We employ an all-particle multireference Fock-space relativistic coupled-cluster (FSRCC) theory to study the $5s^2{\;^1}S_0 - 5s5p{\;^3P^o_0}$ clock transition in both Fermionic and Bosonic isotopes of Sr. We compute the excitation energies, E1 and M1 transition amplitudes, hyperfine reduced matrix elements, and isotope shifts using FSRCC theory. Further, we calculate the lifetime of the metastable clock states for $^{87}$Sr and $^{88}$Sr. Furthermore, we employ perturbed relativistic coupled-cluster (PRCC) theory to compute the ground state electric dipole polarizability of Sr. To improve the accuracy of our results, we incorporate the corrections from the relativistic and quantum electrodynamical (QED) effects, and perturbative triples to all our calculations. Our computed excitation energies are in good agreement with the experimental data for low-lying excited states. Our results for E1, M1 and HFS reduced matrix elements are within the experimental error bars, however, with slight difference from the previous calculations due to more accurate treatment of electron correlations in our calculation. Our computed lifetime of the clock state for $^{87}$Sr is within the error bars of the available experimental results, whereas for $^{88}$Sr, it is an order of magnitude smaller than the only available calculation using model potential. Our PRCC result for the ground state polarizability is in good agreement with the experiment, and smaller than previous calculations. As can be expected, our FSRCC results on isotope shift parameters show differences from the MCDF calculations. From the detailed analysis of our results, we find that the corrections from the Breit interaction, QED effects, and perturbative triples are crucial to get accurate clock transition properties in Sr.

In this paper, the tunneling of scalar particles near the event horizons of Riemann space time, BTZ black hole and Schwarzschild-de Sitter black hole are investigated by applying Hamilton-Jacobi equation with Lorentz violation theory in curved space time. The modified Hamilton-Jacobi equation is derived from Klein-Gordon equation of scalar particles induced by Lorentz violation theory in curved space time. The Hawking temperatures of Riemann space time and the BTZ black hole are modified due to the effect of Lorentz violation theory. Moreover, the Bekenstein-Hawking entropy near the event horizon of Schwarzschild-de Sitter black hole is also modified due to Lorentz violation theory. It is observed that the modified values of Hawking temperatures and change in Bekenstein-Hawking entropy depend upon the ether-like vectors $u^\alpha$.

The second law of thermodynamics governs that nonequilibrium systems evolve towards states of higher entropy over time. However, it does not specify the rate of this evolution and the role of fluctuations that impact the system's dynamics. Entropy production quantifies how far a system is driven away from equilibrium and provides a measure of irreversibility. In stochastic systems, entropy production becomes essential for understanding the approach to nonequilibrium states. While macroscopic observations provide valuable insights, they often overlook the local behaviors of the system, governed by fluctuations. In this study, we focus on measuring the lower bound of entropy production at short time scales for generalized stochastic systems by calculating the Kullback-Leibler divergence (KLD) between the probability density functions of forward and backward trajectories. By analysing the entropy production across sliding time scales, we uncover patterns that reveal distinctions between local, small-scale dynamics and the global, macroscopic behavior, offering deeper insights into the system's departure from equilibrium. We also analysed the effects of switching to different types of noise or fluctuations and found that the observations at larger time scales provide no distinction between the different forms of noise while at short time scales, the distinction is significant.

The impact of renormalization group equations(RGEs) on neutrino masses and mixings at high energy scales in Minimal Supersymmetric Standard Model(MSSM) is studied using two different mixing patterns such as Tri-Bimaximal(TBM) mixing and Golden Ratio(GR) mixing in consistent with cosmological bound of the sum of three neutrino masses, $\sum _{i}|m_{i}|$. Magnifications of neutrino masses and mixing angles at low energy scale, are obtained by giving proper input masses, and mixing angles from TBM mixing matrix and GR mixing matrix at high energy scales. High energy scales, $M_{R}$ such as $10^{13}$GeV,$10^{14}$GeV,$10^{15}$GeV are employed in the analysis. The large solar($\theta_{12}$) and atmospheric($\theta_{23}$) neutrino mixing angles with zero reactor angle ($\theta_{13}$) from both TBM mixing matrix and GR mixing matrix at high scale, can magnify the reactor angle($\theta_{13}$) at low energy scale in 3$\sigma$ confidence level. Both cases of normal hierarchy(NH) and inverted hierarchy(IH) are addressed here. In normal hierarchical case, it is found that $\theta_{23}\simeq51.1^{\circ}$ and that in inverted hierarchical case is $\theta_{23}\simeq39.1^{\circ}$ in both mixing patterns. Possibility of \theta_{23}>45^{\circ} or \theta_{23}<45^{\circ} is observed at low scale. The analysis shows the validity of the two mixing patterns at high energy scale.

