Spin systems with dimerized ground states

In view of the numerous examples in the literature it is attempted to outline a theory of Heisenberg spin systems possessing dimerized ground states (``DGS systems") which comprises all known examples. Whereas classical DGS systems can be completely characterized, it was only possible to provide necessary or sufficient conditions for the quantum case. First, for all DGS systems the interaction between the dimers must be balanced in a certain sense. Moreover, one can identify four special classes of DGS systems: (i) Uniform pyramids, (ii) systems close to isolated dimer systems, (iii) classical DGS systems, and (iv), in the case of $s=1/2$, systems of two dimers satisfying four inequalities. Geometrically, the set of all DGS systems may be visualized as a convex cone in the linear space of all exchange constants. Hence one can generate new examples of DGS systems by positive linear combinations of examples from the above four classes.Comment: With corrections of proposition 4 and other minor change

The State-Vector Space for Two-Mode Parabosons and Charged Parabose Coherent States

The structure of the state-vector space for the two-mode parabose system is investigated and a complete set of state-vectors is constructed. The basis vectors are orthonormal in order $p=2$. In order $p=2$, conserved-charge parabose coherent states are constructed and an explicit completeness relation is obtained.Comment: 13 pages, LaTeX file, no figures and no macro

Coherent states for the hydrogen atom

We construct wave packets for the hydrogen atom labelled by the classical action-angle variables with the following properties. i) The time evolution is exactly given by classical evolution of the angle variables. (The angle variable corresponding to the position on the orbit is now non-compact and we do not get exactly the same state after one period. However the gross features do not change. In particular the wave packet remains peaked around the labels.) ii) Resolution of identity using this overcomplete set involves exactly the classical phase space measure. iii) Semi-classical limit is related to Bohr-Sommerfield quantization. iv) They are almost minimum uncertainty wave packets in position and momentum.Comment: 9 pages, 2 figures, minor change in language and journal reference adde

The Heisenberg antiferromagnet on an anisotropic triangular lattice: linear spin-wave theory

We consider the effect of quantum spin fluctuations on the ground state properties of the Heisenberg antiferromagnet on an anisotropic triangular lattice using linear spin-wave theory. This model should describe the magnetic properties of the insulating phase of the kappa-(BEDT-TTF)_2 X family of superconducting molecular crystals. The ground state energy, the staggered magnetization, magnon excitation spectra and spin-wave velocities are computed as a function of the ratio between the second and first neighbours, J2/J1. We find that near J2/J1 = 0.5, i.e., in the region where the classical spin configuration changes from a Neel ordered phase to a spiral phase, the staggered magnetization vanishes, suggesting the possibility of a quantum disordered state. In this region, the quantum correction to the magnetization is large but finite. This is in contrast to the frustrated Heisenberg model on a square lattice, for which the quantum correction diverges logarithmically at the transition from the Neel to the collinear phase. For large J2/J1, the model becomes a set of chains with frustrated interchain coupling. For J2 > 4 J1, the quantum correction to the magnetization, within LSW, becomes comparable to the classical magnetization, suggesting the possibility of a quantum disordered state. We show that, in this regime, quantum fluctuations are much larger than for a set of weakly coupled chains with non-frustated interchain coupling.Comment: 10 pages, RevTeX + epsf, 5 figures Replaced with published version. Comparison to series expansions energies include

Search for binary black hole mergers in the third observing run of Advanced LIGO-Virgo using coherent WaveBurst enhanced with machine learning

In this work, we use the coherent WaveBurst (cWB) pipeline enhanced with machine learning (ML) to search for binary black hole (BBH) mergers in the Advanced LIGO-Virgo strain data from the third observing run. We detect, with equivalent or higher significance, all gravitational-wave (GW) events previously reported by the standard cWB search for BBH mergers in the third GW Transient Catalog. The ML-enhanced cWB search identifies five additional GW candidate events from the catalog that were previously missed by the standard cWB search. Moreover, we identify three marginal candidate events not listed in third GW Transient Catalog. For simulated events distributed uniformly in a fiducial volume, we improve the sensitive hypervolume with respect to the standard cWB search by approximately 28% and 34% for the stellar-mass and intermediate mass black hole binary mergers respectively, detected with a false-alarm rate less than 1/100 yr-1. We show the robustness of the ML-enhanced search for detection of generic BBH signals by reporting increased sensitivity to the spin-precessing and eccentric BBH events as compared to the standard cWB search. Furthermore, we compare the improvement of the ML-enhanced cWB search for different detector networks

Coherent states for the hydrogen atom: discrete and continuous spectra

We construct the systems of generalised coherent states for the discrete and continuous spectra of the hydrogen atom. These systems are expressed in elementary functions and are invariant under the $SO(3, 2)$ (discrete spectrum) and $SO(4, 1)$ (continuous spectrum) subgroups of the dynamical symmetry group $SO(4, 2)$ of the hydrogen atom. Both systems of coherent states are particular cases of the kernel of integral operator which interwines irreducible representations of the $SO(4, 2)$ group.Comment: 15 pages, LATEX, minor sign corrections, to appear in J.Phys.

Reassessing candidate eccentric binary black holes: Results with a model including higher-order modes

The detection of eccentricity from a gravitational wave signal is expected to help distinguish between formation channels for a given binary. In this study, we reassess all previously-reported binary black holes with previous claims of possible eccentricity as well as a few binaries with more interesting source parameters, for the first time using a model (TEOBResumSGeneral) which accounts for the full eccentricity range possible and incorporates higher-order gravitational emission critical to model emission from highly eccentric orbits. We estimate the eccentricity of these five events. For the first time, we present marginal evidence of eccentricity for one of the events: GW190929. Contrary to previous work with different settings, we do not find evidence supporting eccentric orbits for the same systems. We find the incorporation of eccentricity in our analyses dramatically shifts the posterior in multiple parameters for several events, features could negatively impact other analyses

Correlation search for coherent pion emission in heavy ion collisions

The methods allowing to extract the coherent component of pion emission conditioned by the formation of a quasi-classical pion source in heavy ion collisions are suggested. They exploit a nontrivial modification of the quantum statistical and final state interaction effects on the correlation functions of like and unlike pions in the presence of the coherent radiation. The extraction of the coherent pion spectrum from pi+pi-, pi+pi+ and pi-pi- correlation functions and single--pion spectra is discussed in detail for large expanding systems produced in ultra-relativistic heavy ion collisions.Comment: 21 pages, 3 eps figures, ReVTeX, corrected submission abstract. Version published in PRC 65 (2002) 064904. Added is a detailed explanation of the differences between pure coherent states and charge constrained coherent states in the case of a simple example model. The expressions for two-particle spectra taking into account both the final state interaction and the coherent component of pion emission are derived in a more general and transparent wa

Ownership identity, strategy and performance:business group affiliates versus independent firms in India

We consider whether the impact of entrepreneurial orientation on business performance is moderated by the company affiliation with business groups. Within business groups, we explore the trade-off between inter-firm insurance that enables risk-taking, and inefficient resource allocation. Risk-taking in group affiliated firms leads to higher performance, compared to independent firms, but the impact of proactivity is attenuated. Utilizing Indian data, we show that risk-taking may undermine rather than improve business performance, but this effect is not present in business groups. Proactivity enhances performance, but less so in business groups. Firms can also enhance performance by technological knowledge acquisition, but these effects are not significantly different for various ownership categories