194 research outputs found
Ground-State Quantum-Electrodynamical Density-Functional Theory
In this work we establish a density-functional reformulation of coupled
matter-photon problems subject to general external electromagnetic fields and
charge currents. We first show that for static minimally-coupled matter-photon
systems an external electromagnetic field is equivalent to an external charge
current. We employ this to show that scalar external potentials and transversal
external charge currents are in a one-to-one correspondence to the expectation
values of the charge density and the vector-potential of the correlated
matter-photon ground state. This allows to establish a Maxwell-Kohn-Sham
approach, where in conjunction with the usual single-particle Kohn-Sham
equations a classical Maxwell equation has to be solved. In the magnetic
mean-field limit this reduces to a current-density-functional theory that does
not suffer from non-uniqueness problems and if furthermore the magnetic field
is zero recovers standard density-functional theory
Global fixed point proof of time-dependent density-functional theory
We reformulate and generalize the uniqueness and existence proofs of
time-dependent density-functional theory. The central idea is to restate the
fundamental one-to-one correspondence between densities and potentials as a
global fixed point question for potentials on a given time-interval. We show
that the unique fixed point, i.e. the unique potential generating a given
density, is reached as the limiting point of an iterative procedure. The
one-to-one correspondence between densities and potentials is a straightforward
result provided that the response function of the divergence of the internal
forces is bounded. The existence, i.e. the v-representability of a density, can
be proven as well provided that the operator norms of the response functions of
the members of the iterative sequence of potentials have an upper bound. The
densities under consideration have second time-derivatives that are required to
satisfy a condition slightly weaker than being square-integrable. This approach
avoids the usual restrictions of Taylor-expandability in time of the uniqueness
theorem by Runge and Gross [Phys.Rev.Lett.52, 997 (1984)] and of the existence
theorem by van Leeuwen [Phys.Rev.Lett. 82, 3863 (1999)]. Owing to its
generality, the proof not only answers basic questions in density-functional
theory but also has potential implications in other fields of physics.Comment: 4 pages, 1 figur
One-body reduced density-matrix functional theory in finite basis sets at elevated temperatures
In this review we provide a rigorous and self-contained presentation of
one-body reduced density-matrix (1RDM) functional theory. We do so for the case
of a finite basis set, where density-functional theory (DFT) implicitly becomes
a 1RDM functional theory. To avoid non-uniqueness issues we consider the case
of fermionic and bosonic systems at elevated temperature and variable particle
number, i.e, a grand-canonical ensemble. For the fermionic case the Fock space
is finite-dimensional due to the Pauli principle and we can provide a rigorous
1RDM functional theory relatively straightforwardly. For the bosonic case,
where arbitrarily many particles can occupy a single state, the Fock space is
infinite-dimensional and mathematical subtleties (not every hermitian
Hamiltonian is self-adjoint, expectation values can become infinite, and not
every self-adjoint Hamiltonian has a Gibbs state) make it necessary to impose
restrictions on the allowed Hamiltonians and external non-local potentials. For
simple conditions on the interaction of the bosons a rigorous 1RDM functional
theory can be established, where we exploit the fact that due to the finite
one-particle space all 1RDMs are finite-dimensional. We also discuss the
problems arising from 1RDM functional theory as well as DFT formulated for an
infinite-dimensional one-particle space.Comment: 55 pages, 7 figure
Time-dependent Kohn-Sham approach to quantum electrodynamics
We prove a generalization of the van Leeuwen theorem towards quantum
electrodynamics, providing the formal foundations of a time-dependent Kohn-Sham
construction for coupled quantized matter and electromagnetic fields. Thereby
we circumvent the symmetry-causality problems associated with the
action-functional approach to Kohn-Sham systems. We show that the effective
external four-potential and four-current of the Kohn-Sham system are uniquely
defined and that the effective four-current takes a very simple form. Further
we rederive the Runge-Gross theorem for quantum electrodynamics.Comment: 8 page
Atoms and Molecules in Cavities: From Weak to Strong Coupling in QED Chemistry
In this work, we provide an overview of how well-established concepts in the
fields of quantum chemistry and material sciences have to be adapted when the
quantum nature of light becomes important in correlated matter-photon problems.
Therefore, we analyze model systems in optical cavities, where the
matter-photon interaction is considered from the weak- to the strong coupling
limit and for individual photon modes as well as for the multi-mode case. We
identify fundamental changes in Born-Oppenheimer surfaces, spectroscopic
quantities, conical intersections and efficiency for quantum control. We
conclude by applying our novel recently developed quantum-electrodynamical
density-functional theory to single-photon emission and show how a
straightforward approximation accurately describes the correlated
electron-photon dynamics. This paves the road to describe matter-photon
interactions from first-principles and addresses the emergence of new states of
matter in chemistry and material science
Cavity Born-Oppenheimer Approximation for Correlated Electron-Nuclear-Photon Systems
In this work, we illustrate the recently introduced concept of the cavity
Born-Oppenheimer approximation for correlated electron-nuclear-photon problems
in detail. We demonstrate how an expansion in terms of conditional electronic
and photon-nuclear wave functions accurately describes eigenstates of strongly
correlated light-matter systems. For a GaAs quantum ring model in resonance
with a photon mode we highlight how the ground-state electronic
potential-energy surface changes the usual harmonic potential of the free
photon mode to a dressed mode with a double-well structure. This change is
accompanied by a splitting of the electronic ground-state density. For a model
where the photon mode is in resonance with a vibrational transition, we observe
in the excited-state electronic potential-energy surface a splitting from a
single minimum to a double minimum. Furthermore, for a time-dependent setup, we
show how the dynamics in correlated light-matter systems can be understood in
terms of population transfer between potential energy surfaces. This work at
the interface of quantum chemistry and quantum optics paves the way for the
full ab-initio description of matter-photon systems
- …