A neutrino mass model that can satisfy the exact golden ratio mixing is constructed using $A_{5}$ discrete symmetry group. The deviation from the golden ratio mixing is studied by considering the contribution from the charged lepton sector in a linear seesaw framework. A definite pattern of charged lepton mass matrix predicted by the model controls the leptonic mixing angles. By taking the observed $\theta_{13}$ as the input value, we can obtain the values of all the mixing angles and Dirac CP-violating phase within the current experimental bounds. The model predicts that only the normal neutrino mass ordering is consistent with the current oscillation data. We also study the two body charged lepton flavor violation (cLFV) processes such as $\mu \rightarrow e +\gamma$, $\tau \rightarrow e +\gamma$ and $\tau \rightarrow \mu+ \gamma$ and neutrinoless double beta decay parameter $m_{\beta \beta}$. The present neutrino mass model can explain the current and future sensitivity of $\mu \rightarrow e +\gamma$, $\tau \rightarrow e+ \gamma$ processes and the present sensitivity of neutrinoless double beta decay parameter when the masses of quasi-Dirac neutrinos are in the TeV range. On the other hand, the model cannot reproduce the present sensitivity of $\tau \rightarrow \mu+ \gamma$ but can explain the future sensitivity and the present sensitivity of neutrinoless double beta decay parameter simultaneously when the masses of the quasi-Dirac neutrinos are in the TeV range.

In this work we describe a new technique for numerical exact diagonalization. The method is particularly suitable for cold bosonic atoms in optical lattices, in which multiple atoms can occupy a lattice site. We describe the use of the method for Bose-Hubbard model of a two-dimensional square lattice system as an example; however, the method is general and can be applied to other lattice models and can be adapted to three-dimensional systems. The proposed numerical technique focuses in detail on how to construct the basis states as a hierarchy of wave functions. Starting from single-site Fock states, we construct the basis set in terms of row states and multirow states. This simplifies the application of constraints and calculation of the Hamiltonian matrix. The approach simplifies the calculation of the reduced density matrices, and this has applications in characterizing the topological entanglement of the state. Each step of the method can be parallelized to accelerate the computation. As a case study, we discuss the computation of the spatial bipartite entanglement entropy in the correlated $\nu = 1/2$ fractional quantum Hall state.

Implication of neutrino mass model based on $\Delta$(27) discrete flavor symmetry, on parameters of neutrino oscillations, CP violation and effective neutrino masses is studied using type-I seesaw mechanism. The Standard Model particle content is extended by adding two additional Higgs doublets, three right-handed neutrinos and two scalar triplets under $\Delta$(27) symmetry predicting diagonal charged lepton mass matrix. This can generate the desired deviation from $\mu - \tau$ symmetry. The resulting neutrino oscillation parameters are well agreed with the latest global fit oscillation data. The sum of the three absolute neutrino mass eigenvalues, $\sum\limits_{i}|m_{i}|$ (i=1,2,3) is found to be consistent with that of the value given by latest Planck cosmological data, \sum\limits_{i}|m_{i}|<0.12 eV. The model further predicts effective neutrino masses for neutrinoless double beta decay, 4.15 meV $\leq m_{ee}\leq$ 30.6 meV, tritium beta decay, 8.4 meV $\leq m_{\beta}\leq$ 30.5 meV, Jarlskog invariant, $J_{CP}=\pm 0.022$ for CP violation, baryon asymmetry $Y_{B}=1.15 \times 10^{-10}$ for normal hierarchical case; and also 49.5 meV $\leq m_{ee}\leq$ 51.7 meV, 49.5 meV $\leq m_{\beta}\leq$ 51.4 meV, $J_{CP}=\pm 0.022$, $Y_{B}=1.12\times 10^{-10}$ for inverted hierarchical case respectively.

