Generalized Householder Transformations for the Complex Symmetric Eigenvalue Problem

We present an intuitive and scalable algorithm for the diagonalization of complex symmetric matrices, which arise from the projection of pseudo--Hermitian and complex scaled Hamiltonians onto a suitable basis set of "trial" states. The algorithm diagonalizes complex and symmetric (non--Hermitian) matrices and is easily implemented in modern computer languages. It is based on generalized Householder transformations and relies on iterative similarity transformations T -> T' = Q^T T Q, where Q is a complex and orthogonal, but not unitary, matrix, i.e, Q^T equals Q^(-1) but Q^+ is different from Q^(-1). We present numerical reference data to support the scalability of the algorithm. We construct the generalized Householder transformations from the notion that the conserved scalar product of eigenstates Psi_n and Psi_m of a pseudo-Hermitian quantum mechanical Hamiltonian can be reformulated in terms of the generalized indefinite inner product [integral of the product Psi_n(x,t) Psi_m(x,t) over dx], where the integrand is locally defined, and complex conjugation is avoided. A few example calculations are described which illustrate the physical origin of the ideas used in the construction of the algorithm.Comment: 14 pages; RevTeX; font mismatch in Eqs. (3) and (15) is eliminate

Quantum Dot Potentials: Symanzik Scaling, Resurgent Expansions and Quantum Dynamics

This article is concerned with a special class of the ``double-well-like'' potentials that occur naturally in the analysis of finite quantum systems. Special attention is paid, in particular, to the so-called Fokker-Planck potential, which has a particular property: the perturbation series for the ground-state energy vanishes to all orders in the coupling parameter, but the actual ground-state energy is positive and dominated by instanton configurations of the form exp(-a/g), where a is the instanton action. The instanton effects are most naturally taken into account within the modified Bohr-Sommerfeld quantization conditions whose expansion leads to the generalized perturbative expansions (so-called resurgent expansions) for the energy values of the Fokker-Planck potential. Until now, these resurgent expansions have been mainly applied for small values of coupling parameter g, while much less attention has been paid to the strong-coupling regime. In this contribution, we compare the energy values, obtained by directly resumming generalized Bohr-Sommerfeld quantization conditions, to the strong-coupling expansion, for which we determine the first few expansion coefficients in powers of g^(-2/3). Detailed calculations are performed for a wide range of coupling parameters g and indicate a considerable overlap between the regions of validity of the weak-coupling resurgent series and of the strong-coupling expansion. Apart from the analysis of the energy spectrum of the Fokker-Planck Hamiltonian, we also briefly discuss the computation of its eigenfunctions. These eigenfunctions may be utilized for the numerical integration of the (single-particle) time-dependent Schroedinger equation and, hence, for studying the dynamical evolution of the wavepackets in the double-well-like potentials.Comment: 13 pages; RevTe

Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice

Dirac points lie at the heart of many fascinating phenomena in condensed matter physics, from massless electrons in graphene to the emergence of conducting edge states in topological insulators [1, 2]. At a Dirac point, two energy bands intersect linearly and the particles behave as relativistic Dirac fermions. In solids, the rigid structure of the material sets the mass and velocity of the particles, as well as their interactions. A different, highly flexible approach is to create model systems using fermionic atoms trapped in the periodic potential of interfering laser beams, a method which so far has only been applied to explore simple lattice structures [3, 4]. Here we report on the creation of Dirac points with adjustable properties in a tunable honeycomb optical lattice. Using momentum-resolved interband transitions, we observe a minimum band gap inside the Brillouin zone at the position of the Dirac points. We exploit the unique tunability of our lattice potential to adjust the effective mass of the Dirac fermions by breaking inversion symmetry. Moreover, changing the lattice anisotropy allows us to move the position of the Dirac points inside the Brillouin zone. When increasing the anisotropy beyond a critical limit, the two Dirac points merge and annihilate each other - a situation which has recently attracted considerable theoretical interest [5-9], but seems extremely challenging to observe in solids [10]. We map out this topological transition in lattice parameter space and find excellent agreement with ab initio calculations. Our results not only pave the way to model materials where the topology of the band structure plays a crucial role, but also provide an avenue to explore many-body phases resulting from the interplay of complex lattice geometries with interactions [11, 12]

