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Peter Markoš

Publications and source records attributed to Peter Markoš.

8 recordsLinked to original sources
arXiv2025

On the dynamics of the Meissner and the Becker-London effects

It is generally accepted that the most fundamental property of a superconductor is that it exhibits the Meissner effect. Of similar importance is the Becker-London effect, i.e. generation of magnetic field inside a rotating superconductor. Hirsch has recently pointed out that, within the conventional theory of superconductivity, the question about how these effects are generated dynamically has not even been asked yet. Here we fill in this gap in the literature by a detailed study of the evolution of the electromagnetic field for both of these effects. To this end, we solve the Maxwell equations supplemented by the simplest conventional constitutive equation for a superconductor, namely the London equation. We demonstrate that, contrary to the expectations of Hirsch, the conventional theory does correctly describe the dynamics of both, the Meissner and the Becker-London effect. We find that the dynamics of the studied processes is quite rich and interesting even at this level of description.

cond-mat.supr-con↗
arXiv2023

Low-Dimensional Life of Critical Anderson Electron

We show that critical Anderson electron in 3 dimensions is present in its spatial effective support, which was recently determined to be a region of fractal dimension $\approx \! 8/3$, with probability 1 in infinite volume. Hence, its physics is fully confined to space of this lower dimension. Stated differently, effective description of space occupied by critical Anderson electron becomes a full description in infinite volume. We then show that it is a general feature of the effective counting dimension underlying these concepts, that its subnominal value implies an exact description by effective support.

cond-mat.dis-nn↗
arXiv2023

Counting-Based Effective Dimension and Discrete Regularizations

Fractal-like structures of varying complexity are common in nature, and measure-based dimensions (Minkowski, Hausdorff) supply their basic geometric characterization. However, at the level of fundamental dynamics, which is quantum, structure does not enter via geometry of fixed sets but is encoded in probability distributions on associated spaces. The question then arises whether a robust notion of fractal measure-based dimension exists for structures represented in this way. Starting from effective number theory, we construct all counting-based schemes to select effective supports on collections of objects with probabilities and associate the effective counting dimension (ECD) with each. We then show that ECD is scheme-independent and, thus, a well-defined measure-based dimension with meaning analogous to the Minkowski dimension of fixed sets. In physics language, ECD characterizes probabilistic descriptions arising in a theory or model via discrete ``regularization''. For example, our analysis makes recent surprising results on effective spatial dimensions in quantum chromodynamics and Anderson models well founded. We discuss how to assess the reliability of regularization removals in practice and perform such analysis in the context of 3d Anderson criticality.

hep-lat↗
arXiv2022

Topological Dimensions from Disorder and Quantum Mechanics?

We have recently shown that critical Anderson electron in $D=3$ dimensions effectively occupies a spatial region of infrared (IR) scaling dimension $d_\text{IR} \approx 8/3$. Here we inquire about the dimensional substructure involved. We partition space into regions of equal quantum occurrence probability, such that points comprising a region are of similar relevance, and calculate the IR scaling dimension $d$ of each. This allows us to infer the probability density $p(d)$ for dimension $d$ to be accessed by electron. We find that $p(d)$ has a strong peak at $d$ very close to 2. In fact, our data suggests that $p(d)$ is non-zero on the interval $[d_\text{min}, d_\text{max}] \approx [4/3,8/3]$ and may develop a discrete part ($δ$-function) at $d=2$ in infinite-volume limit. The latter invokes the possibility that combination of quantum mechanics and pure disorder can lead to emergence of topological dimensions. Although $d_\text{IR}$ is based on effective counting of which $p(d)$ has no a priori knowledge, $d_\text{IR} \ge d_\text{max}$ is an exact feature of the ensuing formalism. Possible connection of our results to recent findings of $d_\text{IR} \approx 2$ in Dirac near-zero modes of thermal quantum chromodynamics is emphasized.

cond-mat.dis-nn↗
arXiv2022

Super-Universality in Anderson Localization

We calculate the effective spatial dimension $d_\text{IR}$ of electron modes at critical points of 3D Anderson models in various universality classes (O,U,S,AIII). The results are equal within errors, and suggest the super-universal value $d_\text{IR} \!=\! 2.665(3) \!\approx\! 8/3$. The existence of such a unique marker may help identify natural processes driven by Anderson localization, and provide new insight into the spatial geometry of Anderson transitions. The recently introduced $d_\text{IR}$ is a measure-based dimension of Minkowski/Hausdorff type, designed to characterize probability-induced effective subsets.

cond-mat.dis-nn↗
arXiv2002

Scaling of the conductance distribution near the Anderson transition

The single parameter scaling hypothesis is the foundation of our understanding of the Anderson transition. However, the conductance of a disordered system is a fluctuating quantity which does not obey a one parameter scaling law. It is essential to investigate the scaling of the full conductance distribution to establish the scaling hypothesis. We present a clear cut numerical demonstration that the conductance distribution indeed obeys one parameter scaling near the Anderson transition.

cond-mat.dis-nn↗
arXiv2001

Reconciling Conductance Fluctuations and the Scaling Theory of Localization

We reconcile the phenomenon of mesoscopic conductance fluctuations with the single parameter scaling theory of the Anderson transition. We calculate three averages of the conductance distribution: $\exp(<\ln g>)$, $ $ and $1/ $ where $g$ is the conductance in units of $e^2/h$ and $R=1/g$ is the resistance and demonstrate that these quantities obey single parameter scaling laws. We obtain consistent estimates of the critical exponent from the scaling of all these quantities.

cond-mat.dis-nn↗