Quasi-exact solvability beyond the SL(2) algebraization

We present evidence to suggest that the study of one dimensional quasi-exactly solvable (QES) models in quantum mechanics should be extended beyond the usual \sla(2) approach. The motivation is twofold: We first show that certain quasi-exactly solvable potentials constructed with the \sla(2) Lie algebraic method allow for a new larger portion of the spectrum to be obtained algebraically. This is done via another algebraization in which the algebraic hamiltonian cannot be expressed as a polynomial in the generators of \sla(2). We then show an example of a new quasi-exactly solvable potential which cannot be obtained within the Lie-algebraic approach.Comment: Submitted to the proceedings of the 2005 Dubna workshop on superintegrabilit

Broadband transverse susceptibility in multiferroic Y-type hexaferrite Ba0.5Sr1.5Zn2Fe12O22

Producción CientíficaNoncollinear spin systems with magnetically induced ferroelectricity from changes in spiral magnetic ordering have attracted significant interest in recent research due to their remarkable magnetoelectric effects with promising applications. Single phase multiferroics are of great interest for these new multifunctional devices, being Y-type hexaferrites good candidates, and among them the ZnY compounds due to their ordered magnetic behaviour over room temperature. Polycrystalline Y type hexaferrites with composition Ba0.5Sr1.5Zn2Fe2O22 (BSZFO) were sintered in 1050 °C–1250 °C temperature range. Transverse susceptibility measurements carried out on these BSZFO samples in the temperature range 80–350 K with DC fields up to ± 5000 Oe reveal different behaviour depending on the sintering temperature. Sample sintered at 1250 °C is qualitatively different, suggesting a mixed Y and Z phase like CoY hexaferrites. Sintering at lower temperatures produce single phase Y-type, but the transverse susceptibility behaviour of the sample sintered at 1150 °C is shifted at temperatures 15 K higher. Regarding the DC field sweeps the observed behaviour is a peak that shifts to lower values with increasing temperature, and the samples corresponding to single Y phase exhibit several maxima and minima in the 250 K–330 K range at low DC applied field as a result of the magnetic field induced spin transitions in this compound.Ministerio de Ciencia, Innovación y Universidades; Agencia Estatal de Investigación with FEDER (MAT2016-80784-P

A conjecture on Exceptional Orthogonal Polynomials

Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of Sturm-Liouville problems and generalize in this sense the classical families of Hermite, Laguerre and Jacobi. They also generalize the family of CPRS orthogonal polynomials. We formulate the following conjecture: every exceptional orthogonal polynomial system is related to a classical system by a Darboux-Crum transformation. We give a proof of this conjecture for codimension 2 exceptional orthogonal polynomials (X2-OPs). As a by-product of this analysis, we prove a Bochner-type theorem classifying all possible X2-OPS. The classification includes all cases known to date plus some new examples of X2-Laguerre and X2-Jacobi polynomials

A Family of Quasi-solvable Quantum Many-body Systems

We construct a family of quasi-solvable quantum many-body systems by an algebraic method. The models contain up to two-body interactions and have permutation symmetry. We classify these models under the consideration of invariance property. It turns out that this family includes the rational, hyperbolic (trigonometric) and elliptic Inozemtsev models as the particular cases.Comment: 9 pages, REVTeX4, final versio

Riemann Surfaces of genus g with an automorphism of order p prime and p>g

The present work completes the classification of the compact Riemann surfaces of genus g with an analytic automorphism of order p (prime number) and p > g. More precisely, we construct a parameteriza- tion space for them, we compute their groups of uniformization and we compute their full automorphism groups. Also, we give affine equations for special cases and some implications on the components of the singular locus of the moduli space of smooth curves of genus g.Comment: 28 pages, 5 figure

Exchange operator formalism for N-body spin models with near-neighbors interactions

We present a detailed analysis of the spin models with near-neighbors interactions constructed in our previous paper [Phys. Lett. B 605 (2005) 214] by a suitable generalization of the exchange operator formalism. We provide a complete description of a certain flag of finite-dimensional spaces of spin functions preserved by the Hamiltonian of each model. By explicitly diagonalizing the Hamiltonian in the latter spaces, we compute several infinite families of eigenfunctions of the above models in closed form in terms of generalized Laguerre and Jacobi polynomials.Comment: RevTeX, 31 pages, no figures; important additional conten

Effect of the Photoexcitation Wavelength and Polarization on the Generated Heat by a Nd-Doped Microspinner at the Microscale

Thermal control at small scales is critical for studying temperature-dependent biological systems and microfluidic processes. Concerning this, optical trapping provides a contactless method to remotely study microsized heating sources. This work introduces a birefringent luminescent microparticle of NaLuF4:Nd3+ as a local heater in a liquid system. When optically trapped with a circularly polarized laser beam, the microparticle rotates and heating is induced through multiphonon relaxation of the Nd3+ ions. The temperature increment in the surrounding medium is investigated, reaching a maximum heating of ≈5 °C within a 30 μm radius around the static particle under 51 mW laser excitation at 790 nm. Surprisingly, this study reveals that the particle’s rotation minimally affects the temperature distribution, contrary to the intuitive expectation of liquid stirring. The influence of the microparticle rotation on the reduction of heating transfer is analyzed. Numerical simulations confirm that the thermal distribution remains consistent regardless of spinning. Instead, the orientation-dependence of the luminescence process emerges as a key factor responsible for the reduction in heating. The anisotropy in particle absorption and the lag between the orientation of the particle and the laser polarization angle contribute to this effect. Therefore, caution must be exercised when employing spinning polarization-dependent luminescent particles for microscale thermal analysis using rotation dynamics.Projects CNS2022-135495, PID2023-151078OB-I00 and TED2021-129937B-I00 funded by MCIN/AEI/10.13039/501100011033 and by the “European Union NextGenerationEU/PRTR”Spanish Ministerio de Universidades, through the FPU program (FPU19/04803)Consejería de Universidad, Investigación e Innovación de la Junta de Andalucía and by FEDER “Una manera de hacer Europa” (P18-FR-3583