Structure, Time Propagation and Dissipative Terms for Resonances

For odd anharmonic oscillators, it is well known that complex scaling can be used to determine resonance energy eigenvalues and the corresponding eigenvectors in complex rotated space. We briefly review and discuss various methods for the numerical determination of such eigenvalues, and also discuss the connection to the case of purely imaginary coupling, which is PT-symmetric. Moreover, we show that a suitable generalization of the complex scaling method leads to an algorithm for the time propagation of wave packets in potentials which give rise to unstable resonances. This leads to a certain unification of the structure and the dynamics. Our time propagation results agree with known quantum dynamics solvers and allow for a natural incorporation of structural perturbations (e.g., due to dissipative processes) into the quantum dynamics.Comment: 14 pages; LaTeX; minor change

Acute cholecystitis – early laparoskopic surgery versus antibiotic therapy and delayed elective cholecystectomy: ACDC-study

<p>Abstract</p> <p>Background</p> <p>Acute cholecystitis occurs frequently in the elderly and in patients with gall stones. Most cases of severe or recurrent cholecystitis eventually require surgery, usually laparoscopic cholecystectomy in the Western World. It is unclear whether an initial, conservative approach with antibiotic and symptomatic therapy followed by delayed elective surgery would result in better morbidity and outcome than immediate surgery. At present, treatment is generally determined by whether the patient first sees a surgeon or a gastroenterologist. We wish to investigate whether both approaches are equivalent. The primary endpoint is the morbidity until day 75 after inclusion into the study.</p> <p>Design</p> <p>A multicenter, prospective, randomized non-blinded study to compare treatment outcome, complications and 75-day morbidity in patients with acute cholecystitis randomized to laparoscopic cholecystectomy within 24 hours of symptom onset or antibiotic treatment with moxifloxacin and subsequent elective cholecystectomy. For consistency in both arms moxifloxacin, a fluorquinolone with broad spectrum of activity and high bile concentration is used as antibiotic. Duration: October 2006 – November 2008</p> <p>Organisation/Responsibility</p> <p>The trial was planned and is being conducted and analysed by the Departments of Gastroenterology and General Surgery at the University Hospital of Heidelberg according to the ethical, regulatory and scientific principles governing clinical research as set out in the Declaration of Helsinki (1989) and the Good Clinical Practice guideline (GCP).</p> <p>Trial Registration</p> <p>ClinicalTrials.gov NCT00447304</p

Sterilizing Activity of Second-Line Regimens Containing TMC207 in a Murine Model of Tuberculosis

The sterilizing activity of the regimen used to treat multidrug resistant tuberculosis (MDR TB) has not been studied in a mouse model. (TB) strain H37Rv, treated with second-line drug combinations with or without the diarylquinoline TMC207, and then followed without treatment for 3 more months to determine relapse rates (modified Cornell model).Bactericidal efficacy was assessed by quantitative lung colony-forming unit (CFU) counts. Sterilizing efficacy was assessed by measuring bacteriological relapse rates 3 months after the end of treatment.The relapse rate observed after 12 months treatment with the WHO recommended MDR TB regimen (amikacin, ethionamide, pyrazinamide and moxifloxacin) was equivalent to the relapse rate observed after 6 months treatment with the recommended drug susceptible TB regimen (rifampin, isoniazid and pyrazinamide). When TMC207 was added to this MDR TB regimen, the treatment duration needed to reach the same relapse rate dropped to 6 months. A similar relapse rate was also obtained with a 6-month completely oral regimen including TMC207, moxifloxacin and pyrazinamide but excluding both amikacin and ethionamide.In this murine model the duration of the WHO MDR TB treatment could be reduced to 12 months instead of the recommended 18–24 months. The inclusion of TMC207 in the WHO MDR TB treatment regimen has the potential to further shorten the treatment duration and at the same time to simplify treatment by eliminating the need to include an injectable aminoglycoside

Multigrid renormalization

We combine the multigrid (MG) method with state-of-the-art concepts from the variational formulation of the numerical renormalization group. The resulting MG renormalization (MGR) method is a natural generalization of the MG method for solving partial differential equations. When the solution on a grid of N points is sought, our MGR method has a computational cost scaling as O(log⁡(N)), as opposed to O(N) for the best standard MG method. Therefore MGR can exponentially speed up standard MG computations. To illustrate our method, we develop a novel algorithm for the ground state computation of the nonlinear Schrödinger equation. Our algorithm acts variationally on tensor products and updates the tensors one after another by solving a local nonlinear optimization problem. We compare several different methods for the nonlinear tensor update and find that the Newton method is the most efficient as well as precise. The combination of MGR with our nonlinear ground state algorithm produces accurate results for the nonlinear Schrödinger equation on N=1018grid points in three spatial dimensions