Numerical method for disordered quantum phase transitions in the large−N-N limit

We develop an efficient numerical method to study the quantum critical behavior of disordered systems with $\mathcal{O}(N)$ order-parameter symmetry in the large$-N$ limit. It is based on the iterative solution of the large$-N$ saddle-point equations combined with a fast algorithm for inverting the arising large sparse random matrices. As an example, we consider the superconductor-metal quantum phase transition in disordered nanowires. We study the behavior of various observables near the quantum phase transition. Our results agree with recent renormalization group predictions, i.e., the transition is governed by an infinite-randomness critical point, accompanied by quantum Griffiths singularities. Our method is highly efficient because the numerical effort for each iteration scales linearly with the system size. This allows us to study larger systems, with up to 1024 sites, than previous methods. We also discuss generalizations to higher dimensions and other systems including the itinerant antiferomagnetic transitions in disordered metals.Comment: 8 pages, 6 eps figures, published versio

Quantum Griffiths singularities in ferromagnetic metals

We present a theory of the quantum Griffiths phases associated with the ferromagnetic quantum phase transition in disordered metals. For Ising spin symmetry, we study the dynamics of a single rare region within the variational instanton approach. For Heisenberg symmetry, the dynamics of the rare region is studied using a renormalization group approach. In both cases, the rare region dynamics is even slower than in the usual quantum Griffiths case because the order parameter conservation of an itinerant ferromagnet hampers the relaxation of large magnetic clusters. The resulting quantum Griffiths singularities in ferromagnetic metals are stronger than power laws. For example, the low-energy density of states $\rho(\epsilon)$ takes the asymptotic form $\exp[\{-\tilde{\lambda}\log (\epsilon_0/\epsilon)\}^{3/5}]/\epsilon$ with $\tilde{\lambda}$ being non-universal. We contrast these results with the antiferromagnetic case in which the systems show power-law quantum Griffiths singularities in the vicinity of the quantum critical point. We also compare our result with existing experimental data of ferromagnetic alloy ${\rm{Ni}}_{x}{\rm{V}}_{1-x}$.Comment: 7 pages, 1 eps figure, published versio

Contact process on generalized Fibonacci chains: infinite-modulation criticality and double-log periodic oscillations

We study the nonequilibrium phase transition of the contact process with aperiodic transition rates using a real-space renormalization group as well as Monte-Carlo simulations. The transition rates are modulated according to the generalized Fibonacci sequences defined by the inflation rules A $\to$ AB$^k$ and B $\to$ A. For $k=1$ and 2, the aperiodic fluctuations are irrelevant, and the nonequilibrium transition is in the clean directed percolation universality class. For $k\ge 3$, the aperiodic fluctuations are relevant. We develop a complete theory of the resulting unconventional "infinite-modulation" critical point which is characterized by activated dynamical scaling. Moreover, observables such as the survival probability and the size of the active cloud display pronounced double-log periodic oscillations in time which reflect the discrete scale invariance of the aperiodic chains. We illustrate our theory by extensive numerical results, and we discuss relations to phase transitions in other quasiperiodic systems.Comment: 12 pages, 9 eps figures included, final version as publishe

Radiation immunity in cable harnesses and differential P/N skew in PCB

We develop an efficient method to model RF immunity of multiwire cable harnesses and study differential P/N skew effects on channels, channel performance and specifically on the eye diagrams at the SerDes receiver. External radiation can induce unwanted signals in transmission lines. For example, external radiation from an antenna induces common-mode currents on the outer surface of cable shields. This common-mode signal makes its way through the shied due to its imperfections, inducing the inner common mode. When twisted pairs inside the cable are not balanced, inner common mode is in turn converted to the differential mode, which might compromise performance of sensitive electronics connected to the cable harness. In paper I, we develop the equivalent circuit model and the methodology for prediction of the worst-case envelope for differential mode signals induced in cable harnesses placed over a ground plane. The cable harness consists of twisted wires which are slightly unbalanced within the harness connector region. The induced signals are calculated using the transmission line theory avoiding the need for any 3D calculations. The results are validated by experimental measurements. Differential P/N skew is one of the main performance-limiting issue for high-speed SerDes links. The P/N skew is arrival time difference between two single-ended signals in a differential pair. It is commonly caused by unmatched delays of P/N lines of a differential pair but even for perfectly matched physical length cases, P/N skew can be caused by any other asymmetry between P/N lines. In the printed circuit board, relative location of fiber bundles with respect to conductors is random and results in uncontrolled P/N skew. In papers II, III, we derive analytical equations for S-parameters as a function of the P/N skew and frequency for weakly and strong coupled transmission lines. We also study the P/N skew effect on SerDes performance by measurements --Abstract, page v

