Duality and quantum-algebra symmetry of the AN−1 open spin chain with diagonal boundary fields

We show that the transfer matrix of the A_N−1⁽¹⁾ open spin chair with diagonal boundary fields has the symmetry U_q(SU(l)) × U_q(SU(N−l)) × U(1), as well as a “duality” symmetry which maps l ↔ N − l. We exploit these symmetries to compute exact boundary S-matrices in the regime with q real.     

Systematic study of α decay half-lives for even–even nuclei within a deformed two-potential approach

In this work, we systematically study the α decay half-lives of 196 even–even nuclei using a two-potential approach improved by considering nuclear deformation. The results show that the accuracy of this model has been improved after considering nuclear deformation. In addition, we extend this model to predict the α decay half-lives of Z = 118 and 120 isotopes by inputting the α decay energies extracted from the Weizsacker–Skyrme-type (WS-type) mass model, a simple nuclear mass formula, relativistic continuum Hartree–Bogoliubov theory and Duflo-Zuker-19 (DZ19) mass model. It is useful for identifying the new superheavy elements or isotopes for future experiments. Finally, the predicted α decay energies and half-lives of Z = 118 and 120 isotopes are analyzed, and the shell structure of superheavy nuclei is discussed. It shows that the shell effect is obvious at N = 184, while the shell effect at N = 178 depends on the nuclear mass model.     

Gadolinium clusters at finite temperature: exact results in the framework of a quantum Heisenberg model

The magnetic properties of clusters with N13 atoms were investigated as a function of the temperature in the framework of Heisenberg model. The canonical partition function was calculated using all the spectrum obtained by an exact numerical diagonalization method. Interesting results are observed for the average total spin S as a function of the ratio between nearest neighbors ferromagnetic and next-nearest neighbors antiferromagnetic coupling. Our model is applied to rare-earth magnets and qualitatively describes the magnetic behavior of gadolinium clusters.     

Examination of n-T_9 conditions required by N=50,82,126 waiting points in r-process

We examined the conditions of neutron density(n) and temperature(T_9) required for the N = 50, 82,and 126 isotopes to be waiting points(WP) in the r-process. The nuclear mass based on experimental data presented in the AME2020 database(AME and AME ±Δ) and that predicted using FRDM,WS4, DZ10, and KTUY models were employed in our estimations. We found that the conditions required by the N = 50 WP significantly overlap with those required by the N = 82 ones, except for the WS4 model. In addition, the upper(or lower) bounds of the n-T_9 conditions based on the models are different from each other due to the deviations in the two-neutron separation energies.The standard deviations in the nuclear mass of 108 isotopes in the three N = 50, 82, and 126 groups are about rms = 0.192 and 0.434 Me V for the pairs of KTUY-AME and WS4-KTUY models,respectively. We found that these mass uncertainties result in a large discrepancy in the nn-T_9 conditions, leading to significant differences in the conditions for simultaneously appearing all the three peaks in the r-process abundance. The newly updated FRDM and WS4 calculations can give the overall conditions for the appearance of all the peaks but vice versa for their old versions in a previous study. The change in the final r-process isotopic abundance due to the mass uncertainty is from a few factors to three orders of magnitude. Therefore, accurate nuclear masses of the r-process key nuclei, especially for ~(76) Fe,~(81)Cu,~(127)Rh,~(132)Cd,~(192)Dy, and ~(197)Tm, are highly recommended to be measured in radioactive-ion beam facilities for a better understanding of the r-process evolution.     

Nuclear properties of Z=114 isotopes and shell structure of ~(298)114

The two-neutron separation energies(S_(2n)) and α-decay energies(Q_α) of the Z=114 isotopes are calculated by the deformed Skyrme-Hartree-Fock-Bogoliubov(SHFB) approach with the SLy5,T22,T32 and T43 interactions.It is found that the tensor force effect on the bulk properties is weak and the shell closure at N=184 is seen evidently with these interactions by analyzing the S_(2n) and Q_α evolutions with neutron number N.Meanwhile,the single-particle energy spectra of ~(298)114 are studied using the spherical SHFB approach with these interactions to furthermore examine the shell structure of the magic nucleus ~(298)114.It is shown that the shell structure is almost not changed by the inclusion of the tensor force in the Skyrme interactions.Finally,by examining the energy splitting of the three pairs of pseudospin partners for the protons and neutrons of ~(298)114,it is concluded that the pseudospin symmetry of the neutron states is preserved better than that of the proton states and not all of the pseudospin symmetries of the proton and neutron states are influenced by the tensor force.     

