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The main motivation of this article is to derive sufficient conditions for dynamical stability of periodically driven quantum systems described by a Hamiltonian H(t), i.e. conditions under which it holds true sup_{t ∈ ℝ}|〈ψ_t, H(t)ψ_t〉| < ∞ where ψ_t denotes a trajectory at time t of the quantum system under consideration. We start from an analysis of the domain of the quasi-energy operator. Next, we show, under certain assumptions, that if the spectrum of the monodromy (Floquet) operator U(T, 0) is pure point then there exists a dense subspace of initial conditions for which the mean value of the energy is uniformly bounded in the course of time. Further, we show that if the propagator admits a differentiable Floquet decomposition then ‖H(t)ψ_t‖ is bounded in time for any initial condition ψ₀, and one employs the quantum KAM algorithm to prove the existence of this type of decomposition for a fairly large class of H(t). In addition, we derive bounds uniform in time on transition probabilities between different energy levels, and we also propose an extension of this approach to the case of a higher order of differentiability of the Floquet decomposition. The procedure is demonstrated on a solvable example of the periodically time-dependent harmonic oscillator.

Two stable barium phosphides, Ba₂P and BaP, are predicted by an evolutionary algorithm and first-principles calculations. Ba₂P is a layered structure and isostructural to rhombohedral anti-CdCl₂. The interlayer distance between Ba–P–Ba layers is larger than the intralayer distance of the Ba–P–Ba layers. BaP adopts a body-centered orthorhombic structure composed of P dumbbells. Rhombohedral Ba₂P is metallic, whereas body-centered orthorhombic BaP is a semiconductor that exhibits a band gap of 0.345 eV; the dynamical stabilities of these two compounds were confirmed by phonon calculations and analysis. These findings should encourage further experimental study of the Ba–P system.

We discuss modified teleparallel gravity with function $f(T,T_G)$ in the action, where the function depends on two arguments: torsion scalar $T$ and analogue of Gauss–Bonnet invariant $T_G$. In contradistinction to usual teleparallel gravity $f(T)$, this theory contains higher derivative terms, which may produce different instabilities. We discuss Minkowski stability problem in such kind of theories and explicitly demonstrate that for stability it must be $f_T(0,0)<0$, $f_{T_G{T}_G}>0$. We apply these restrictions for the few types of functions discussed by the early authors.

In this work, we have extensively investigated the characteristics of ternary half-Heusler (HH) materials, specifically NaAlX (X$=$C, Si and Ge), employing ab-initio computations in density functional theory (DFT) framework. Various aspects, including stability parameters, electronic, optical and thermoelectric (TE) parameters have been examined. The computed lattice constants of NaAlX (X$=$C, Si and Ge) were found to be, respectively, 5.398, 6.301 and 6.389Å which are in excellent agreement with the previously available data. The electronic band structures showed that the studied materials exhibit semiconducting behavior with a corresponding band gap of 1.961, 0.999 and 0.846eV, respectively. Specifically, NaAlC and NaAlGe compounds were found to have a direct energy band gap at the $\mathrm{\Gamma }$-point, while NaAlSi displayed an indirect band gap at the $\mathrm{\Gamma }$–X point. Elastic and thermodynamic parameters were examined, confirming that the titled compounds possess mechanical, dynamic and thermal stability. Additionally, the optical response of the materials has been analyzed within an energy range of 0–13eV. The TE parameters exhibited maximum ZT values of 0.998, 0.992 and 0.990 for NaAlX (X$=$C, Si and Ge) materials, respectively, at 300K, suggesting promising TE performance at room temperature.

If the causality condition [the speed of sound always remains less than that of light in vacuum, i.e. v≤c=1] is imposed on the spheres of homogeneous energy density, the "ratio of the specific heats", γ≤2.59457, constraints the compaction parameter, u[≡(M/a), mass to size ratio in geometrized units] of the dynamically stable configurations ≤0.34056 [corresponding to a surface redshift (z_a)≤0.771]. Apparently, the maximum value of u obtained in this manner belongs to an absolute upper bound, and gives: (i) The maximum value for static neutron star masses as 5.4 M_⊙, if we substitute the density at the surface of the configuration equal to the average nuclear density, E=2×10¹⁴g cm^-3 [e.g. Nature, 259, 377 (1976)]. (ii) However, if the density of the static configuration is constrained to the value 1.072×10¹⁴g cm^-3, by imposing the empirical result that the minimum rotation period of the fastest rotating pulsar known to date, PSR 1937+21, is 1.558 ms, the maximum mass value for static neutron stars exceed upto 7.4 M_⊙. These masses have important implications for the massive compact objects, such as Cyg X-1, Cyg XR-1, LMC-X3, etc., which may not, necessarily, represent black holes. (iii) The minimum rotation periods for a static 1.442 M_⊙ neutron star to be 0.3041 ms. (iv) A suitable stable model of ultra-compact objects [u>(1/3)] which has important astrophysical significance.

