Disentangling phase transitions and critical points in the proton-neutron interacting boson model by catastrophe theory

We introduce the basic concepts of catastrophe theory needed to derive analytically the phase diagram of the proton-neutron interacting boson model (IBM-2). Previous studies [1,2,3] were based on numerical solutions. We here explain the whole IBM-2 phase diagram including the precise order of the phase transitions in terms of the cusp catastrophe.Comment: To be published in Physics Letters

Integrability and Quantum Phase Transitions in Interacting Boson Models

The exact solution of the boson pairing hamiltonian given by Richardson in the sixties is used to study the phenomena of level crossings and quantum phase transitions in the integrable regions of the sd and sdg interacting boson models.Comment: 5 pages, 5 fig. Erice Conferenc

Quantum Phase Transitions in the Interacting Boson Model: Integrability, level repulsion and level crossing

We study the quantum phase transition mechanisms that arise in the Interacting Boson Model. We show that the second-order nature of the phase transition from U(5) to O(6) may be attributed to quantum integrability, whereas all the first-order phase transitions of the model are due to level repulsion with one singular point of level crossing. We propose a model Hamiltonian with a true first-order phase transition for finite systems due to level crossings.Comment: Accepted in PR

Excited-state quantum phase transitions in a two-fluid Lipkin model

Background: Composed systems have became of great interest in the framework of the ground state quantum phase transitions (QPTs) and many of their properties have been studied in detail. However, in these systems the study of the so called excited-state quantum phase transitions (ESQPTs) have not received so much attention. Purpose: A quantum analysis of the ESQPTs in the two-fluid Lipkin model is presented in this work. The study is performed through the Hamiltonian diagonalization for selected values of the control parameters in order to cover the most interesting regions of the system phase diagram. [Method:] A Hamiltonian that resembles the consistent-Q Hamiltonian of the interacting boson model (IBM) is diagonalized for selected values of the parameters and properties such as the density of states, the Peres lattices, the nearest-neighbor spacing distribution, and the participation ratio are analyzed. Results: An overview of the spectrum of the two-fluid Lipkin model for selected positions in the phase diagram has been obtained. The location of the excited-state quantum phase transition can be easily singled out with the Peres lattice, with the nearest-neighbor spacing distribution, with Poincar\'e sections or with the participation ratio. Conclusions: This study completes the analysis of QPTs for the two-fluid Lipkin model, extending the previous study to excited states. The ESQPT signatures in composed systems behave in the same way as in single ones, although the evidences of their presence can be sometimes blurred. The Peres lattice turns out to be a convenient tool to look into the position of the ESQPT and to define the concept of phase in the excited states realm

Effect of Contrast-Enhanced Echocardiograms on the Prognosis of Infective Endocarditis

Objective - Infective endocarditis (IE) is an infectious disease of the cardiac valves where bacteria colonize the valves; typically, via the formation of vegetations. Recent research has shown that the microbubbles in a contrast-enhanced ultrasound (CEUS) examination can move and dislodge bacterial vegetations in vitro. This study investigated whether CEUS resulted in faster resolution of IE in vivo by dislodging the vegetations. Methods - This IRB approved retrospective study reviewed 36 patients who were diagnosed with IE via echocardiography. Data was sourced from patients within the Jefferson University Hospital’s Cardiology EMR system by searching for contrast and vegetation from January 1st, 2013 – January 1st, 2018. Fifteen patients were not given contrast, whereas 21 patients were given contrast via agitated saline (n=16) or an ultrasound contrast agent (n=5). All patients received an echocardiogram after blood cultures confirmed an infection, but before resolution of infection (defined by negative blood cultures). A student’s t-test was used for analyses. Results - The study population was heterogeneous in terms of sex (67.5% male) and race (70% Caucasian, 25% African American, and 5% Asian), with an average age of 51±20 years, and an average BMI of 29.65±7.43 in the contrast group and 27.67±3.16 in the non-contrast group (p=0.37). Following ultrasound, no patients had documented stroke, pulmonary embolism, or systemic blood clot, which physicians could have attributed to a thrombus resulting from dislodging of bacterial vegetation. Overall, blood cultures did not clear faster in patients receiving CEUS compared to those undergoing standard echocardiography, (2.63±2.69 days vs. 1.34 ±1.11 days, p=0.09). CEUS also did not shorten the admission length in patients with IE, (16.9±7.7 days vs. 19.9±12.1 days; p=0.36). Conclusion - Based on this limited sample size, patients who underwent CEUS did not have a different prognosis when compared to patients who received a non-contrast echocardiogram

Phase diagram of an extended Agassi model

Background: The Agassi model is an extension of the Lipkin-Meshkov-Glick model that incorporates the pairing interaction. It is a schematic model that describes the interplay between particle-hole and pair correlations. It was proposed in the 1960's by D. Agassi as a model to simulate the properties of the quadrupole plus pairing model. Purpose: The aim of this work is to extend a previous study by Davis and Heiss generalizing the Agassi model and analyze in detail the phase diagram of the model as well as the different regions with coexistence of several phases. Method: We solve the model Hamiltonian through the Hartree-Fock-Bogoliubov (HFB) approximation, introducing two variational parameters that play the role of order parameters. We also compare the HFB calculations with the exact ones. Results: We obtain the phase diagram of the model and classify the order of the different quantum phase transitions appearing in the diagram. The phase diagram presents broad regions where several phases, up to three, coexist. Moreover, there is also a line and a point where four and five phases are degenerated, respectively. Conclusions: The phase diagram of the extended Agassi model presents a rich variety of phases. Phase coexistence is present in extended areas of the parameter space. The model could be an important tool for benchmarking novel many-body approximations.Comment: Accepted for publication in PR

An extended Agassi model: algebraic structure, phase diagram, and large size limit

The Agassi model is a schematic two-level model that involves pairing and monopole-monopole interactions. It is, therefore, an extension of the well known Lipkin-Meshkov-Glick (LMG) model. In this paper we review the algebraic formulation of an extension of the Agassi model as well as its bosonic realization through the Schwinger representation. Moreover, a mean-field approximation for the model is presented and its phase diagram discussed. Finally, a $1/j$ analysis, with $j$ proportional to the degeneracy of each level, is worked out to obtain the thermodynamic limit of the ground state energy and some order parameters from the exact Hamiltonian diagonalization for finite$-j$.Comment: Accepted in Physica Scripta. Focus on SSNET 201