We have implemented an all-particle multireference Fock-space relativistic coupled-cluster theory to probe $6s^2{\;^1}S_{0} - 6s6p{\;^3P^o_{0}}$ clock transition in an even isotope of Pb$^{2+}$. We have computed, excitation energy for several low lying states, E1 and M1 transition amplitudes, and the lifetime of the clock state. Moreover, we have also calculated the ground state dipole polarizability using perturbed relativistic coupled-cluster theory. To improve the accuracy of results, we incorporated the corrections from the relativistic and QED effects in all our calculations. The contributions from triple excitations are accounted perturbatively. Our computed excitation energies are in excellent agreement with the experimental values for all the states. Our result for lifetime, $9.76\times10^{6}$ s, of clock state is $\approx$ 8.5\% larger than the previous value using CI+MBPT [Phys. Rev. Lett. {\bf 127}, 013201 (2021)]. Based on our analysis, we find that the contributions from the {\em valence-valence} correlations arising from higher energy configurations and the corrections from the perturbative triples and QED effects are essential to get accurate clock transition properties in Pb$^{2+}$. Our computed value of dipole polarizability is in good agreement with the available theoretical and experimental data.

In this paper, we introduce a new concept in Nil-semicommutative modules and present it as an extension of Nil-semicommutative rings to modules. We prove that the class of Nil-semicommutative modules is contained in the class of Weakly semicommutative modules while that of the converse may not be true. We also show that in case of Semicommutative modules and Nil-semicommutative modules, one does not imply the other. Moreover, for a given Nil-semicommutative ring, we provide the conditions under which the same can be extended to a Nil-semicommutative module. Lastly, we also prove that for a left $R$-module $M$, $_RM$ is Nil-semicommutative iff it's localization $S^{-1}M$ over the ring $S^{-1}R$ is also this http URL other examples and propositions highlighting the comparative studies of this new class of modules with different classes of modules are also discussed in order to validate the concept.

Prions are proteinaceous infectious particles that cause neurodegenerative diseases in humans and animals. The complex nature of prions, with respect to their conformations and aggregations, has been an important area of research for quite some time. Here, we develop a model of prion dynamics prior to the formation of oligomers and subsequent development of prion diseases within a stochastic framework, based on the analytical Master Equation and Stochastic Simulation Algorithm by Gillespie. The results that we obtain shows that solvent water molecules act as driving agents in the dynamics of prion aggregation. Further, it is found that aggregated and non-aggregated proteins tend to co-exist in an equilibrium state, depending upon the reaction rate constants. These results may provide a theoretical and qualitative contexts of possible therapeutic strategies in the treatment of prion diseases.

Armendariz and semicommutative rings are generalizations of reduced rings. In \cite{IN}, I.N. Herstein introduced the notion of a hypercenter of a ring to generalize the center subclass. For a ring $R$, an element $a \in R$ is called hypercentral if $ax^{n}=x^{n}a$ for all $x \in R$ and for some $n=n(x,a) \in \mathbb{N}$. Motivated by this definition, we introduce $\mathscr{H}$-Semicommutative rings as a generalization of semicommutative rings and investigate their relations with other classes of rings. We have proven that the class of $\mathscr{H}$-Semicommutative rings lies strictly between Zero-Insertive rings (ZI) and Abelian rings. Additionally, we have demonstrated that if $R$ is $\mathscr{H}$-semicommutative, then for any $n \in \mathbb{N}$, the matrix subring $S_{n}^{'}(R)$ is also $\mathscr{H}$-semicommutative. Among other significant results, we have established that if $R$ is $\mathscr{H}$-semicommutative and left $SF$, then $R$ is strongly regular. We have also shown that $\mathscr{H}$-semicommutative rings are 2-primal, providing sufficient conditions for a ring $R$ to be nil-singular. Additionally, we have proven that if every simple singular module over $R$ is wnil-injective and $R$ is $\mathscr{H}$-semicommutative, then $R$ is reduced. Furthermore, we have studied the relationship of $\mathscr{H}$-semicommutative rings with the classes of Baer, Quasi-Baer, p.p. rings, and p.q. rings in this article, and we have provided some more relevant results.

In this paper we propose a class of embedded solutions of Einstein's field equations describing non-rotating Reissner-Nordstrom-Vaidya and rotating Kerr-Newman-Vaidya black holes.

