Symmetry Duality: Exploring Exotic Oscillators And Dissipative Dynamics Through The Glass Of Newton-Hooke

Motivated by the symmetry in the non-relativistic limit of anti-de Sitter geometry, we employ planar dynamical models featuring exotic (deformed) harmonic oscillators, presented through direct and indirect Lagrangian representations. The latter introduces Bateman dissipative oscillator system. Analyzing these dynamic systems with a first-order Lagrangian scheme, our phase-space-based approach utilizes the moment map components to reveal the underlying symmetry algebra. This obtained algebra, interpreted as an extended version of Newton-Hooke (NH) cosmological symmetry algebras, has the potential to cast an augmented non-relativistic shadow over the expanding universe, offering an insightful perspective on extended NH spacetime in 2+1 dimensions through our dynamical realizations

Low frequency gravitational waves emerge Berry phase

The detection of low frequency gravitational waves (LFGWs) astronomy has marked an advent of new era in the domain of astrophysics and general relativity. Using the framework of interaction between GWs and a point two-particles like detector, within linearized gravity approach, we propose a toy detector model whose quantum state is being investigated at a low-frequency of GWs. The detector is in simultaneous interaction with GWs and an external time-dependent (tuneable) two-dimensional harmonic potential. We observe that the interaction with low frequency GWs naturally provides adiabatic approximation in the calculation, and thereby can lead to a quantal geometric phase in the quantum states of the detector. Moreover this can be controlled by tuning the frequency of the external harmonic potential trap. We argue that such geometric phase detection may serve as a manifestation of the footprint of GWs. More importantly, our theoretical model may be capable of providing a layout for the detection of very small frequency GWs through Berry phase.Comment: Revised version, title changed, to appear in Phys. Rev.

Particle Dynamics and Lie-algebraic type of Non-commutativity of space-time

In this paper, we present the results of our investigation relating particle dynamics and non-commutativity of space-time by using Dirac's constraint analysis. In this study, we re-parameterise the time $t=t(\tau)$ along with $x=x(\tau)$ and treat both as configuration space variables. Here, $\tau$ is a monotonic increasing parameter and the system evolves with this parameter. After constraint analysis, we find the deformed Dirac brackets similar to the $\kappa$-deformed space-time and also, get the deformed Hamilton's equations of motion. Moreover, we study the effect of non-commutativity on the generators of Galilean group and Poincare group and find undeformed form of the algebra. Also, we work on the extended space analysis in the Lagrangian formalism. We find the primary as well as the secondary constraints. Strikingly on calculating the Dirac brackets among the phase space variables, we obtain the classical version of $\kappa$-Minkowski algebra.Comment: 15 page

Our Trysts with `Bal' and Noncommutative Geometry

This contributory article begins with our fond and sincere reminiscences about our beloved Prof. A.P. Balachandran. In the main part, we discuss our recent formulation of quantum mechanics on (1+1)D noncommutative space-time using Hilbert-Schmidt operators. As an application, we demonstrate how geometrical phase in a system of time-dependent forced harmonic oscillator living in the Moyal space-time can emerge.Comment: In Honor of A.P.Balachandran on the Occasion of His 85th Birthday (To be published in the Festschrift volume: Particles, Fields and Topology by World Scientific, Singapore

Extraction, Characterization and Pharmacological Evaluation of Aegle marmelos Leaves

In the present day, antibiotic drugs are gradually becoming obsolete due to the development of antimicrobial resistance. As a result, the scientific community is in search of new antibiotic drugs which can be safely administered to the patents. Natural products are generally known for their nontoxic nature and many of them are known to produce a variety of pharmacological activities. The aim of this work is to extract the leaves of Aegle marmelos, phytochemical characterization of the extract, identification of phytoconstituents by thin layer chromatography, ATR-FTIR Spectroscopy of extract and evaluation of its antimicrobial activity. Extraction of the leaves of Aegle marmelos has been conducted using a Soxhlet apparatus. About 10.32% yield of extract was obtained. Phytochemical screening of the ethanolic leaf extract by standard methods showed the presence of secondary metabolites such as alkaloids, carbohydrates, phenolic compounds, flavonoids, saponins and triterpenoids which were confirmed by TLC. ATR-FTIR Spectroscopic study was conducted to determine the type of functional groups present in extract. The ethanolic leaf extract also produced antibacterial activity against gram positive bacteria Staphylococcus aureus and gram-negative bacteria Escherichia coli and zone of inhibition was 14 mm and 16 mm respectively when compared to standard antibiotic tetracycline. From this research it can be inferred that ethanolic leaf extract of Aegle marmelos has antimicrobial activity because of the presence of secondary metabolites in it. Further investigation will hereby be conducted in future regarding the route of administration of the extract and the type of dosage form. &nbsp

