Extending Romanovski polynomials in quantum mechanics

Some extensions of the (third-class) Romanovski polynomials (also called Romanovski/pseudo-Jacobi polynomials), which appear in bound-state wavefunctions of rationally-extended Scarf II and Rosen-Morse I potentials, are considered. For the former potentials, the generalized polynomials satisfy a finite orthogonality relation, while for the latter an infinite set of relations among polynomials with degree-dependent parameters is obtained. Both types of relations are counterparts of those known for conventional polynomials. In the absence of any direct information on the zeros of the Romanovski polynomials present in denominators, the regularity of the constructed potentials is checked by taking advantage of the disconjugacy properties of second-order differential equations of Schr\"odinger type. It is also shown that on going from Scarf I to Scarf II or from Rosen-Morse II to Rosen-Morse I potentials, the variety of rational extensions is narrowed down from types I, II, and III to type III only.Comment: 25 pages, no figure, small changes, 3 additional references, published versio

Readmissions with multidrug-resistant infection in patients with prior multidrug resistant infection

OBJECTIVETo determine incidence of and risk factors for readmissions with multidrug-resistant organism (MDRO) infections among patients with previous MDRO infection.DESIGNRetrospective cohort of patients admitted between January 1, 2006, and October 1, 2015.SETTINGBarnes-Jewish Hospital, a 1,250-bed academic tertiary referral center in St Louis, Missouri.METHODSWe identified patients with MDROs obtained from the bloodstream, bronchoalveolar lavage (BAL)/bronchial wash, or other sterile sites. Centers for Disease Control and prevention (CDC) and European CDC definitions of MDROs were utilized. All readmissions ≤1 year from discharge from the index MDRO hospitalization were evaluated for bloodstream, BAL/bronchial wash, or other sterile site cultures positive for the same or different MDROs.RESULTSIn total, 4,429 unique patients had a positive culture for an MDRO; 3,453 of these (78.0%) survived the index hospitalization. Moreover, 2,127 patients (61.6%) were readmitted ≥1 time within a year, for a total of 5,849 readmissions. Furthermore, 512 patients (24.1%) had the same or a different MDRO isolated from blood, BAL/bronchial wash, or another sterile site during a readmission. Bone marrow transplant, end-stage renal disease, lymphoma, methicillin-resistant Staphylococcus aureus, or carbapenem-resistant Pseudomonas aeruginosa during index hospitalization were factors associated with increased risk of having an MDRO isolated during a readmission. MDROs isolated during readmissions were in the same class of MDRO as the index hospitalization 9%–78% of the time, with variation by index pathogen.CONCLUSIONSReadmissions among patients with MDRO infections are frequent. Various patient and organism factors predispose to readmission. When readmitted patients had an MDRO, it was often a pathogen in the same class as that isolated during the index admission, with the exception of Acinetobacter (~9%).Infect Control Hosp Epidemiol 2018;39:12–19</jats:sec

Fluctuation theorems for a quantum channel

We establish the general framework of quantum fluctuation theorems by finding the symmetry between the forward and backward transitions of any given quantum channel. The Petz recovery map is adopted as the reverse quantum channel, and the notion of entropy production in thermodynamics is extended to the quantum regime. Our result shows that the fluctuation theorems, which are normally considered for thermodynamic processes, can be a powerful tool to study the detailed statistics of quantum systems as well as the effect of coherence transfer in an arbitrary non-equilibrium quantum process. We introduce a complex-valued entropy production to fully understand the relation between the forward and backward processes through the quantum channel. We find the physical meaning of the imaginary part of entropy production to witness the broken symmetry of the quantum channel. We also show that the imaginary part plays a crucial role in deriving the second law from the quantum fluctuation theorem. The dissipation and fluctuation of various quantum resources including quantum free energy, asymmetry and entanglement can be coherently understood in our unified framework. Our fluctuation theorem can be applied to a wide range of physical systems and dynamics to query the reversibility of a quantum state for the given quantum processing channel involving coherence and entanglement