often than not we face the fact that the electronic states have finite lifetimes because
of the coupling to the environment or to a continuum of states (resonance processes). Even if we were able to prepare a perfectly isolated quantum system, we
would need to regard a measurement of the system as bringing the system into
contact with an environment. Already a single atom in vacuum cannot be regarded
as completely isolated, because the atom is embedded in the surrounding photon
field (spontaneous emission). Other examples where the coupling to the surrounding plays a prominent role include hot electron relaxation in bulk systems and
surfaces after laser irradiation, thermalization caused by electron–phonon coupling,
decoherence in pump–probe experiments, exciton propagation and relaxation in
biological chromophores, and vibrational relaxation in nanomaterials and molecular systems. Understanding these decay mechanisms provides important information about electron correlations, quantum coherence, dissipative and decoherence
processes, and control of these processes has important implications. For instance,
this would make it possible to enhance the performance of molecular/solid-based
optoelectronic devices.
In this context, density-functional theory (DFT) provides an exact theoretical
framework which could yield observable quantities directly, by-passing the need to
calculate the many-body wavefunction Ψ. Hohenberg and Kohn [1] proved that all
observable properties of a static many-electron system can be extracted exactly
from the one-body ground-state density alone (density–potential mapping). Later,
Runge and Gross extended this theorem to time-dependent systems [2]. Timedependent density-functional theory (TDDFT) is a rigorous reformulation of the
non-relativistic time-dependent quantum mechanics of many-body systems. The
central theorem of TDDFT is the Runge–Gross theorem which proves a one-to-one
correspondence between the time-dependent external potential ν ext (r, t) and the
electronic one-body density n(r, t) for many-body systems evolving from a fixed
initial state Ψ 0 . This implies that the time-dependent electronic density determines
all properties of the interacting many-electron system: all observable properties of a
many-electron system can be extracted from the one-body time-dependent density
alone [2]. What has made both DFT and TDDFT so successful is the Kohn–Sham
scheme [3]: the density of the interacting many-electron system is obtained as the
density of an auxiliary system of non-interacting fermions, living in a one-body
potential. Because of the excellent balance between the computational load it
requires and the accuracy it provides, TDDFT is now a tool of choice for quite
accurate and reliable predictions for excited-state properties in solid state physics,
chemistry, and biophysics, in both the linear and nonlinear regimes. However, there
exist many situations where the electronic degrees of freedom are not isolated but
must be treated as a subsystem embedded in an environment, which influences it in
a non-negligible way. Those situations go beyond the realm of the original formulation of TDDFT which is meant to tackle the isolated dynamics of electronic
systems. It is therefore clear that there is a need to extend density-functional
approaches to the realm of open quantum systems to allow us to treat the processes
described above.
Burke and co-workers recently introduced a TDDFT approach based on a Kohn–
Sham master equation [4], and in recent work this has been pursued by the group of
Dynamical Processes in Open Quantum Systems from a TDDFT Perspective:. . .
221
of the coupling to the environment or to a continuum of states (resonance processes). Even if we were able to prepare a perfectly isolated quantum system, we
would need to regard a measurement of the system as bringing the system into
contact with an environment. Already a single atom in vacuum cannot be regarded
as completely isolated, because the atom is embedded in the surrounding photon
field (spontaneous emission). Other examples where the coupling to the surrounding plays a prominent role include hot electron relaxation in bulk systems and
surfaces after laser irradiation, thermalization caused by electron–phonon coupling,
decoherence in pump–probe experiments, exciton propagation and relaxation in
biological chromophores, and vibrational relaxation in nanomaterials and molecular systems. Understanding these decay mechanisms provides important information about electron correlations, quantum coherence, dissipative and decoherence
processes, and control of these processes has important implications. For instance,
this would make it possible to enhance the performance of molecular/solid-based
optoelectronic devices.
In this context, density-functional theory (DFT) provides an exact theoretical
framework which could yield observable quantities directly, by-passing the need to
calculate the many-body wavefunction Ψ. Hohenberg and Kohn [1] proved that all
observable properties of a static many-electron system can be extracted exactly
from the one-body ground-state density alone (density–potential mapping). Later,
Runge and Gross extended this theorem to time-dependent systems [2]. Timedependent density-functional theory (TDDFT) is a rigorous reformulation of the
non-relativistic time-dependent quantum mechanics of many-body systems. The
central theorem of TDDFT is the Runge–Gross theorem which proves a one-to-one
correspondence between the time-dependent external potential ν ext (r, t) and the
electronic one-body density n(r, t) for many-body systems evolving from a fixed
initial state Ψ 0 . This implies that the time-dependent electronic density determines
all properties of the interacting many-electron system: all observable properties of a
many-electron system can be extracted from the one-body time-dependent density
alone [2]. What has made both DFT and TDDFT so successful is the Kohn–Sham
scheme [3]: the density of the interacting many-electron system is obtained as the
density of an auxiliary system of non-interacting fermions, living in a one-body
potential. Because of the excellent balance between the computational load it
requires and the accuracy it provides, TDDFT is now a tool of choice for quite
accurate and reliable predictions for excited-state properties in solid state physics,
chemistry, and biophysics, in both the linear and nonlinear regimes. However, there
exist many situations where the electronic degrees of freedom are not isolated but
must be treated as a subsystem embedded in an environment, which influences it in
a non-negligible way. Those situations go beyond the realm of the original formulation of TDDFT which is meant to tackle the isolated dynamics of electronic
systems. It is therefore clear that there is a need to extend density-functional
approaches to the realm of open quantum systems to allow us to treat the processes
described above.
Burke and co-workers recently introduced a TDDFT approach based on a Kohn–
Sham master equation [4], and in recent work this has been pursued by the group of
Dynamical Processes in Open Quantum Systems from a TDDFT Perspective:. . .
221