Dynamic mean-field and cavity methods for diluted Ising systems

We compare dynamic mean-field and dynamic cavity as methods to describe the stationary states of dilute kinetic Ising models. We compute dynamic mean-field theory by expanding in interaction strength to third order, and compare to the exact dynamic mean-field theory for fully asymmetric networks. We show that in diluted networks the dynamic cavity method generally predicts magnetizations of individual spins better than both first order ("naive") and second order ("TAP") dynamic mean field theory

The dynamic magnetic behaviors of the Blume-Capel Ising bilayer system

The dynamic magnetic behaviors of the spin-1 Blume-Capel Ising bilayer system (BCIS) are studied in an oscillating external magnetic field on a two-layer square lattice by utilizing the mean field theory based on Glauber-type stochastic dynamics (DMFT). The dynamic equations describing the time-dependencies of the average magnetizations are obtained with the Master equation. The dynamic phases in this system are found by solving these dynamic equations. The temperature dependence of the dynamic order parameters is examined to characterize the nature (continuous or discontinuous) of the phase transitions and to obtain the dynamic phase transition points (DPT). The dynamic phase diagrams are shown for ferromagnetic / ferromagnetic, antiferromagnetic / antiferromagnetic, antiferromagnetic / antiferromagnetic interactions in the plane of the reduced temperature versus magnetic field amplitude and they display dynamic tricritical and reentrant behavior as well as the dynamic triple point

Unifying static and dynamic properties in 3D quantum antiferromagnets

Quantum Monte Carlo simulations offer an unbiased means to study the static and dynamic properties of quantum critical systems, while quantum field theory provides direct analytical results. We study three dimensional, critical quantum antiferromagnets by performing a combined analysis using both quantum field theory calculations and quantum Monte Carlo data. Explicitly, we analyze the order parameter (staggered magnetization), N\'eel temperature, quasiparticle gaps, and the susceptibilities in the scalar and vector channels. We connect the two approaches by deriving descriptions of the quantum Monte Carlo observables in terms of the quasiparticle excitations of the field theory. The remarkable agreement not only unifies the description of the static and dynamic properties of the system, but also constitutes a thorough test of perturbative O(3) quantum field theory and opens new avenues for the analytical guidance of detailed numerical studies.Comment: New, improved, extended discussion throughout and in particular of Higgs linewidth compariso

Static and Dynamic Chain Structures in the Mean-Field Theory

We give a brief overview of recent work examining the presence of $\alpha$-clusters in light nuclei within the Skyrme-force Hartree-Fock model. Of special significance are investigations into $\alpha$-chain structures in carbon isotopes and $^{16}$O. Their stability and possible role in fusion reactions are examined in static and time-dependent Hartree-Fock calculations. We find a new type of shape transition in collisions and a centrifugal stabilization of the $4\alpha$ chain state in a limited range of angular momenta. No stabilization is found for the $3\alpha$ chain.Comment: Fusionn 11 Conference, St. Malo, France, 201

Modeling multiple time scales during glass formation with phase-field crystals

The dynamics of glass formation in monatomic and binary liquids are studied numerically using a microscopic field theory for the evolution of the time-averaged atomic number density. A stochastic framework combining phase field crystal free energies and dynamic density functional theory is shown to successfully describe several aspects of glass formation over multiple time scales. Agreement with mode coupling theory is demonstrated for underdamped liquids at moderate supercoolings, and a rapidly growing dynamic correlation length is found to be associated with fragile behavior.Comment: 4+ pages, 4 figures, to appear in Physical Review Letter

Mean field and Monte Carlo studies of the magnetization-reversal transition in the Ising model

Detailed mean field and Monte Carlo studies of the dynamic magnetization-reversal transition in the Ising model in its ordered phase under a competing external magnetic field of finite duration have been presented here. Approximate analytical treatment of the mean field equations of motion shows the existence of diverging length and time scales across this dynamic transition phase boundary. These are also supported by numerical solutions of the complete mean field equations of motion and the Monte Carlo study of the system evolving under Glauber dynamics in both two and three dimensions. Classical nucleation theory predicts different mechanisms of domain growth in two regimes marked by the strength of the external field, and the nature of the Monte Carlo phase boundary can be comprehended satisfactorily using the theory. The order of the transition changes from a continuous to a discontinuous one as one crosses over from coalescence regime (stronger field) to nucleation regime (weaker field). Finite size scaling theory can be applied in the coalescence regime, where the best fit estimates of the critical exponents are obtained for two and three dimensions.Comment: 16 pages latex, 13 ps figures, typos corrected, references adde

Two-site dynamical mean field theory for the dynamic Hubbard model

At zero temperature, two-site dynamical mean field theory is applied to the Dynamic Hubbard model. The Dynamic Hubbard model describes the orbital relaxation that occurs when two electrons occupy the same site, by using a two-level boson field at each site. At finite boson frequency, the appearance of a Mott gap is found to be enhanced even though it shows a metallic phase with the same bare on-site interaction $U$ in the conventional Hubbard model. The lack of electron-hole symmetry is highlighted through the quasi-particle weight and the single particle density of states at different fillings, which qualitatively differentiates the dynamic Hubbard model from other conventional Hubbard-like models.Comment: 13 pages, 15 figure

Optimization of quantum cascade laser operation by geometric design of cascade active band in open and closed models

Using the effective mass and rectangular potential approximations, the theory of electron dynamic conductivity is developed for the plane multilayer resonance tunnel structure placed into a constant electric field within the model of open nanosystem, and oscillator forces of quantum transitions within the model of closed nanosystem. For the experimentally produced quantum cascade laser with four-barrier active band of separate cascade, it is proven that just the theory of dynamic conductivity in the model of open cascade most adequately describes the radiation of high frequency electromagnetic field while the electrons transport through the resonance tunnel structure driven by a constant electric field.Comment: 10 pages, 2 figure