This work presents an elastic model to study the interplay between entropic and energetic networks in confined hydrogel particles. We consider a quasi-two-dimensional system composed of spherical hydrogel beads confined in a circular container, where particle growth occurs through hydration. Based on experimental observations, an elastic potential is introduced to model interactions between particles and between particles and the confining wall. Computational simulations based on energy minimization identify the lowest-energy configurations adopted during growth. Analysis of the resulting energy landscapes reveals emergent self-organization, adaptability, and cooperativity arising from the competition between entropic and energetic networks.
A theoretical framework is developed for the electron miniband structure in one-dimensional chains of spherical quantum dots subjected to weak positional disorder. Within the tight-binding approximation and effectivemedium approach, stochastic fluctuations of the inter-dot spacing are mapped onto the renormalization of key Hamiltonian parameters: the hopping integral B, overlap integral Q, and on-site energy shift M. Analytical expressions for these parameters are derived by performing an ensemble average over a narrow Gaussian distribution of positional deviations (σ ≪ a). The resulting generalized dispersion relation reveals that weak positional disorder broadens the minibands. For typical fabrication fluctuations σ = 0.1a, the miniband width increases by 8-12% , depending on the mean inter-dot distance a. This sensitivity to disorder decreases rapidly with increasing lattice period due to the exponential decay of electron wave functions. In this weak-disorder regime, the Anderson localization lengh significantly exceeds the lattice constant, meaning states remain delocalized.
We establish a rigorous framework for quantum systems with geometric deformations by constructing a strictly self-adjoint deformed momentum operator through the generalized extended momentum operator (GEMO) formalism. Unlike previous approaches relying on boundary-condition hermiticity, our method ensures intrinsic self-adjointness for both linear (μ(x)=αx) and quadratic (μ(x)=αx 2) deformations within a unified non-Hermitian supersymmetric factorization scheme. This yields exact analytical spectra while revealing hidden su (1, 1) symmetry structures. Crucially, we provide the first complete thermodynamic characterization of such systems by analytically evaluating the partition function via the Euler-Maclaurin approximation. Geometric deformation fundamentally reshapes the density of states ρ(E), producing distinct thermal signatures: a divergent heat capacity peak for linear deformation due to state accumulation near a maximal energy, and a saturation C/kB → 0.6 (below the Dulong-Petit limit) for quadratic deformation. These results establish geometric deformation as a tunable parameter for engineering quantum thermodynamic responses in curved nanostructures.
Herein, the fundamental physical characteristics like structural, electronic, optical parameters of the Ca3PX3 (X = F, Cl, Br, I) materials have been investigated for their potential optoelectronic applications, particularly for solar cells and related devices. To the crystallographic investigations, Ca3PI3 has the most stable configuration among all investigated materials. From the band structure analyses of these materials indicate that all materials have a direct bandgap in the range of 2.0 eV to 3.788 eV, which makes them ideal for light absorption. For the photovoltaic applications, we have analysed first-principles spectroscopic screening limited maximum efficiency (SLME) which confirms that the Ca3PI3 material exhibits the highest solar cell efficiency 29.6% and Ca3PF3 and shows lower efficiency for solar cell suitability 0.6%. Thus, these results demonstrate the real potential and abilities of halide substitution to tune the materials for particular optoelectronic devices.