Magnetostriction in terms of hexagonal and cubic harmonics up to degree 6

Tables are given which allow the magnetostriction constants ^j_kΛ^μ_l6 and magnetoelastic coupling coefficients ^J_kB^μ_l6 to be evaluated from the Fourier coefficients of Δl/l in various crystallographic planes. The difference between anisotropy coefficients at zero strain and zero stress is given for hexagonal crystals for the first time in terms of the ^j_kB^μ_l . At all stages the indices which indicate the symmetry type of a function (μ, i) are clearly distinguished from those which do not (j, k, l).     

The Cartesian analytical solutions for the N-dimensional compressible Navier–Stokes equations with density-dependent viscosity

In this paper, we prove the existence of general Cartesian vector solutions u = b(t) + A(t)x for the N-dimensional compressible Navier–Stokes equations with density-dependent viscosity, based on the matrix and curve integration theory. Two exact solutions are obtained by solving the reduced systems.     

On the Curie temperature of a spin one XY ferromagnet with uniaxial anisotropy

A spin one XY ferromagnet with uniaxial anisotropy has been investigated, using Green's function technique in random phase approximation (RPA). The Green functions associated with the anisotropy energy are treated without decoupling. A set of coupled equations have been obtained to find the critical temperature T_c and (S^Z)² at T_c as function of the uniaxial anisotropy parameter D. T_c and (S^Z)² at T_c are found to increase with D. The results are compared with the earlier results obtained in the Narath type of RPA.     

Entanglement measures of a new type pseudo-pure state in accelerated frames

In this work we analyze the characteristics of quantum entanglement of the Dirac field in noninertial reference frames in the context of a new type pseudo-pure state, which is composed of the Bell states. This will help us to understand the relationship between the relativity and quantum information theory. Some states will be changed from entangled states into separable ones around the critical value F = 1/4, but there is no such a critical value for the variable y related to acceleration a. We find that the negativity N_ABI (ρ^TA_ABI) increases with F but decreases with the variable y, while the variation of the negativity N_BIBII(ρ^TA_ABI) is opposite to that of the negativity N_ABI (ρ^TA_ABI). We also study the von Neumann entropies S(ρ_ABI) and S(ρ_BIBII). We find that the S(ρ_ABI) increases with variable y but S(ρ_BIBII) is independent of it. However, both S(ρ_ABI) and S(ρ_BIBII) first decreases with F and then increases with it. The concurrences C(ρ_ABI) and C(ρ_BIBII) are also discussed. We find that the former decreases with y while the latter increases with y but both of them first increase with F and then decrease with it.     

The large N limit of the O(N) Heisenberg spin system in two dimensions

The large N limit of the O(N) Heisenberg spin system in two dimensions (a lattice version of the non-linear σ-model) is analysed by the collective field technique. A compact expression for the mass gap and the β-function is obtained for arbitrary but fixed gN. The strong and weak coupling limits of this expression correctly reproduce the known results.     

Explicit counteraction algorithms in higher dimensions

Using the background field method we construct algorithms for the one-loop counterterms of a field theory in a space-time of dimension 2, 4, 6, 8 or 10. From the d = 6 algorithm we demonstrate the one-loop finiteness of N = 2 supersymmetric Yang-Mills theories and also N = 1 Yang-Mills theory. All other N = 1 Yang-Mills theories + N = 1 matter theories in d = 6 are shown to have a divergent one-loop S-matrix.

We also present partial results for two- and three-loop algorithms in d = 6 and d = 4 respectively.     

Using Pantheon and Hubble parameter data to constrain the Ricci dark energy in a Bianchi I Universe

In this work, we use the most recent publicly available type Ia supernova (SNIa) compilations and H(z) data. A well formulated cosmological model based on Bianchi type I (BI) metric is implemented in the presence of the Ricci dark energy model. Using the maximum likelihood technique, we estimate the present value of Hubble's constant H₀ = 70.339 ± 0.743, matter density parameter ${{\rm{\Omega }}}_{{m}_{0}}=0.297\pm 0.031$, anisotropy parameter ${{\rm{\Omega }}}_{{\sigma }_{0}}=\,$−0.004 01 ± 0.001 07 within $1\sigma ^{\prime} $ confidence level by bounding our derived model with recent joint Pantheon and H(z) data. We have constrained the present value of the equation of state parameter as ω_de = −1.17 joint with the observational data. The present value of the deceleration parameter of the Universe in the derived model is obtained as ${q}_{0}=-{0.749}_{-0.086}^{+0.076}$. Transition redshift is also derived as ${z}_{\mathrm{tr}}\sim 0.551$ with the recent observations (Pantheon + H(z)) datasets. Finally, we compare the anisotropy effects on the evolution of H(z) for the proposed model under consideration with different observational datasets.     

