Investigation of the Models of Magnetic Dendrimers by the Wang–Landau Method

Physics of the Solid State - The thermodynamic properties of the models of magnetic dendrimers were studied by the Monte Carlo method. The system state density is calculated; the ground state...     

Magnetization plateaus of the frustrated Ising Shastry–Sutherland system: Wang–Landau simulation

The Wang–Landau algorithm is used to study the magnetic properties of the Ising model on the Shastry–Sutherland lattice in order to understand the interesting magnetization plateaus observed in TmB₄. The simulated results demonstrate that the equilibrium state of the model produces only the 1/3 and 1/2 magnetization plateaus at low temperatures even when the random-exchange term or the long-range interactions are taken into account. This confirms our earlier conclusion (Huang et al., 2013) [20] that those fractional plateaus observed in experiments may be due to the magnetization dynamics.     

Calculation of Free Energy of the Integrable Landau—Lifshitz model

The generalized Bethe-ansatz method of thermodynamic analysis of integrable systems was employed to compute the free energy of a classical integrable model,i.e.the Landau-Lifshitz model.Using the action-angle variables of the model and by imposing a periodic boundary condition.we derive a phase-shifted density of states for the excitations of the system.The free energy,in the thermodynamic limit,can be expressed analytic in terms of two coupled nonlinear integral equations of the finie temperature excited energy for effective phonons and kinks (antikinks).we solve these equations iteratively for a special case that the model is in the limit of anisotropic strong yz coupling.     

Dilute modulation of spin frustration in triangular Ising antiferromagnetic model: Wang–Landau simulation

To understand the thermodynamic and magnetic properties of the dilute antiferromagnetic Ising model on a triangular lattice, the Wang–Landau algorithm is applied to perform a Monte Carlo simulation. Based on the simulated density of states, the thermodynamic and magnetic behaviors of system with different dilute concentrations are evaluated, and compared to explore the dilute modulation of spin frustration. It is revealed that for the typical frustrated triangular system, a little dilution can lift the degeneracy of ground states greatly, weaken the frustration-induced relaxation, and consequently influence the thermodynamic and magnetic behaviors of system.     

A Simplified Algorithm for Impedance Calculation of Arbitrarily Shaped Radiators

It is well known that a computationally efficient model for calculation of radiation impedance of an arbitrarily shaped piston has been developed. We simplify the proposed algorithm by using geometric characteristics and intrinsic relationship between the analytic expressions. As an example, the method accuracy is illustrated and the radiation impedance of a right-angled triangular piston is calculated. The numerical results are in good agreement with that obtained directly by the quadruple integral method.     

Fluctuation of Density of States for 1d Schrödinger Operators

We consider the 1d Schrödinger operator with random decaying potential and compute the 2nd term asymptotics of the density of states, which shows substantial differences between the cases \(\alpha > \frac{1}{2}\), \(\alpha < \frac{1}{2}\) and \(\alpha = \frac{1}{2}\).     

Measure-and-Resend Attack and Improvement on “A Scheme to Share Information via Employing Discrete Algorithm to Quantum States”

In 2011, Kang and Fang (Commun. Theor. Phys. 55:239–243, 2011) presented a quantum direct communication protocol using single photons. This study points out a pitfall in Kang and Fang’s scheme, in which an eavesdropper can launch a measure-and-resend attack on this scheme to reveal the secret message. Furthermore, an improved scheme is proposed to avoid the attack.     

Free or Quasi-Free Electronic Density of States in a Confined Atom

A new general formula, for energy normalization of radial wave-functions of free electron and of quasi-free electron in confined atom, is derived in central field approximation, which can flexibly be applied to the cases of relativity,non-relativity, and of free atom.     

Stability of the Landau–Fermi Liquid Theory

The stability of the Landau–Fermi liquid theory is investigated. It has been shown that if the interaction function of the Fermi system is a finite function of the angle between the momenta of two particles at the Fermi surface, then the liquid can be stable. We have shown that the absolute value of the expansion coefficients of the interaction functions in Legendre polynomials are decreasing function of the coefficients indices. We solve the stability condition for one photon exchange (OPE) in an electron gas. The results show that we must use the massive boson propagator (higher order corrections to the photon propagator). Similar to previous works (Abrikosov et al. in Method of Quantum Field Theory in Statistical Physics, Pergamon, Elmsford, 1965), our result is proportional to g ². The density and temperature dependence of results is occulted in the effective mass of the system.     