Development of Derivatives of 3, 3′-Diindolylmethane as Potent Leishmania donovani Bi-Subunit Topoisomerase IB Poisons

Background: The development of 3, 39-diindolyl methane (DIM) resistant parasite Leishmania donovani (LdDR50) by adaptation with increasing concentrations of the drug generates random mutations in the large and small subunits of heterodimeric DNA topoisomerase I of Leishmania (LdTOP1LS). Mutation of large subunit of LdTOP1LS at F270L is responsible for resistance to DIM up to 50 mM concentration. Methodology/Principal Findings: In search of compounds that inhibit the growth of the DIM resistant parasite and inhibit the catalytic activity of mutated topoisomerase I (F270L), we have prepared three derivatives of DIM namely DPDIM (2,29diphenyl 3,39-diindolyl methane), DMDIM (2,29-dimethyl 3,39-diindolyl methane) and DMODIM (5,59-dimethoxy 3,39diindolyl methane) from parent compound DIM. All the compounds inhibit the growth of DIM resistant parasites, induce DNA fragmentation and stabilize topo1-DNA cleavable complex with the wild type and mutant enzyme. Conclusion: The results suggest that the three derivatives of DIM can act as promising lead molecules for the generation of new anti-leishmanial agents

Insights into the mechanism of abscisic acid-induced 2, 4-D tolerance in maize (Zea mays L.) seedlings: Study on the regulation of osmolytes, fluorescence, photosynthetic carbon reactions, and antioxidant metabolism

In this experiment, maize plants were subjected to different concentrations (0, 50, 100, and 250 µM) of the herbicide 2, 4-dichlorophenoxyacetic acid (2, 4-D), with some groups primed with abscisic acid (ABA) and others not. Initial observations showed that after five days of incubation, seedlings exposed to the highest concentration of 2, 4-D exhibited stunted growth and a reduction in chlorophyll accumulation. Key parameters such as relative water content, relative growth rate, and net assimilation rate decreased (by 25%, 39%, and 35% respectively) under this condition. However, these parameters partially recovered with ABA priming, showing average improvements (8%, 14%, and 16%). Recovery in tissue hydration was also noted, coinciding with increased concentrations of proline (Pro) and glycine betaine (GB), and a decrease in the Na+/K+ ratio. When exposed to the highest concentration of the herbicide, fluorescence activity was reduced, but this too was reversed with ABA treatment. A notable inhibition of photosynthesis occurred, particularly at the decarboxylation reactions involving NADP-malic enzyme and phosphoenolpyruvate carboxylase, affecting total sugar concentrations. Under the influence of 2, 4-D, there was a significant increase in reactive oxygen species, such as superoxide (35%) and hydrogen peroxide (78%), but these levels significantly diminished with ABA priming. Abscisic acid priming also mitigated oxidative stress, evidenced by a reduction in malondialdehyde (by 10%) and carbonyl content (by 11%), along with lower electrolyte leakage. The regulation of oxidative pathways through ABA priming was apparent as the plants showed increased activity of enzymes such as peroxidases, catalases, and those involved in glutathione metabolism, including glutathione reductase and glutathione S-transferase. The study also discussed how ABA metabolism regulates sensitivity to 2, 4-D and highlighted certain parameters for selecting redox homeostasis against herbicidal toxicity

Symmetries of κ-Minkowski space-time: a possibility of exotic momentum space geometry?

Abstract The quest for a quantum gravity phenomenology has inspired a quantum notion of space-time, which motivates us to study the fate of the relativistic symmetries of a particular model of quantum space-time, as well as its intimate connection with the plausible emergent curved “physical momentum space”. We here focus on the problem of Poincare symmetry of κ-Minkowski type non-commutative (quantum) space-time, where the Poincare algebra, on its own, remains undeformed, but in order to preserve the structure of the space-time non-commutative (NC) algebra, the actions of the algebra generators on the operator-valued space-time manifold must be enveloping algebra valued that lives in entire phase space i.e. the cotangent bundle on the space-time manifold (at classical level). Further, we constructed a model for a spin-less relativistic massive particle enjoying the deformed Poincare symmetry, using the first order form of geometric Lagrangian, that satisfies a new deformed dispersion relation and explored a feasible regime of a future Quantum Gravity theory in which the momentum space becomes curved. In this scenario there is only a mass scale (Planck mass m p ), but no length scale. Finally, we relate the deformed mass shell to the geodesic distance in this curved momentum space, where the mass of the particle gets renormalized as a result of noncommutativity. We show, that under some circumstances, the Planck mass provides an upper bound for the observed renormalized mass