On the importance of anisotropic exchange coupling on to the structure of spin-polarized clusters in layered cuprates

The low energy spectrum of spin-polarized clusters in layered cuprates is examined. Two types of clusters confining the motion of oxygen holes are discussed. The ground state of the pentanuclear copper cluster has a total spin S = 2, whereas the one of the tetranuclear copper cluster is characterised by S= 3/2. Anisotropic exchange coupling splits the magnetic ground state into a sequence of state, which in a natural way provide e.g. an explanation of EPR data for La₂CuO_4+δ compounds.     

Entanglement Dynamics of Two Coupled Spins in a Spin Star Environment

We theoretically study the entanglement dynamics of two coupled spins in a spin star environment, whose elements are coupled to local bosonic baths. It is shown that the dynamics of the entanglement depends on the initial state of the system and the coupling strength between the two coupled central spins, the interactions between the central system and the environment, as well as interactions between the bath spin and the reservoir. We also investigate the effect of non-Markovian dynamics in contrast with the Markovian case. It is found that the non-Markovian dynamics has a significant effect on the disentanglement between the two central spins.     

Swampland dS conjecture in mimetic f(R,T) gravity

In this paper, we study a theory of gravity called mimetic f(R, T) in the presence of swampland dS conjecture. For this purpose, we introduce several inflation solutions of the Hubble parameter H(N) from f(R, T) = R + δT gravity model, in which R is Ricci scalar, and T denotes the trace of the energy–momentum tensor. Also, δ and N are the free parameter and a number of e-fold, respectively. Then we calculate quantities such as potential, Lagrange multiplier, slow-roll, and some cosmological parameters such as n_s and r. Then we challenge the mentioned inflationary model from the swampland dS conjecture. We discuss the stability of the model and investigate the compatibility or incompatibility of this inflationary scenario with the latest Planck observable data.     

Branched polymers from a double-scaling limit of matrix models

Multicritical potentials and correlation functions are given for models of rectangular M × N matrices, in the limit that N goes to infinity. These models are soluble without using orthogonal polynomials, and describe filamentary random surfaces, or, equivalently, a phase of branched polymers. It is shown that the equations describing multicritical behaviour are obtained from the hierarchy of flows that preserve Burgers' equation. Instanton solutions are studied - they imply that only the k = 2 model is unitary, and that the coefficients (for arbitrary k) of g_st^l is the perturbative expansion of the specific heat grow as l!.     

Current-induced step bunching at vicinal surfaces during crystal sublimation

The limits of the applicability of the generalized BCF model of electromigration-affected sublimation are discussed in detail. Only in surface-diffusion limited sublimation are the steps boundaries, effectively separating the transport processes at neighbouring terraces. In the opposite case of high surface mobility and slow exchange between the 2D gas of mobile adatoms and the crystal, many atoms simply cross the steps, spending some time in an intermediate state of adsorption at the step edge, but never becoming “crystal atoms”. In this regime of sublimation the steps are no longer boundaries. Therefore, one cannot analyze diffusion and desorption on one separate terrace (as in the generalized BCF model) since the coupling between the adatom concentration fields on neighbouring terraces cannot be neglected. A relevant model for this regime of electromigration-affected sublimation is proposed in this paper. This model manifests step buching at the step-up direction of the adatom electromigration. The central result of the mathematical treatment is the formula (x₂−x₁)^{n + 2}=(4kT/F) l^{n + 1}₀, relating the interstep distance x₂−x₁ in a stable pair of steps with the electromigration inducing force F. Here n and l₀ determine the form and the magnitude of the step-step interaction. The formula obtained for x₂−x₁ provides a gound to evaluate n and l₀ from a set of experimental data on sublimation by combined DC and radiative heating.     

Anomalous behavior of l = 0 transitions in Mo(d,p) and Mo(d,t) reactions

The states of ⁹⁹Mo dominantly populated by l = 0 transitions in ⁹⁸Mo(d,p) and in ¹⁰⁰Mo(d,t) are not the same. The ratio S(d,t)/S(d,p) for these states differs by a factor of 21 which is an order of magnitude larger than in any other known case. This represents a breakdown of the quasi-particle model.     

From Planck to GUT via dimensional transmutation

Consider a gauge singlet superfield S coupled to a pair of adjoint fields in a SUSY-GUT. If the tree-level vacuum is flat in S, the vev S which defines the GUT scale will be determined via dimensional transmutation at a scale M where the soft-breaking (mass)² vanishes as a result of running from M_P = (8πG_N)^−1/2. Because of the large number of adjoint fields N_A coupled to S, one finds that M can be generically close to M_GUT = 2 × 10¹⁶GeV:

, where λ is a Yukawa 0.7. This work examines the symmetries and dynamical constraints required in a SUSY-GUT in order that the desired flatness in S is achieved, and that this flatness may survive in a supergravity framework.