Axially loaded micro/nano-beams supported on foundations are extensively applied in micro/nano-electro-mechanical systems. This paper deals with the problems of free vibration, buckling and dynamical stability of Timoshenko micro/nano-beam supported on Winkler–Pasternak foundation subjected to a follower axial periodic load. Based on Hamilton’s principle, the governing equations of the system are derived in conjunction with nonlocal strain gradient and Timoshenko theory. The transition parameter is introduced to describe the follower direction of axial load during the deformation of the micro/nano-beam. Employing the weighted residual method, the variational consistency boundary conditions (BCs) can be derived according to the governing equations. Using differential quadrature method (DQM), the governing equations are discretized and numerical solutions of the natural frequencies, critical buckling load and instability region are obtained. Numerical examples are performed to verify present solutions by those available in the literature. Significant effects of the transition parameter and variational consistency BCs are revealed on the free vibration, buckling and dynamical stability of the axially loaded micro/nano-beam. The present analysis is of significance to axially-loaded micro/nano-beam mechanical system, especially for determination of the direction of follower axial force.

This paper is focused on the in/stability of a collapsing anisotropic self-gravitating spherically symmetric compact fluid under the influence of non-minimally coupled f(R, T) gravitational theory, where R and T are traces of Ricci tensor and stress-energy tensor, respectively. We explore the f(R, T) equations of motion as well as conservation equations. We utilize the perturbation technique on dynamical equations, and physical quantities to get the collapse equation in a similar scenario. In the presence of considered f(R, T)-function (i.e. $f(R,T)=R-\zeta R_{c}tanh(\frac{R}{R_c})+\lambda RT$), to explain the dynamical behavior of the considered anisotropic relativistic fluid system. Furthermore, to address the issue of in/stability, the conditions on adiabatic index $\mathrm{\Gamma }$ i.e. stiffness parameter of fluid, are developed for Newtonian $(\mathrm{\text{N}})$-$epoch$ and post-Newtonian ($p\mathrm{\text{N}})$-$epoch$. Several physical constraints are imposed to maintain the un/stable fluid structure.

In this paper, we study the dynamical stability analysis by considering the torsion field $\varphi$ which is proportional to the Hubble parameter and barotropic equation-of-state parameter in the framework of the homogenous and isotropic FLRW metric with non-zero torsion in the scenario of dark matter and dark energy interacting terms. We discuss the stability of the critical points corresponding to the eigenvalues in the presence of dust and radiation at quintessence, $\mathrm{\Lambda }$CDM and phantom regimes by utilizing the different linear and nonlinear interaction models which depend on the energy density. As a result, we observe that the first linear model shows the stable behavior throughout the universe for dust and radiation phase. The other linear and nonlinear models show the stable critical points, computing with the eigenvalues at phantom and $\mathrm{\Lambda }$CDM era with the best fit value of interaction strength and coupling constant for dust and radiation.

The emerging need for new functional materials has recently been engaged in a large quest to predict the alternative green and low-cost energy industry. To this end, thermoelectric as well as spintronic applications remain challenging. In this study, we present, for the first time, a density functional calculation on the IrFeSi half-Heusler compound. The calculation gives a deep analysis of the stability within the calculation of phonon spectra and elastic constants as well as Gibbs energy. The electronic and magnetic properties show that the investigated compound is a half-metallic ferromagnetic material. We show that IrFeSi has an integer magnetic moment of 3${\mu }_B$ in good agreement with the Slater–Pauling (SP) rule. By means of the Boltzman theory, we find that the investigated compound exhibits an interesting thermoelectric performance at room temperature.

The Sturm–Liouville eigenvalue equation for eigenmodes of the radial oscillations is determined for spherically symmetric perfect fluid configurations in spacetimes with a nonzero cosmological constant and applied in the cases of configurations with uniform distribution of energy density and polytropic spheres. It is shown that a repulsive cosmological constant rises the critical adiabatic index and decreases the critical radius under which the dynamical instability occurs.

Recently the role of huge magnetic fields in white dwarfs (WDs) has been explore. It was proposed the existence of WDs with a magnetic field of 10¹⁸ G with a critical mass M_max ≈ 2.58M_⊙ much larger than the Chandrasekhar limit ∼ 1.4M_⊙. These Ultra-magnetized super-Chandrasekhar white dwarfs were obtained not considering some physical aspects as virial theorem, breaking of spherical symmetry, inverse β-decay, and pycnonuclear fusion reactions, making them unstable. Taking in account these points, ultra-magnetized, supermassive and stable white dwarfs, with magnetic fields in their interior at maximum of the order of 10¹³ − 10¹⁴G, even difficult to be formed, are possible to exist at least theoretically.