This thesis is devoted to the formulation and implications of the time-dependent density functional theory (TDDFT). The work is divided into two main parts. In the first part we develop rigorous theorems for the density-potential mapping in quantum many-body systems on a lattice. We prove the uniqueness of the TDDFT map and demonstrate that a given density is v-representable if the initial many-body state and the density satisfy certain well defined conditions. In particular, we show that for a system evolving from its ground state any density with a continuous second time derivative is v-representable. Then the lattice TDDFT formulation is extended to cover system of interacting lattice electrons strongly coupled to cavity photons.We prove that under some mathematical conditions the electron-photon wave function is a unique functional of the electronic density and the expectation value of the photonic coordinate. Then we further generalize the ground state v representability theorem to include the ground state of a general lattice electron-photon Hamiltonian.This thesis is devoted to the formulation and implications of the time-dependent density functional theory (TDDFT). The work is divided into two main parts. In the first part we develop rigorous theorems for the density-potential mapping in quantum many-body systems on a lattice. We prove the uniqueness of the TDDFT map and demonstrate that a given density is v-representable if the initial many-body state and the density satisfy certain well defined conditions. In particular, we show that for a system evolving from its ground state any density with a continuous second time derivative is v-representable. Then the lattice TDDFT formulation is extended to cover system of interacting lattice electrons strongly coupled to cavity photons.We prove that under some mathematical conditions the electron-photon wave function is a unique functional of the electronic density and the expectation value of the photonic coordinate. Then we further generalize the ground state v representability theorem to include the ground state of a general lattice electron-photon Hamiltonian.

Jan 1, 20150 citations

Quantum electrodynamical time-dependent density functional theory for many-electron systems on a lattice

Mehdi Farzanehpour, I. V. Tokatly

We present a rigorous formulation of the time-dependent density-functional theory for interacting lattice electrons strongly coupled to cavity photons. We start with an example of one particle on a Hubbard dimer coupled to a single photonic mode, which is equivalent to the single mode spin-boson model or the quantum Rabi model. For this system we prove that the electron-photon wave function is a unique functional of the electronic density and the expectation value of the photonic coordinate, provided the initial state and the density satisfy a set of well defined conditions. Then we generalize the formalism to many interacting electrons on a lattice coupled to multiple photonic modes and prove the general mapping theorem. We also show that for a system evolving from the ground state of a lattice Hamiltonian any density with a continuous second time derivative is locally v representable.We present a rigorous formulation of the time-dependent density-functional theory for interacting lattice electrons strongly coupled to cavity photons. We start with an example of one particle on a Hubbard dimer coupled to a single photonic mode, which is equivalent to the single mode spin-boson model or the quantum Rabi model. For this system we prove that the electron-photon wave function is a unique functional of the electronic density and the expectation value of the photonic coordinate, provided the initial state and the density satisfy a set of well defined conditions. Then we generalize the formalism to many interacting electrons on a lattice coupled to multiple photonic modes and prove the general mapping theorem. We also show that for a system evolving from the ground state of a lattice Hamiltonian any density with a continuous second time derivative is locally v representable.

Bulletin of the American Physical SocietyMar 6, 20150 citations

Density Functional Calculations for Strongly Correlated Systems

O. Gunnarsson, O. K. Andersen, A. Svane

NATO ASI series. Series B : PhysicsJan 1, 19890 citations

Aspects of Density Functional Approach to Many-Electron Systems

Swapan K. Ghosh

Lecture notes in chemistryJan 1, 19890 citations

Quantum electrodynamical time-dependent density-functional theory for many-electron systems on a lattice

Mehdi Farzanehpour, I. V. Tokatly

We present a rigorous formulation of the time-dependent density-functional theory for interacting lattice electrons strongly coupled to cavity photons. We start with an example of one particle on a Hubbard dimer coupled to a single photonic mode, which is equivalent to the single mode spin-boson model or the quantum Rabi model. For this system we prove that the electron-photon wave function is a unique functional of the electronic density and the expectation value of the photonic coordinate, provided the initial state and the density satisfy a set of well defined conditions. Then we generalize the formalism to many interacting electrons on a lattice coupled to multiple photonic modes and prove the general mapping theorem. We also show that for a system evolving from the ground state of a lattice Hamiltonian any density with a continuous second time derivative is locally $v$ representable.We present a rigorous formulation of the time-dependent density-functional theory for interacting lattice electrons strongly coupled to cavity photons. We start with an example of one particle on a Hubbard dimer coupled to a single photonic mode, which is equivalent to the single mode spin-boson model or the quantum Rabi model. For this system we prove that the electron-photon wave function is a unique functional of the electronic density and the expectation value of the photonic coordinate, provided the initial state and the density satisfy a set of well defined conditions. Then we generalize the formalism to many interacting electrons on a lattice coupled to multiple photonic modes and prove the general mapping theorem. We also show that for a system evolving from the ground state of a lattice Hamiltonian any density with a continuous second time derivative is locally $v$ representable.

arXiv:1408.6324Physical Review BNov 26, 201411 citations

v

representable.