Quantum phase transitions in disordered magnets

We study the effects of quenched weak disorder on quantum phase transitions in disordered magnets. The presence of disorder in the system can lead to a variety of exotic phenomena, e.g., the smearing of transitions or quantum Griffiths singularities. Phase transitions are smeared if individual spatial regions can order independently of the bulk system. In paper I, we study smeared quantum phase transitions in binary alloys A₁₋ₓBₓ that are tuned by changing the composition x. We show that in this case the ordered phase is extended over all compositions x \u3c 1. We also study the composition dependence of observables. In paper II, we investigate the influence of spatial disorder correlations on smeared phase transitions. As an experimental example, we demonstrate in paper III, that the composition-driven ferromagnetic-toparamagnetic quantum phase transition in Sr₁₋ₓCaₓ RuO₃ is smeared. When individual spatial regions cannot order but fluctuate slowly, the phase transition is characterized by strong singularities in the quantum Griffiths phase. In paper IV, we develop a theory of the quantum Griffiths phases in disordered ferromagnetic metals. We show that the quantum Griffiths singularities are stronger than the usual power-law quantum Griffiths singularities in insulating magnets. In paper V, we present an efficient numerical method for studying quantum phase transitions in disordered systems with O(N) order parameter symmetry in the large-N limit. Our algorithm solves iteratively the large-N self-consistent equations for the renormalized distances from criticality. Paper VI is devoted to the study of transport properties in the quantum Griffiths phase associated with the antiferromagnetic quantum phase transition in a metal. We find unusual behavior of transport properties which is in contrast to the normal Fermi-liquid behavior --Abstract, page v

Impediments to the development of European Union's common security and defence policy

The global geopolitical rift has presented challenges as Russia's revisionism policy, a spread of Islamic extremism and terrorism, instability in Eastern and Southern neighbourhood causing migration crisis, the rise of ultranationalist populism igniting Euro-scepticism. The situation requires a coherent and comprehensive approach from the European Union, however, we observe the lack of motivation and sufficient instruments to react. The European security initiatives finally resulted into Common Security and Defence Policy (CSDP), however, Europeans inability to deliver an effective response to existing challenges is encapsulated into impediments derived from differences of views and goals of leading EU members. Therefore this work is designed to explore European security and defence initiative focusing on problem why CSDP failed to expand and develop deeper, and respond to the research question what are such a wide differences of views on CSDP of leading European countries such as the UK, France and Germany? Our tasks in the dissertation are at first to identify major strategic divergences of leading EU member states such as the UK, France, and Germany and secondly to identify and describe key factors that have contributed to those strategic divergences. To respond stated research tasks within dissertation has been used case study method exploring three EU state to see differences in their motivations and goals and trace the process in order to identify key ruptures which facilitated impediments to European security initiative. During research, we identified stumbling blocks which have been generalised into conclusion. It emphasises major problem of post-World War II European order inherited in modernity where the USA holds hegemonic power and plays the decisive role in foreign and security affairs of Europe preventing the emergence of European power core. The nature of EU and its internal settings are also causing for the imperfection of system which cannot overcome obstruction and develop the common defence. In addition, some states perceive European integration in foreign and security area as a threat to own sovereignty inducing them to act it in opposition.http://www.ester.ee/record=b4684484*es

Modification of smeared phase transitions by spatial disorder correlations

Phase transitions in disordered systems can be smeared if rare spatial regions develop true static order while the bulk system is in the disordered phase. Here, we study the effects of spatial disorder correlations on such smeared phase transitions. The behaviors of observables are determined within optimal fluctuation theory. We show that even short-range correlations can qualitatively modify smeared phase transitions. For positive correlations (like impurity atoms attract each other), the order parameter is enhanced, while it is suppressed for repulsive correlations (like atoms repel each other). We use computer simulations to generate various types of disorder correlations, and to verify our theoretical predictions.Comment: submitted to the Proceedings of the XVII Training Course in the Physics of Strongly Correlated Systems, builds on arXiv:1109.4290, 5 pages, 2 figure