Aghorekamini Prakashchandra Mahavidyalaya

A two dimensional classical ferromagneticXYmodel with its bound vortex-antivortex dominated quasi long range ordered phase at low temperatures is a long standing as well as well studied problem of interest in the field of condensed matter. We conduct a detailed Monte Carlo study of such model in a square lattice with rather unexplored extensions where additional anisotropic exchange coupling and Dzyaloshinskii-Moriya interactions (DMI) together affect the Kosterlitz-Thouless transition in presence/absence of symmetry breaking fields. Without DMI, the exchange term promotes collinear (ferromagnetic) order, whereas the DMI term induces spin cantings. By tuning anisotropy upto Ising limit, we document energy, specific-heat, magnetizations as well as helicity modulus and vortex densities for different temperatures and DMI strength. We also compute the 2nd moment of correlation lengths in order to probe the spatial correlation of the spins. Furthermore, the effect ofU(1) symmetry breaking 4-fold and 8-fold symmetrich4andh8fields are explored which shows how the double-peaked specific heat profiles changes in presence of DMI. Overall, our findings append many important updates in the low temperature phases of a topologicalXYferromagnet when additional DMI and isotropy-breaking exchange and/or field terms are considered thereby providing a few practical blueprints for suitably engineering topological spin systems.

We study a two dimensional (2D) Su-Schrieffer-Heeger (SSH) model on a square lattice in presence of domain walls (DW)/vortices or quasi-periodic disorders to investigate the nature of topology and localizations in its quantum states. While in a pure 2D SSH model, zero energy states (ZES) lie within the dispersion continuum and the bound states in continuum are localized at the corners, a continuous distributions of DWs can produce localized ZES along the DW lines or at the DW center depending on the orientations of the DWs. Moreover with such DWs, one can witness nonzero energy in-gap states showing localizations at the edges, along the DWs or at the DW center. For probing disorder effect, we introduce on-site quasiperiodic potentials (QP) in such systems that show the usual tendency of the states to localize. But exotic reentrant localization behavior is also captured for judicious choice of the QP term. We also examine the scenario for different hopping periodicities in the SSH Hamiltonian. Interestingly for anisotropic hopping modulations, the bulk ZES gets exhausted leaving only topological boundary modes at zero energies. The fate of these states in presence of the DWs are also discussed. Our present study with its plethora of exotic outcomes can thus inspire varied applications in the field of topological quantum computations.

Transdermal and mucoadhesive drug delivery systems have emerged as innovative, patient-centric approaches that address many limitations associated with conventional oral and injectable therapies. These advanced delivery platforms offer non-invasive, controlled, and sustained release of therapeutics, thereby improving adherence among populations who struggle with frequent dosing, gastrointestinal side effects, needle phobia, or complex treatment regimens. Transdermal drug delivery systems (TDDS) utilize the skin as a permeation route, enabling steady drug absorption while avoiding first-pass metabolism and minimizing fluctuations in plasma drug concentration. Meanwhile, mucoadhesive delivery systems leverage the adhesive properties of polymers to anchor drugs to mucosal tissues such as buccal, nasal, ocular, and vaginal surfaces allowing rapid onset, improved bioavailability, and reduced dosing frequency. Recent advancements in polymer science, nanotechnology, and permeation-enhancement strategies have further expanded the capabilities of both systems, enabling the delivery of larger molecules, hydrophilic compounds, and drugs with narrow therapeutic windows. As healthcare increasingly prioritizes comfort, convenience, and longterm adherence, transdermal and mucoadhesive formulations offer a transformative opportunity to enhance patient compliance while maintaining therapeutic effectiveness. This paper explores the mechanisms, design considerations, technological innovations, and comparative advantages of these delivery approaches, highlighting their critical role in next-generation drug administration.

Motivated by the unique dispersions close to the two dimensional band crossing in a topologically charged nodal surface semimetal (NSSM) spectrum, we perform theoretical analysis of quantum tunnelling through a junction consisting of such NSSM, an insulator and a s-wave superconductor (acronymed NSSM-I-SC junction). In particular, for excitation energies both more and less than the superconducting gap potential $Δ$ we probe the normal and Andreev conductance for different incident orientations and thereby find the tunnelling electrical conductance through the heterostructure. The present work considers only the thin barrier limit which witness the conductance G to oscillate periodically with frequency $π$ as a function of the barrier strength, both in high and low doping limit. Such periodic behavior is also observed while calculating the thermal conductance $κ$ through the junction. Novelty of this problem is that the behavior of these G or $κ$ with insulator width are, in many respect, different compared to that from a normal metal - insulator - superconductor (NIS) junction on graphene or silicene. The findings can thus motivate experimentalists to culture renewed control over electric or thermal transport on topological materials.

Moksha, the supreme goal of human existence in Indian philosophy, represents the liberation of the soul from the cycle of birth and death (samsara). This paper delves into the concept of Moksha, examining its roots in ancient scriptures, including the Upanishads and Bhagavad Gita. We explore the various paths to achieving Moksha – Jnana (knowledge), Bhakti (devotion), Karma (action), and Raja Yoga (meditation) – and discuss its implications for individual and societal transformation. By analyzing key philosophical perspectives, this article illuminates Moksha's enduring significance as a pursuit of ultimate freedom, guiding seekers toward spiritual awakening and transcendence.