Coherent motion in the interaction model of cold glasses

We have studied the collective phenomena of multicomponent glasses at ultra low temperatures [Strehlow, et. al, Phys. Rev. Lett 80, 5361 (1998)] by taking into account the proper interaction between tunneling centers. We have considered both double and triple well potentials with different types of interactions. We show that a phase with coherent motion appears for a range of parameters when the path of tunneling is coursed by an interaction of the XY type, while the usual Ising like interaction does not lead to the expected collective phenomena. In the phase of coherent motion, the dipole moment and the low-energy levels oscillate with a frequency proportional to the number of tunneling centers in the system. Simultaneous level crossing occurs between the ground and first excited states. The effects of long-range interactions and also of random couplings have been also studied for a one- and two-dimensional array of tunneling centers. We find that long-range interactions do not affect the coherent motion, while a wide distribution of random couplings destroys the collective effects.Comment: 11 pages, 11 figures, shorter version appears in Phys. rev.

Synthesis of nonlinear control strategies from fuzzy logic control algorithms

Fuzzy control has been recognized as an alternative to conventional control techniques in situations where the plant model is not sufficiently well known to warrant the application of conventional control techniques. Precisely what fuzzy control does and how it does what it does is not quite clear, however. This important issue is discussed and in particular it is shown how a given fuzzy control scheme can resolve into a nonlinear control law and that in those situations the success of fuzzy control hinges on its ability to compensate for nonlinearities in plant dynamics

Phase diagram of J1-J2 transverse field Ising model on the checkerboard lattice: a plaquette-operator approach

We study the effect of quantum fluctuations by means of a transverse magnetic field ($\Gamma$) on the antiferromagnetic $J_1-J_2$ Ising model on the checkerboard lattice, the two dimensional version of the pyrochlore lattice. The zero-temperature phase diagram of the model has been obtained by employing a plaquette operator approach (POA). The plaquette operator formalism bosonizes the model, in which a single boson is associated to each eigenstate of a plaquette and the inter-plaquette interactions define an effective Hamiltonian. The excitations of a plaquette would represent an-harmonic fluctuations of the model, which lead not only to lower the excitation energy compared with a single-spin flip but also to lift the extensive degeneracy in favor of a plaquette ordered solid (RPS) state, which breaks lattice translational symmetry, in addition to a unique collinear phase for $J_2>J_1$. The bosonic excitation gap vanishes at the critical points to the N\'{e}el ($J_2 < J_1$) and collinear ($J_2 > J_1$) ordered phases, which defines the critical phase boundaries. At the homogeneous coupling ($J_2=J_1$) and its close neighborhood, the (canted) RPS state, established from an-harmonic fluctuations, lasts for low fields, $\Gamma/J_1\lesssim 0.3$, which is followed by a transition to the quantum paramagnet (polarized) phase at high fields. The transition from RPS state to the N\'{e}el phase is either a deconfined quantum phase transition or a first order one, however a continuous transition occurs between RPS and collinear phases.Comment: To appear in EPJB, 12 pages, 15 figures, 1 tabl

Numerical study of the primary instability in a separated boundary layer transition under elevated free-stream turbulence

Numerical studies of laminar-to-turbulent transition in a separation bubble subjected to two free-stream turbulence levels (FST) have been performed using Large-Eddy Simulation (LES). Separation of the laminar boundary layer occurs at a curvature change over a plate with a semi-circular leading edge at Re = 3450 based on the plate thickness and the uniform inlet velocity. A numerical trip is used to produce the targeted free-stream turbulence levels and the decay of free-stream turbulence is well predicted. A dynamic sub-grid-scale model is employed in the current study and a good agreement has been obtained between the LES results and the experimental data. Detailed analysis of the LES data has been carried out to investigate the primary instability mechanism. The flow visualisations and spectral analysis of the separated shear layer reveal that the 2D Kelvin-Helmholtz instability mode, well known to occur at low FST levels, is bypassed at higher levels leading to earlier breakdown to turbulence

Thermodynamic Properties of XXZ model in a Transverse Field

We have numerically studied the thermodynamic properties of the spin 1/2 XXZ chain in the presence of a transverse (non commuting) magnetic field. The thermal, field dependence of specific heat and correlation functions for chains up to 20 sites have been calculated. The area where the specific heat decays exponentially is considered as a measure of the energy gap. We have also obtained the exchange interaction between chains in a bulk material using the random phase approximation and derived the phase diagram of the three dimensional material with this approximation. The behavior of the structure factor at different momenta verifies the antiferromagnetic long range order in y-direction for the three dimensional case. Moreover, we have concluded that the Low Temperature Lanczos results [M. Aichhorn et al., Phys. Rev. B 67, 161103(R) (2003)] are more accurate for low temperatures and closer to the full diagonalization ones than the results of Finite Temperature Lanczos Method [J. Jaklic and P. Prelovsek, Phys. Rev. B 49, 5065 (1994)].Comment: 7 pages, 10 eps figure