We study a 3+1 active-sterile neutrino mixings model using an $A_4$ triplet right-handed neutrino $\nu_R$ and a singlet eV-scale sterile neutrino under $A_4\times Z_3 \times Z_2$ discrete symmetry. Four scalar flavons are considered to reproduce neutrino oscillation parameters within the experimental 3$\sigma$ range. The model also studies the effective mass parameter in neutrinoless double beta decay experiments. Deviation from $\mu-\tau$ symmetry in the active neutrino mass matrix is generated through an antisymmetric interaction of $\nu_R$. This model successfully explains active-sterile neutrino mixings consistent with the cosmological upper bound on the sum of active neutrino mass \sum m_i < 0.113 eV (0.145 eV) in NH(IH).

This paper studies the scalar, electromagnetic field and Dirac field perturbations of spherically symmetric black hole within the framework of Einstein-bumblebee gravity model with global monopole and cosmological constant. We investigate the effective potentials, greybody factors and quasinormal modes (QNMs) by applying the Klein-Gordon equation, electromagnetic field equation and Dirac equation expressed in Newman-Penrose (NP) formalism. Using the general method of rigorous bound, the greybody factors of scalar, electromagnetic and Dirac field are derived. Applying the sixth order WKB approximation and Padé approximation, the QNM frequencies are derived. We also discuss the impact of global monopole $\eta$, cosmological constant $\Lambda$ and Lorentz violation parameter $L$ to the effective potential, greybody factor and QNMs. Increasing the parameter $\eta$ prevents the rise of effective potential for both Schwarzschild-de Sitter (SdS)-like and Schwarzschild-Anti de Sitter (SAdS)-like black holes with global monopole and consequently increases the greybody factors. However, decreasing the parameter $L$ reduces the rise of effective potential for the SAdS-like black hole with global monopole and it increases the greybody factor but increasing the parameter $L$ has an opposite effect for SdS-like black hole with global monopole. It is also shown that the shadow radius increases with increasing the parameter $\eta$ for both dS and AdS cases. Increasing the value of $L$ tends to increase the shadow radius for dS black hole but it has an opposite effect in AdS case. A careful studying is being carried out to investigate how the absorption cross-section gets affected when the parameter $L$ appears into the picture.

The introduction of disorder in Bose-Hubbard model gives rise to new glassy quantum phases, namely the Bose-glass (BG) and disordered solid (DS) phases. In this work, we present the rich phase diagram of interacting bosons in disordered two-dimensional optical lattice, modelled by the disordered Bose-Hubbard model. We systematically probe the effect of long-range interaction truncated to the nearest neighbors and next-nearest neighbors on the phase diagram. We investigate the zero-temperature ground-state quantum phases using the single-site Gutzwiller mean field (SGMF) theory. We also employ strong-coupling perturbative expansion to identify the nature of ground-state solid phases analytically. At sufficiently high disorder strength, we observe a quantum phase transition between the DS and BG phases. We have investigated this transition in greater detail using cluster Gutzwiller mean field theory to study the effect of inter-site correlations which is absent in the SGMF method. We have also studied this phase transition from the perspective of percolation theory.

In this paper, we investigate the Dirac field, scalar field and electromagnetic field perturbations of Reissner-Nordstorm-de Sitter (RNdS) and Reissner-Nordstorm-(anti)-de Sitter (RNAdS)-like black holes within the frame work of Einstein-bumblebee gravity. The effective potential, greybody factor and quasinormal modes (QNMs) are also explored by using Dirac equation, Klein-Gordon equation and Maxwell's equation. We find that for RNdS-like black hole increasing the Lorentz violation parameter $L$ consistently leads to decrease in the effective potential for all types of perturbations but for RNAdS case the influence of $L$ varies depending on the types of perturbation. Further for both RNdS and RNAdS-like black holes, increasing charge $Q$ reduces the effective potential in all the perturbations. The greybody factors of all the types of perturbations are also discussed. The results show that the greybody factors depend on the shape of the effective potential: higher (lower) potentials gives lower (higher) greybody factors. The QNMs frequencies of RNdS-like black hole for the massless field perturbations are discussed by using 6th order WKB approximation and Pad\'e approximation. We also analyze the time-domain profiles of the perturbations. The effects of Lorentz violation parameter $L$ and charge $Q$ to the photon sphere radius and shadow radius are also discussed. It is noted that increasing $Q$ and $L$ reduce the rise of shadow radius for RNdS-like black hole.

