatic extension of the ALDA fails for finite systems but becomes correct in the thermodynamic limit.

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PubMed2005

Time-dependent Kohn-Sham theory with memory.

In time-dependent density-functional theory, exchange and correlation (xc) beyond the adiabatic approximation can be described by viscoelastic stresses in the electron liquid. In the time domain, the resulting velocity-dependent xc vector potential has a memory containing short- and long-range components, leading to decoherence and energy relaxation. We solve the associated time-dependent Kohn-Sham equations, including the dependence on densities and currents at previous times, for the case of charge-density oscillations in a quantum well. We illustrate xc memory effects, clarify the dissipation mechanism, and extract intersubband relaxation rates for weak and strong excitations.

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PubMed2004

Excitation energies from time-dependent density-functional theory beyond the adiabatic approximation.

Time-dependent density-functional theory in the adiabatic approximation has been very successful for calculating excitation energies in molecular systems. This paper studies nonadiabatic effects for excitation energies, using the current-density functional of Vignale and Kohn [Phys. Rev. Lett. 77, 2037 (1996)]. We derive a general analytic expression for nonadiabatic corrections to excitation energies of finite systems and calculate singlet s-->s and s-->p excitations of closed-shell atoms. The approach works well for s-->s excitations, giving a small improvement over the adiabatic local-density approximation, but tends to overcorrect s-->p excitations. We find that the observed problems with the nonadiabatic correction have two main sources: (1) the currents associated with the s-->p excitations are highly nonuniform and, in particular, change direction between atomic shells, (2) the so-called exchange-correlation kernels of the homogeneous electron gas, f(xc) (L) and f(xc) (T), are incompletely known, in particular in the high-density atomic core regions.

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PubMed2002

Degeneracy in density functional theory: topology in the v and n spaces.

This paper clarifies the topology of the mapping between the v and n spaces in fermionic systems. Density manifolds corresponding to degeneracies g=1 and g>1 are shown to have the same mathematical measure: Every density near a g-ensemble-v-representable (g-VR) n(r) is also g-VR (except "boundary densities" of lower measure). The role of symmetry and the connection between T=0 and T=0(+) are discussed. A lattice model and the Be series are used as illustrations.

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PubMed2001

Kohn-Sham theory for ground-state ensembles.

An electron density distribution n(r) which can be represented by that of a single-determinant ground state of noninteracting electrons in an external potential v(r) is called pure-state v-representable (P-VR). Most physical electronic systems are P-VR. Systems which require a weighted sum of several such determinants to represent their density are called ensemble v-representable (E-VR). This paper develops formal Kohn-Sham equations for E-VR physical systems, using the appropriate coupling constant integration. It also derives local density- and generalized gradient approximations, and conditions and corrections specific to ensembles.

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PubMed2001

Theory of the linewidth of intersubband plasmons in quantum wells.

Intersubband (ISB) plasmons in remotely doped wide quantum wells acquire a linewidth even at zero temperature and in-plane wave vector q(parallel) = 0 by a combination of intrinsic (electron-electron interaction) and extrinsic effects (impurities and interface roughness). We present a quantitatively accurate theory of the linewidth that treats both effects on equal footing and from first principles by a combination of time-dependent density-functional theory with the memory function formalism. Comparison with recent optical absorption experiments shows that the ISB plasmon linewidth has a significant contribution from electron-electron interaction, and is only weakly related to the mobility.

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