Review of biorthogonal coupled cluster representations for electronic excitation

Single reference coupled-cluster (CC) methods for electronic excitation are based on a biorthogonal representation (bCC) of the (shifted) Hamiltonian in terms of excited CC states, also referred to as correlated excited (CE) states, and an associated set of states biorthogonal to the CE states, the latter being essentially configuration interaction (CI) configurations. The bCC representation generates a non-hermitian secular matrix, the eigenvalues representing excitation energies, while the corresponding spectral intensities are to be derived from both the left and right eigenvectors. Using the perspective of the bCC representation, a systematic and comprehensive analysis of the excited-state CC methods is given, extending and generalizing previous such studies. Here, the essential topics are the truncation error characteristics and the separability properties, the latter being crucial for designing size-consistent approximation schemes. Based on the general order relations for the bCC secular matrix and the (left and right) eigenvector matrices, formulas for the perturbation-theoretical (PT) order of the truncation errors (TEO) are derived for energies, transition moments, and property matrix elements of arbitrary excitation classes and truncation levels. In the analysis of the separability properties of the transition moments, the decisive role of the so-called dual ground state is revealed. Due to the use of CE states the bCC approach can be compared to so-called intermediate state representation (ISR) methods based exclusively on suitably orthonormalized CE states. As the present analysis shows, the bCC approach has decisive advantages over the conventional CI treatment, but also distinctly weaker TEO and separability properties in comparison with a full (and hermitian) ISR method

Non-Hermitian matrix description of the PT symmetric anharmonic oscillators

Schroedinger equation H \psi=E \psi with PT - symmetric differential operator H=H(x) = p^2 + a x^4 + i \beta x^3 +c x^2+i \delta x = H^*(-x) on L_2(-\infty,\infty) is re-arranged as a linear algebraic diagonalization at a>0. The proof of this non-variational construction is given. Our Taylor series form of \psi complements and completes the recent terminating solutions as obtained for certain couplings \delta at the less common negative a.Comment: 18 pages, latex, no figures, thoroughly revised (incl. title), J. Phys. A: Math. Gen., to appea

Influence of Coulomb and Phonon Interaction on the Exciton Formation Dynamics in Semiconductor Heterostructures

A microscopic theory is developed to analyze the dynamics of exciton formation out of incoherent carriers in semiconductor heterostructures. The carrier Coulomb and phonon interaction is included consistently. A cluster expansion method is used to systematically truncate the hierarchy problem. By including all correlations up to the four-point (i.e. two-particle) level, the fundamental fermionic substructure of excitons is fully included. The analysis shows that the exciton formation is an intricate process where Coulomb correlations rapidly build up on a picosecond time scale while phonon dynamics leads to true exciton formation on a slow nanosecond time scale.Comment: 18 pages, 7 figure

Green function techniques in the treatment of quantum transport at the molecular scale

The theoretical investigation of charge (and spin) transport at nanometer length scales requires the use of advanced and powerful techniques able to deal with the dynamical properties of the relevant physical systems, to explicitly include out-of-equilibrium situations typical for electrical/heat transport as well as to take into account interaction effects in a systematic way. Equilibrium Green function techniques and their extension to non-equilibrium situations via the Keldysh formalism build one of the pillars of current state-of-the-art approaches to quantum transport which have been implemented in both model Hamiltonian formulations and first-principle methodologies. We offer a tutorial overview of the applications of Green functions to deal with some fundamental aspects of charge transport at the nanoscale, mainly focusing on applications to model Hamiltonian formulations.Comment: Tutorial review, LaTeX, 129 pages, 41 figures, 300 references, submitted to Springer series "Lecture Notes in Physics

Random-phase approximation and its applications in computational chemistry and materials science

The random-phase approximation (RPA) as an approach for computing the electronic correlation energy is reviewed. After a brief account of its basic concept and historical development, the paper is devoted to the theoretical formulations of RPA, and its applications to realistic systems. With several illustrating applications, we discuss the implications of RPA for computational chemistry and materials science. The computational cost of RPA is also addressed which is critical for its widespread use in future applications. In addition, current correction schemes going beyond RPA and directions of further development will be discussed.Comment: 25 pages, 11 figures, published online in J. Mater. Sci. (2012

Ultrahigh-Field MRI in Human Ischemic Stroke – a 7 Tesla Study

INTRODUCTION: Magnetic resonance imaging (MRI) using field strengths up to 3 Tesla (T) has proven to be a powerful tool for stroke diagnosis. Recently, ultrahigh-field (UHF) MRI at 7 T has shown relevant diagnostic benefits in imaging of neurological diseases, but its value for stroke imaging has not been investigated yet. We present the first evaluation of a clinically feasible stroke imaging protocol at 7 T. For comparison an established stroke imaging protocol was applied at 3 T. METHODS: In a prospective imaging study seven patients with subacute and chronic stroke were included. Imaging at 3 T was immediately followed by 7 T imaging. Both protocols included T1-weighted 3D Magnetization-Prepared Rapid-Acquired Gradient-Echo (3D-MPRAGE), T2-weighted 2D Fluid Attenuated Inversion Recovery (2D-FLAIR), T2-weighted 2D Fluid Attenuated Inversion Recovery (2D-T2-TSE), T2* weighted 2D Fast Low Angle Shot Gradient Echo (2D-HemoFLASH) and 3D Time-of-Flight angiography (3D-TOF). RESULTS: The diagnostic information relevant for clinical stroke imaging obtained at 3 T was equally available at 7 T. Higher spatial resolution at 7 T revealed more anatomical details precisely depicting ischemic lesions and periinfarct alterations. A clear benefit in anatomical resolution was also demonstrated for vessel imaging at 7 T. RF power deposition constraints induced scan time prolongation and reduced brain coverage for 2D-FLAIR, 2D-T2-TSE and 3D-TOF at 7 T versus 3 T. CONCLUSIONS: The potential of 7 T MRI for human stroke imaging is shown. Our pilot study encourages a further evaluation of the diagnostic benefit of stroke imaging at 7 T in a larger study