This paper explores H-Toeplitz operators on the Fock space, unifying aspects of Toeplitz and Hankel operators while introducing novel structural properties. We derive explicit matrix representations for these operators with respect to the orthonormal basis of monomials, analyze their commutativity, and establish compactness criteria. Key results include the characterization of commuting H-Toeplitz operators with harmonic symbols and the proof that non-zero H-Toeplitz operators cannot be Hilbert-Schmidt. Additionally, we introduce directed H-Toeplitz graphs to visualize adjacency relations encoded by these operators, demonstrating their structural patterns through indegree and outdegree sequences. Our findings bridge theoretical operator theory with graphical representations, offering insights into the interplay between analytic function spaces and operator algebras.

We employ an all-particle multireference Fock-space relativistic coupled-cluster (FSRCC) theory to compute the ionization potential, excitation energy, transition rate and hyperfine structure constants associated with $7s^2\;^{1}S_{0}\rightarrow 7s7p\;^{3}P_{1}$ and $7s^2\;^{1}S_{0}\rightarrow 7s7p\;^1P_{1}$ transitions in nobelium (No). Using our state-of-the-art calculations in conjunction with available experimental data \cite{raeder-18}, we extract the values of nuclear magnetic dipole ($\mu$) and electric quadrupole ($Q$) moments for $^{253}$No. Further, information on nuclear deformation in even-mass isotopes is extracted from the isotope shift calculations. Moreover, we employ a perturbed relativistic coupled-cluster (PRCC) theory to compute the ground state electric dipole polarizability of No. In addition, to assess the accuracy of our calculations, we compute the ionization potential and dipole polarizability of lighter homolog ytterbium (Yb). To account for strong relativistic and quantum electrodynamical (QED) effects in No, we incorporate the corrections from Breit interaction, vacuum polarization and self-energy in our calculations. The contributions from triple excitations in coupled-cluster is accounted perturbatively. Our calculations reveal a significant contribution of $\approx$10\% from the perturbative triples to the transition rate of $7s^2\;^1S_{0}\rightarrow 7s7p\;^3P_{1}$ transition. The largest cumulative contribution from Breit+QED is observed to be $\approx$4\%, to the magnetic dipole hyperfine structure constant of $7s7p\;^1P_{1}$ state. Our study provides a comprehensive understanding of atomic and nuclear properties of nobelium with valuable insights into the electron correlation and relativistic effects in superheavy elements.

Patterns in complex systems store hidden information of the system which is needed to be explored. We present a simple model of cytokine and T-cells interaction and studied the model within stochastic framework by constructing Master equation of the system and solving it. The solved probability distribution function of the model show classical Poisson pattern in the large population limit $M,Z\rightarrow large$ indicating the system has the tendency to attract a large number small-scale random processes of the cytokine population towards the basin of attraction of the system by segregating from nonrandom processes. Further, in the large $\langle Z\rangle$ limit, the pattern transform to classical Normal pattern, where, uncorrelated small-scale fluctuations are wiped out to form a regular but memoryless spatiotemporal aggregated pattern. The estimated noise using Fano factor shows clearly that the cytokine dynamics is noise induced process driving the system far away from equilibrium.

Climate variability is a complex phenomenon resulting from numerous interacting components of a climate system across a wide range of temporal and spatial scales. Although significant advances have been made in understanding global climate variability, there are relatively less studies on regional climate modeling, particularly in developing countries. In this work, we propose a framework of data driven hybrid dynamical stochastic modeling to investigate the variability of maximum temperature recorded for the capital city of Imphal in the state of Manipur, located in the Northeast India. In light of increasing concerns over global warming, studying maximum temperature variability over varying time scales is an important area of research. Analysis using publicly available climate data over the course of 73 years, our approach yields key insights into the temperature dynamics, such as a positive increase in temperature in the region during the period investigated. Our hybrid model, combining spectral analysis and Fourier decomposition methods with stochastic noise terms and nonlinear feedback mechanisms, is found to effectively reproduce the observed dynamics of maximum temperature variability with high accuracy. Our results are validated by robust statistical and qualitative tests. We further derive Langevin and Fokker-Planck equations for the maximum temperature dynamics, offering the theoretical ground and analytical interpretation of the model that links the temperature dynamics with underlying physical principles.