Computational Approach to Dissipative Nonequilibrium Phenomena in Quantum Magnets

Edwin Miles Stoudenmire

Vladimir V. Prudnikov, Pavel Vladimirovich Prudnikov, P. N. Malyarenko +1 more

Abstract The influence of various initial magnetizations m0 and structural defects on the nonequilibrium critical behavior of the two-dimensional Ising model is numerically simulated by Monte Carlo methods. Based on analysis of the time dependence of magnetization and the two-time dependences of autocorrelation function and dynamic susceptibility, we revealed the influence of logarithmic corrections and the crossover phenomena of percolation behavior on the nonequilibrium characteristics and the critical exponents. Violation of the fluctuation–dissipation theorem is studied, and the limiting fluctuation–dissipation ratio is calculated for the case of high-temperature initial state. The influence of various initial states on the limiting fluctuation–dissipation ratio is investigated. The nonequilibrium critical dynamics of weakly disordered systems with spin concentrations p ≥ 0.9 is shown to belong to the universality class of the nonequilibrium critical behavior of the pure model and to be characterized by the same critical exponents and the same limiting fluctuation–dissipation ratios. The nonequilibrium critical behavior of systems with p ≤ 0.85 demonstrates that the universal characteristics of the nonequilibrium critical behavior depend on the defect concentration and the dynamic scaling is violated, which is related to the influence of the crossover effects of percolation behavior.

Stephan Langer, Markus Heyl, Ian P. McCulloch +1 more

A. O. Caldeira

Reviewing macroscopic quantum phenomena and quantum dissipation, from the phenomenology of magnetism and superconductivity to the presentation of alternative models for quantum dissipation, this book develops the basic material necessary to understand the quantum dynamics of macroscopic variables. Macroscopic quantum phenomena are presented through several examples in magnetism and superconductivity, developed from general phenomenological approaches to each area. Dissipation naturally plays an important role in these phenomena, and therefore semi-empirical models for quantum dissipation are introduced and applied to the study of a few important quantum mechanical effects. The book also discusses the relevance of macroscopic quantum phenomena to the control of meso- or nanoscopic devices, particularly those with potential applications in quantum computation or quantum information. It is ideal for graduate students and researchers.

Andrei A. Fedorenko, S Trimper

We adapt the nonlinear σ model to study the nonequilibrium critical dynamics of O( n ) symmetric ferromagnetic system. Using the renormalization group analysis in d = 2 + ε dimensions we investigate the pure relaxation of the system starting from a completely ordered state. We find that the average magnetization obeys the long-time scaling behaviour almost immediately after the system starts to evolve while the correlation and response functions demonstrate scaling behaviour which is typical for aging phenomena. The corresponding fluctuation-dissipation ratio is computed to first order in ε and the relation between transverse and longitudinal fluctuations is discussed.

Philip C. E. Stamp