Time-Dependent Density Functional Theory

## Time-Dependent Density Functional Theory (TDDFT)

### Brief introduction

TDDFT extends the concept of stationary DFT to time-dependent situations: For any interacting quantum many-particle system subject to a given time-dependent potential all physical observables are uniquely determined by knowledge of the time-dependent density and the state of the system at an arbitrary, single instant in time [1]. In particular, if the time-dependent potential is switched on at some time $t$0 and the system has been in its ground state until $t$0, all observables are unique functionals of only the density: In this case the initial state of the system at time $t$0 is a unique functional of the density at $t$0, which is identical with the ground state density of the stationary system one has before $t$0 (for all times until $t$0 the one-to-one correspondence is guaranteed by the Hohenberg-Kohn theorem for stationary systems). This unique relationship allows to derive a calculational scheme in which the effect of the particle-particle interaction is represented by a density-dependent single-particle potential, so that the time evolution of an interacting system can be studied by solving a time-dependent auxiliary single-particle problem. Additional simplifications are obtained in the linear response regime [2]. Like in stationary DFT the major task of TDDFT is to find suitable approximations for the exchange-correlation (xc) part of the effective single-particle potential.

In our group the TDDFT approach has been applied to the photo absorption of metal clusters using both the time-dependent local density approximation [3,4] and the exact exchange (on the basis of the optimized-potential-method [5]) as approximations for the effective xc-potential. In particular, we have developed an adiabatic linear response type approximation to the full time-dependent optimized-potential-method [6].

### References

1. E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984).
2. E. K. U. Gross and W. Kohn, Phys. Rev. Lett. 55, 2850 (1985).
3. A. Zangwill and P. Soven, Phys. Rev. A 21, 1561 (1980).
4. W. Ekardt, Phys. Rev. B 31, 6360 (1985).
5. C. A. Ullrich and E. K. U. Gross, Phys. Rev. Lett. 74, 872 (1995).
6. Th. Maier, PhD thesis, Univ. of Frankfurt (1997).

Home Top