Geometry of mixed states and degeneracy structure of geometric phases for multi-level quantum systems. A unitary group approach

We analyze the geometric aspects of unitary evolution of general states for a multilevel quantum system by exploiting the structure of coadjoint orbits in the unitary group Lie algebra. Using the same method in the case of SU(3) we study the effect of degeneracies on geometric phases for three-level systems. This is shown to lead to a highly nontrivial generalization of the result for two-level systems in which degeneracy results in a "monopole" structure in parameter space. The rich structures that arise are related to the geometry of adjoint orbits in SU(3). The limiting case of a two-level degeneracy in a three-level system is shown to lead to the known monopole structure.Comment: Latex, 27 p

Patelloplasty with and without circumpatellar denervation in reducing anterior knee pain in primary total knee arthroplasty: a comparative prospective study

Background: Anterior knee pain (AKP) following total knee arthroplasty (TKA) ­­­­­­is one of the complication which cause dissatisfaction in patients. Incidence estimated to be 4-49%. The aim of our study is to know the efficacy of patelloplasty with circumpatellar denervation with diathermy in reducing AKP in primary TKA.Methods: A total of 130 unilateral TKAs’ are divided into 2 groups. Group I (control) includes 65 patients in which only patelloplasty was done. Group II (intervention) includes 65 patients in which both patelloplasty and circumpatellar denervation with diathermy was done and analysed. Mean follow up period was 18 months. Patients were assessed both preoperatively and postoperatively at final follow up.Results: The overall incidence of AKP at follow up (18 months) was 16.9%, with 7.7% in the intervention group and 26.1% in the control group (p<0.05).  Western Ontario and McMaster Universities osteoarthritis index scores were significantly  better in intervention group when compared to control group (28.71±3.948 vs 31.40±3.860). Better results were also found in knee society scores for intervention group compared to control group (166.57±7.941 vs 161.23±11.219); Feller patellar score of  intervention group was significantly better when compared to control group (23.28±2.546 vs 20.69±3.729); the range of knee flexion was similar in both the groups (94.62±12.6 vs 93.54±10.7). In terms of pain referred by the patient at 72 hrs postoperatively, there was statistically significant difference observed according to visual analogue scale.Conclusions: There is statistically significant difference with respect to AKP in patients who have undergone patelloplasty with circumpatellar denervation using diathermy compared with patelloplasty alone.

States of physical systems in classical and quantum mechanics

We discuss the descriptions of states of physical systems in classical and quantum mechanics. We show that while it is possible to evolve a terminology common to both, the differences in the underlying mathematical structures lead to significant points of departure between the two descriptions both at mathematical and conceptual levels. We analyse the state spaces associated with physical systems described by two and three dimensional complex Hilbert spaces in considerable detail to illustrate how subtle this question can in general be. We highlight the role the Bargmann invariants play in the passage from the Hilbert space to the ray space, the space of states in quantum mechanics, and also in the context of Wigner's theorem on symmetries in quantum mechanics where they originally appeared

Squeezing of a coupled state of two spinors

The notion of spin squeezing involves reduction in the uncertainty of a component of the spin vector below a certain limit. This aspect has been studied earlier for pure and mixed states of definite spin. In this paper, this study has been extended to coupled spin states which do not possess sharp spin value. A general squeezing criterion has been obtained by requiring that a direct product state for two spinors is not squeezed. The squeezing aspect of entangled states is studied in relation to their spin- spin correlations.Comment: Typeset in LaTeX 2e using the style iopart, packages iopams,times,amssymb,graphicx; 17 pages, 5 eps figure file

Factors determining the range of motion in primary total knee arthroplasty

Background: Total knee arthroplasty (TKA) ­­­­­­is one of the most successful surgical procedure with over 90% survival rate at 10 to 15 years. It provides a stable, pain free range of motion (ROM) for day to day activities. The aim of this study is to evaluate various factors determining ROM after TKA.Methods: 348 patients with 390 knees treated with TKA using cruciate retaining (CR) and posterior stabilized (PS) prosthesis were included and analysed. Mean follow up period was 18 months. Patients were analysed for factors like age, sex, diagnosis, body mass index (BMI), pre-operative exercises, ROM, deformity, posterior femoral condylar offset (PFCO), posterior tibial slope (PTS), post-operative rehabilitation and implant design (CR vs PS). Statistical analysis of above factors on knee ROM was done. Patients were assessed pre-operatively, at 6 weeks, 3, 6, 12 and 18 months post-operatively.Results: Age and sex did not affect the final ROM. The mean knee ROM improved from 86.87° to 96.95°. Factors like BMI, deformity had negative correlation and Pre-operative diagnosis, exercises, knee scores, good preoperative ROM, PFCO, PTS had positive correlation on ROM.Conclusions: Pre-operative exercises, diagnosis, ROM, deformity, BMI, PFCO and PTS were important factors which influence ROM in TKA. Patient selection and preoperative counselling are important for good clinical outcome

Symmetries and conservation laws in classical and quantum mechanics. 1. Classical mechanics

We describe the connection between continuous symmetries and conservation laws in classical mechanics. This is done at successively more sophisticated levels, bringing out important features at each level: the Newtonian, the Euler-Lagrange, and the Hamiltonian phase-space forms of mechanics. The role of the Action Principle is emphasised, and many examples are given

CONTROLLING AND ONLINE VIDEO MONITORING OF LABORATORIES USING PHOTOVOLTAIC SYSTEM

With the involvement of graduating engineering students, a remotely accessible solar energy laboratory has been developed, in order to simulate a small photovoltaic system. The laboratory includes two photovoltaic cells, a charge controller, batteries and a dummy load. A Raspberry PI microcontroller enables to control the different inputs, measures the voltages and the currents in the circuit and provides a remote access through the web. The lab intends to be a prototype of remote lab for the University, in terms of realization costs, communication protocols and software interface. It will be used by graduate students in the Electrical Engineering courses, enabling them to perform some experiments at distance