A possible method for non-Hermitian and non-PTPT-symmetric Hamiltonian systems

A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator $\eta_+$ and defining the annihilation and creation operators to be $\eta_+$-pseudo-Hermitian adjoint to each other. The operator $\eta_+$ represents the $\eta_+$-pseudo-Hermiticity of Hamiltonians. As an example, a non-Hermitian and non-$PT$-symmetric Hamiltonian with imaginary linear coordinate and linear momentum terms is constructed and analyzed in detail. The operator $\eta_+$ is found, based on which, a real spectrum and a positive-definite inner product, together with the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution, are obtained for the non-Hermitian and non-$PT$-symmetric Hamiltonian. Moreover, this Hamiltonian turns out to be coupled when it is extended to the canonical noncommutative space with noncommutative spatial coordinate operators and noncommutative momentum operators as well. Our method is applicable to the coupled Hamiltonian. Then the first and second order noncommutative corrections of energy levels are calculated, and in particular the reality of energy spectra, the positive-definiteness of inner products, and the related properties (the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution) are found not to be altered by the noncommutativity.Comment: 15 pages, no figures; v2: clarifications added; v3: 16 pages, 1 figure, clarifications made clearer; v4: 19 pages, the main context is completely rewritten; v5: 25 pages, title slightly changed, clarifications added, the final version to appear in PLOS ON

The Vacuum in Light-Cone Field Theory

This is an overview of the problem of the vacuum in light-cone field theory, stressing its close connection to other puzzles regarding light-cone quantization. I explain the sense in which the light-cone vacuum is ``trivial,'' and describe a way of setting up a quantum field theory on null planes so that it is equivalent to the usual equal-time formulation. This construction is quite helpful in resolving the puzzling aspects of the light-cone formalism. It furthermore allows the extraction of effective Hamiltonians that incorporate vacuum physics, but that act in a Hilbert space in which the vacuum state is simple. The discussion is fairly informal, and focuses mainly on the conceptual issues. [Talk presented at {\sc Orbis Scientiae 1996}, Miami Beach, FL, January 25--28, 1996. To appear in the proceedings.]Comment: 20 pages, RevTeX, 4 Postscript figures. Minor typos correcte

Recent advances in electronic structure theory and their influence on the accuracy of ab initio potential energy surfaces

Recent advances in electronic structure theory and the availability of high speed vector processors have substantially increased the accuracy of ab initio potential energy surfaces. The recently developed atomic natural orbital approach for basis set contraction has reduced both the basis set incompleteness and superposition errors in molecular calculations. Furthermore, full CI calculations can often be used to calibrate a CASSCF/MRCI approach that quantitatively accounts for the valence correlation energy. These computational advances also provide a vehicle for systematically improving the calculations and for estimating the residual error in the calculations. Calculations on selected diatomic and triatomic systems will be used to illustrate the accuracy that currently can be achieved for molecular systems. In particular, the F+H2 yields HF+H potential energy hypersurface is used to illustrate the impact of these computational advances on the calculation of potential energy surfaces

Full quantum distribution of contrast in interference experiments between interacting one dimensional Bose liquids

We analyze interference experiments for a pair of independent one dimensional condensates of interacting bosonic atoms at zero temperature. We show that the distribution function of fringe amplitudes contains non-trivial information about non-local correlations within individual condensates and can be calculated explicitly using methods of conformal field theory. We point out interesting relations between these distribution functions, the partition function for a quantum impurity in a one-dimensional Luttinger liquid, and transfer matrices of conformal field theories. We demonstrate the connection between interference experiments in cold atoms and a variety of statistical models ranging from stochastic growth models to two dimensional quantum gravity. Such connection can be used to design a quantum simulator of unusual two-dimensional models described by nonunitary conformal field theories with negative central charges.Comment: 9 pages, 5 figures; Accepted for publication in Nature Physic

