Quantum Phase Transitions and the Extended Coupled Cluster Method

We discuss the application of an extended version of the coupled cluster method to systems exhibiting a quantum phase transition. We use the lattice O(4) non-linear sigma model in (1+1)- and (3+1)-dimensions as an example. We show how simple predictions get modified, leading to the absence of a phase transition in (1+1) dimensions, and strong indications for a phase transition in (3+1) dimensions

The formation of peptide-like molecules on interstellar dust grains

Molecules with an amide functional group resemble peptide bonds, the molecular bridges that connect amino acids, and may thus be relevant in processes that lead to the formation of life. In this study, the solid state formation of some of the smallest amides is investigated in the laboratory. To this end, CH$_{4}$:HNCO ice mixtures at 20 K are irradiated with far-UV photons, where the radiation is used as a tool to produce the radicals required for the formation of the amides. Products are identified and investigated with infrared spectroscopy and temperature programmed desorption mass spectrometry. The laboratory data show that NH$_{2}$CHO, CH$_{3}$NCO, NH$_{2}$C(O)NH$_{2}$, CH$_{3}$C(O)NH$_{2}$ and CH$_{3}$NH$_{2}$ can simultaneously be formed. The NH$_{2}$CO radical is found to be key in the formation of larger amides. In parallel, ALMA observations towards the low-mass protostar IRAS 16293-2422B are analysed in search of CH$_{3}$NHCHO (N-methylformamide) and CH$_{3}$C(O)NH$_{2}$ (acetamide). CH$_{3}$C(O)NH$_{2}$ is tentatively detected towards IRAS 16293-2422B at an abundance comparable with those found towards high-mass sources. The combined laboratory and observational data indicates that NH$_{2}$CHO and CH$_{3}$C(O)NH$_{2}$ are chemically linked and form in the ice mantles of interstellar dust grains. A solid-state reaction network for the formation of these amides is proposed.Comment: Accepted for publication in MNRA

The formation of CO2_2 through consumption of gas-phase CO on vacuum-UV irradiated water ice

[Abridged] Observations of protoplanetary disks suggest that they are depleted in gas-phase CO. It has been posed that gas-phase CO is chemically consumed and converted into less volatile species through gas-grain processes. Observations of interstellar ices reveal a CO$_2$ component within H$_2$O ice suggesting co-formation. The aim of this work is to experimentally verify the interaction of gas-phase CO with solid-state OH radicals above the sublimation temperature of CO. Amorphous solid water (ASW) is deposited at 15 K and followed by vacuum-UV (VUV) irradiation to dissociate H$_2$O and create OH radicals. Gas-phase CO is simultaneously admitted and only adsorbs with a short residence time on the ASW. Products in the solid state are studied with infrared spectroscopy and once released into the gas phase with mass spectrometry. Results show that gas-phase CO is converted into CO$_2$, with an efficiency of 7-27%, when interacting with VUV irradiated ASW. Between 40 and 90 K, CO$_2$ production is constant, above 90 K, O$_2$ production takes over. In the temperature range of 40-60 K, the CO$_2$ remains in the solid state, while at temperatures $\geq$ 70 K the formed CO$_2$ is released into the gas phase. We conclude that gas-phase CO reacts with solid-state OH radicals above its sublimation temperature. This gas-phase CO and solid-state OH radical interaction could explain the observed CO$_2$ embedded in water-rich ices. It may also contribute to the observed lack of gas-phase CO in planet-forming disks, as previously suggested. Our experiments indicate a lower water ice dissociation efficiency than originally adopted in model descriptions of planet-forming disks and molecular clouds. Incorporation of the reduced water ice dissociation and increased binding energy of CO on a water ice surfaces in these models would allow investigation of this gas-grain interaction to its full extend.Comment: Accepted for publication in Astronomy & Astrophysic

The Extended Coupled Cluster Treatment of Correlations in Quantum Magnets

The spin-half XXZ model on the linear chain and the square lattice are examined with the extended coupled cluster method (ECCM) of quantum many-body theory. We are able to describe both the Ising-Heisenberg phase and the XY-Heisenberg phase, starting from known wave functions in the Ising limit and at the phase transition point between the XY-Heisenberg and ferromagnetic phases, respectively, and by systematically incorporating correlations on top of them. The ECCM yields good numerical results via a diagrammatic approach, which makes the numerical implementation of higher-order truncation schemes feasible. In particular, the best non-extrapolated coupled cluster result for the sublattice magnetization is obtained, which indicates the employment of an improved wave function. Furthermore, the ECCM finds the expected qualitatively different behaviours of the linear chain and the square lattice cases.Comment: 22 pages, 3 tables, and 15 figure

Explicitly Covariant Light-Front Dynamics and Relativistic Few-Body Systems

The wave function of a composite system is defined in relativity on a space-time surface. In the explicitly covariant light-front dynamics, reviewed in the present article, the wave functions are defined on the plane \omega \cd x=0, where $\omega$ is an arbitrary four-vector with $\omega^2=0$. The standard non-covariant approach is recovered as a particular case for $\omega = (1,0,0,-1)$. Using the light-front plane is of crucial importance, while the explicit covariance gives strong advantages emphasized through all the review. The properties of the relativistic few-body wave functions are discussed in detail and are illustrated by examples in a solvable model. The three-dimensional graph technique for the calculation of amplitudes in the covariant light-front perturbation theory is presented. The structure of the electromagnetic amplitudes is studied. We investigate the ambiguities which arise in any approximate light-front calculations, and which lead to a non-physical dependence of the electromagnetic amplitude on the orientation of the light-front plane. The elastic and transition form factors free from these ambiguities are found for spin 0, 1/2 and 1 systems. The formalism is applied to the calculation of the relativistic wave functions of two-nucleon systems (deuteron, scattering state), with particular attention to the role of their new components in the deuteron elastic and electrodisintegration form factors and to their connection with meson exchange currents. Straigthforward applications to the pion and nucleon form factors and the $\rho-\pi$ transition are also made.Comment: latex.tar.gz file, 162 pages, 42 figures, to be published in Physics Reports (next issues

The Generalized Gell-Mann--Low Theorem for Relativistic Bound States

The recently established generalized Gell-Mann--Low theorem is applied in lowest perturbative order to bound-state calculations in a simple scalar field theory with cubic couplings. The approach via the generalized Gell-Mann--Low Theorem retains, while being fully relativistic, many of the desirable features of the quantum mechanical approaches to bound states. In particular, no abnormal or unphysical solutions are found in the model under consideration. Both the non-relativistic and one-body limits are straightforward and consistent. The results for the spectrum are compared to those of the Bethe-Salpeter equation (in the ladder approximation) and related equations.Comment: 24 pages, 6 pspicture diagrams, 4 postscript figure