Hölder Equicontinuity of the Integrated Density of States at Weak Disorder

Hölder continuity, |N(E)–N(E)| C |E – E|, with a constant C independent of the disorder strength is proved for the integrated density of states N(E) associated to a discrete random operator H=H_o + V consisting of a translation invariant hopping matrix H_o and i.i.d. single site potentials V with an absolutely continuous distribution, under a regularity assumption for the hopping term.Mathematics Subject Classifications (2000). 82D30, 46N55, 47N55.     

The Structure of the Kac–Wang–Yan Algebra

The Lie algebra \({\mathcal{D}}\) of regular differential operators on the circle has a universal central extension \({\hat{\mathcal{D}}}\). The invariant subalgebra \({\hat{\mathcal{D}}^+}\) under an involution preserving the principal gradation was introduced by Kac, Wang, and Yan. The vacuum \({\hat{\mathcal{D}}^+}\)-module with central charge \({c \in \mathbb{C}}\), and its irreducible quotient \({\mathcal{V}_c}\), possess vertex algebra structures, and \({\mathcal{V}_c}\) has a nontrivial structure if and only if \({c \in \frac{1}{2}\mathbb{Z}}\). We show that for each integer \({n > 0}\), \({\mathcal{V}_{n/2}}\) and \({\mathcal{V}_{-n}}\) are \({\mathcal{W}}\)-algebras of types \({\mathcal{W}(2, 4,\dots,2n)}\) and \({\mathcal{W}(2, 4,\dots, 2n^2 + 4n)}\), respectively. These results are formal consequences of Weyl’s first and second fundamental theorems of invariant theory for the orthogonal group \({{\rm O}(n)}\) and the symplectic group \({{\rm Sp}(2n)}\), respectively. Based on Sergeev’s theorems on the invariant theory of \({{\rm Osp}(1, 2n)}\) we conjecture that \({\mathcal{V}_{-n+1/2}}\) is of type \({\mathcal{W}(2, 4,\dots, 4n^2 + 8n + 2)}\), and we prove this for \({n = 1}\). As an application, we show that invariant subalgebras of \({\beta\gamma}\)-systems and free fermion algebras under arbitrary reductive group actions are strongly finitely generated.     

Density–temperature properties of Ga–Sb alloy melt

In an experiment, the improved Archimedes method was used to test and analyze density–temperature properties of Ga, Sb and Ga–Sb melts. The experimental results indicated that the density of Ga₇Sb₉₃ melt shows a linear trend of decline when its temperature changes within the experimental range, whereas the densities of Ga_36.5Sb_63.5 and Ga₃₀Sb₇₀ melts show a non-continuous change near the melting point, which rises first and then drops abnormally. These results were analyzed from the perspective of a liquid–liquid structure transition according to the property changes of Ga–Sb melt.     

Hölder Continuity of the Integrated Density of States for the Fibonacci Hamiltonian

We obtain the asymptotics of the optimal global Hölder exponent of the integrated density of states of the Fibonacci Hamiltonian for large and small couplings.     

Lyapunov Exponent and Density of States of a One-Dimensional Non-Hermitian Schrödinger Equation

We calculate, using numerical methods, the Lyapunov exponent (E) and the density of states (E) at energy E of a one-dimensional non-Hermitian Schrödinger equation with off-diagonal disorder. For the particular case we consider, both (E) and (E) depend only on the modulus of E. We find a pronounced maximum of (|E|) at energy E=2/ , which seems to be linked to the fixed point structure of an associated random map. We show how the density of states (E) can be expanded in powers of E. We find (|E|)=(1/ ²)+(4/3 ³) |E|²+. This expansion, which seems to be asymptotic, can be carried out to an arbitrarily high order.     

Effects of Microphase Separation and Density–Density Correlations in Amorphous Polymer Films

Physics of the Solid State - The topology of density fluctuations on the surfaces of amorphous thin films prepared from solutions of some flexible-chain polymers has been studied based on electron...     

Variational Calculation of 4He Tetramer Ground and Excited States Using Realistic 4He–4He Potentials

We calculated binding energies and wave functions of the ⁴He tetramer ground and excited states employing various realistic ⁴He?⁴He potentials which includes the currently most accurate one with the adiabatic, relativistic, QED and residual retardation corrections. We used our Gaussian expansion method (GEM) for ab initio variational calculations of few-body systems. We found that precisely the same shape of the short-range correlation (r _ij < 4Å) in the dimer appear in the ground and excited states of trimer and tetramer. The four kinds of the binding energies of the trimer and tetramer ground and excited states, ${B_3^{(0)}, B_3^{(1)}, B_4^{(0)}}$ and ${B_4^{(1)}}$ , for the different potentials exhibit perfect linear correlations over the range of binding energies relevant for ⁴He atoms; namely, six types of the generalized atomic Tjon lines were observed.