New evidence for a massive black hole at the centre of the quiescent galaxy M32

Massive black holes are thought to reside at the centres of many galaxies, where they power quasars and active galactic nuclei. But most galaxies are quiescent, indicating that any central massive black hole present will be starved of fuel and therefore detectable only through its gravitational influence on the motions of the surrounding stars. M32 is a nearby, quiescent elliptical galaxy in which the presence of a black hole has been suspected; however, the limited resolution of the observational data and the restricted classes of models used to interpret this data have made it difficult to rule out alternative explanations, such as models with an anisotropic stellar velocity distribution and no dark mass or models with a central concentration of dark objects (for example, stellar remnants or brown dwarfs). Here we present high-resolution optical HST spectra of M32, which show that the stellar velocities near the centre of this galaxy exceed those inferred from previous ground-based observations. We use a range of general dynamical models to determine a central dark mass concentration of (3.4 +/- 1.6) x 10^6 solar masses, contained within a region only 0.3 pc across. This leaves a massive black hole as the most plausible explanation of the data, thereby strengthening the view that such black holes exist even in quiescent galaxies.Comment: 8 pages, LaTeX, 3 figures; mpeg animation of the stellar motions in M32 available at http://oposite.stsci.edu/pubinfo/Anim.htm

Fundamental Strings, Holography, and Nonlinear Superconformal Algebras

We discuss aspects of holography in the AdS_3 \times S^p near string geometry of a collection of straight fundamental heterotic strings. We use anomalies and symmetries to determine general features of the dual CFT. The symmetries suggest the appearance of nonlinear superconformal algebras, and we show how these arise in the framework of holographic renormalization methods. The nonlinear algebras imply intricate formulas for the central charge, and we show that in the bulk these correspond to an infinite series of quantum gravity corrections. We also makes some comments on the worldsheet sigma-model for strings on AdS_3\times S^2, which is the holographic dual geometry of parallel heterotic strings in five dimensions.Comment: 25 page

Creatine Protects against Excitoxicity in an In Vitro Model of Neurodegeneration

Creatine has been shown to be neuroprotective in aging, neurodegenerative conditions and brain injury. As a common molecular background, oxidative stress and disturbed cellular energy homeostasis are key aspects in these conditions. Moreover, in a recent report we could demonstrate a life-enhancing and health-promoting potential of creatine in rodents, mainly due to its neuroprotective action. In order to investigate the underlying pharmacology mediating these mainly neuroprotective properties of creatine, cultured primary embryonal hippocampal and cortical cells were challenged with glutamate or H2O2. In good agreement with our in vivo data, creatine mediated a direct effect on the bioenergetic balance, leading to an enhanced cellular energy charge, thereby acting as a neuroprotectant. Moreover, creatine effectively antagonized the H2O2-induced ATP depletion and the excitotoxic response towards glutamate, while not directly acting as an antioxidant. Additionally, creatine mediated a direct inhibitory action on the NMDA receptor-mediated calcium response, which initiates the excitotoxic cascade. Even excessive concentrations of creatine had no neurotoxic effects, so that high-dose creatine supplementation as a health-promoting agent in specific pathological situations or as a primary prophylactic compound in risk populations seems feasible. In conclusion, we were able to demonstrate that the protective potential of creatine was primarily mediated by its impact on cellular energy metabolism and NMDA receptor function, along with reduced glutamate spillover, oxidative stress and subsequent excitotoxicity

Biopsy confirmation of metastatic sites in breast cancer patients:clinical impact and future perspectives

Determination of hormone receptor (estrogen receptor and progesterone receptor) and human epidermal growth factor receptor 2 status in the primary tumor is clinically relevant to define breast cancer subtypes, clinical outcome,and the choice of therapy. Retrospective and prospective studies suggest that there is substantial discordance in receptor status between primary and recurrent breast cancer. Despite this evidence and current recommendations,the acquisition of tissue from metastatic deposits is not routine practice. As a consequence, therapeutic decisions for treatment in the metastatic setting are based on the features of the primary tumor. Reasons for this attitude include the invasiveness of the procedure and the unreliable outcome of biopsy, in particular for biopsies of lesions at complex visceral sites. Improvements in interventional radiology techniques mean that most metastatic sites are now accessible by minimally invasive methods, including surgery. In our opinion, since biopsies are diagnostic and changes in biological features between the primary and secondary tumors can occur, the routine biopsy of metastatic disease needs to be performed. In this review, we discuss the rationale for biopsy of suspected breast cancer metastases, review issues and caveats surrounding discordance of biomarker status between primary and metastatic tumors, and provide insights for deciding when to perform biopsy of suspected metastases and which one (s) to biopsy. We also speculate on the future translational implications for biopsy of suspected metastatic lesions in the context of clinical trials and the establishment of bio-banks of biopsy material taken from metastatic sites. We believe that such bio-banks will be important for exploring mechanisms of metastasis. In the future,advances in targeted therapy will depend on the availability of metastatic tissue