Continuous transformation between ferro and antiferro circular structures in J1−J2−J3J_1-J_2-J_3 frustrated Heisenberg model

Frustrated magnetic compounds, in particular low-dimensional, are topical research due to persistent uncover of novel nontrivial quantum states and potential applications. The problem of this field is that many important results are scattered over the localized parameter ranges, while areas in between still contain hidden interesting effects. We consider $J_1-J_2-J_3$ Heisenberg model on the square lattice and use the spherically symmetric self-consistent approach for spin-spin Green's functions in "quasielastic" approximation. We have found a new local order in spin liquids: antiferromagnetic isotropical helices. On the structure factor we see circular concentric dispersionless structures, while on any radial direction the excitation spectrum has "roton" minima. That implies nontrivial magnetic excitations and consequences in magnetic susceptibility and thermodynamics. On the $J_1-J_2-J_3$ exchange parameters globe we discover a crossover between antiferromagnetic-like local order and ferromagnetic-like; we find stripe-like order in the middle. In fact, our "quasielastic" approach allows investigation of the whole $J_1-J_2-J_3$ globe.Comment: 9 pages, 12 figure

Is normalization necessary for stable model reference adaptive control?

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Conditions for Almost Global Attractivity of a Synchronous Generator Connected to an Infinite Bus

Conditions for existence and global attractivity of the equilibria of a realistic model of a synchronous generator with constant field current connected to an infinite bus are derived. First, necessary and sufficient conditions for existence and uniqueness of equilibrium points are provided. Then, sufficient conditions for local asymptotic stability and almost global attractivity of one of these equilibria are given. The analysis is carried out by employing a new Lyapunov–like function to establish convergence of bounded trajectories, while the latter is proven using the powerful theoretical framework of cell structures pioneered by Leonov and Noldus. The efficiency of the derived sufficient conditions is illustrated via extensive numerical experiments based on two benchmark examples taken from the literature

Almost Global Attractivity of a Synchronous Generator Connected to an Infinite Bus

The problem of deriving verifiable conditions for stability of the equilibria of a realistic model of a synchronous generator with constant field current connected to an infinite bus is studied in the paper. Necessary and sufficient conditions for existence and uniqueness of equilibrium points are provided. Furthermore, sufficient conditions for almost global attractivity are given. To carry out this analysis a new Lyapunov–like function is proposed to establish convergence of bounded trajectories, while the latter is proven using the powerful theoretical framework of cell structures pioneered by Leonov and Noldus

Relaxing the conditions of ISS for multistable periodic systems

The input-to-state stability property of nonlinear dynamical systems with multiple invariant solutions is analyzed under the assumption that the system equations are periodic with respect to certain state variables. It is shown that stability can be concluded via a sign-indefinite function, which explicitly takes the systems’ periodicity into account. The presented approach leverages some of the difficulties encountered in the analysis of periodic systems via positive definite Lyapunov functions proposed in Angeli and Efimov (2013, 2015). The new result is established based on the framework of cell structure introduced in Leonov (1974) and illustrated via the global analysis of a nonlinear pendulum with a constant persistent input

Many-Body Approch to Spin-Dependent Transport in Quantum Dot Systems

By means of a diagram technique for Hubbard operators we show the existence of a spin-dependent renormalization of the localized levels in an interacting region, e.g. quantum dot, modeled by the Anderson Hamiltonian with two conduction bands. It is shown that the renormalization of the levels with a given spin direction is due to kinematic interactions with the conduction sub-bands of the opposite spin. The consequence of this dressing of the localized levels is a drastically decreased tunneling current for ferromagnetically ordered leads compared to that of paramagnetically ordered leads. Furthermore, the studied system shows a spin-dependent resonant tunneling behaviour for ferromagnetically ordered leads.Comment: 8 pages, 5 figure

The J_1-J_2 antiferromagnet with Dzyaloshinskii-Moriya interaction on the square lattice: An exact diagonalization study

We examine the influence of an anisotropic interaction term of Dzyaloshinskii-Moriya (DM) type on the groundstate ordering of the J_1-J_2 spin-1/2-Heisenberg antiferromagnet on the square lattice. For the DM term we consider several symmetries corresponding to different crystal structures. For the pure J_1-J_2 model there are strong indications for a quantum spin liquid in the region of 0.4 < J_2/J_1 < 0.65. We find that a DM interaction influences the breakdown of the conventional antiferromagnetic order by i) shifting the spin liquid region, ii) changing the isotropic character of the groundstate towards anisotropic correlations and iii) creating for certain symmetries a net ferromagnetic moment.Comment: 7 pages, RevTeX, 6 ps-figures, to appear in J. Phys.: Cond. Ma

The 51^{51}Cr neutrino source and Borexino: a desirable marriage

Exposure to a $^{51}$Cr neutrino source as that used in Gallex will provide an excellent overall performance test of Borexino, which should collect about 1400 source induced events, with an initial rate of about 35 counts per day. This will be particularly important if MSW-small-angle turns out to be the solution of the solar neutrino problem. In addition, if an independent, accurate calibration is available, one will have an interesting experiment on neutrino properties: as an example, a neutrino magnetic moment of the order $5\cdot10^{-11}\mu_B$could be detected/excluded at the 90\% C.L.Comment: 7 pages, RevTeX, plus 3 postscripts figures, tarred, compresse