Related papers: Power dissipation in fractal AC circuits
Since the recent dissertation by Steffen Winter, for certain self-similar sets $F$ the growth behaviour of the Minkowski functionals of the parallel sets $F_\varepsilon := \{x\in \mathbb R^d : d(x,F)\leq \varepsilon\}$ as $\varepsilon…
A new approach is introduced to study QCD amplitudes at high energy and comparatively small momentum transfer. Novel cut diagrams, representing resummation of Feynman diagrams, are used to simplify calculation and to avoid delicate…
Diffusion of electrons in two-dimensional disordered systems with spin-orbit interactions is investigated numerically. Asymptotic behaviors of the second moment of the wave packet and of the temporal auto-correlation function are examined.…
We derive a set of isometric fluctuation relations, which constrain the order parameter fluctuations in finite-size systems at equilibrium and in the presence of a broken symmetry. These relations are exact and should apply generally to…
Understanding and analyzing cascading failures in power grids have been the focus of many researchers for years. However, the complex interactions among the large number of components in these systems and their contributions to cascading…
Numerical simulations based on electronic structure calculations are finding ever growing applications in many areas of physics. A major limiting factor is however the cubic scaling of the algorithms used. Building on previous work [F. R.…
In a recent paper, we combined the technique of bosonization with the concept of a Rayleigh dissipation function to develop a model for resistances in one-dimensional systems of interacting spinless electrons [arXiv:1011.5058]. We also…
We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several…
The properties of a fictitious, fermionic, many-body system based on the complex zeros of the Riemann zeta function are studied. The imaginary part of the zeros are interpreted as mean-field single-particle energies, and one fills them up…
In this paper, we give a review of fractal calculus which is an expansion of standard calculus. Fractal calculus is applied for functions which are not differentiable or integrable on totally disconnected fractal sets such as middle-$\mu$…
A new statistical model for the combined effects of decoherence, energy redistribution and dissipation on electron transport in large quantum systems is introduced. The essential idea is to consider the electron phase information to be lost…
Self-similar structures occur naturally and have been employed to engineer exotic physical properties. Here we show that acoustic modes of a fractal-like system of tensioned strings can display increased mechanical quality factors due to…
In this work, we introduce new methods for the quantization, decomposition, and extraction (from electromagnetic simulations) of lumped-element circuit models for superconducting quantum devices. Our flux-charge symmetric procedures center…
The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…
We develop a numerically exact method for the summation of irreducible Feynman diagrams for fermionic self-energy in the thermodynamic limit. The technique, based on the Diagrammatic Determinant Monte Carlo and its recent extension to…
We report some new applications of functional complex networks on acoustic emission waveforms from frictional interfaces. Our results show that laboratory faults undergo a sequence of generic phases as well as strengthening, weakening or…
Power grids exhibit patterns of reaction to outages similar to complex networks. Blackout sequences follow power laws, as complex systems operating near a critical point. Here, the tolerance of electric power grids to both accidental and…
Partial energy fluctuations are known tools to reconstruct microcanonical heat capacities. For experimental applications, approximations have been developed to infer fluctuations at freeze out from the observed fragment partitions. The…
While the universe becomes more and more homogeneous at large scales, statistical analysis of galaxy catalogs have revealed a fractal structure at small-scales (\lambda < 100 h^{-1} Mpc), with a fractal dimension D=1.5-2 (Sylos Labini et al…
In the quest to produce quantum technology, superconducting networks, working at temperatures just above absolute zero, have arisen as one of the most promising physical implementations. The precise analysis and synthesis of such circuits…