From Chaos to Order in Mesoscopic Systems

Nazmitdinov, R. G.

doi:10.1134/s1547477119030154

Cited by 4 publications

(6 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This dependence of the quantum effects and bulk properties on the fractal structure, can be attributed to the interplay between regular and chaotic dynamics of particles, confined in fractal-like regions. This interplay in classical and quantum systems leads to the emergence of dynamical symmetries, and are related to the existence of conserved quantities of the dynamics and integrability under certain conditions [29].…”

Section: Introductionmentioning

confidence: 99%

Small-Angle Scattering from Fractals: Differentiating between Various Types of Structures

Anitas

2020

Symmetry

View full text Add to dashboard Cite

Small-angle scattering (SAS; X-rays, neutrons, light) is being increasingly used to better understand the structure of fractal-based materials and to describe their interaction at nano- and micro-scales. To this aim, several minimalist yet specific theoretical models which exploit the fractal symmetry have been developed to extract additional information from SAS data. Although this problem can be solved exactly for many particular fractal structures, due to the intrinsic limitations of the SAS method, the inverse scattering problem, i.e., determination of the fractal structure from the intensity curve, is ill-posed. However, fractals can be divided into various classes, not necessarily disjointed, with the most common being random, deterministic, mass, surface, pore, fat and multifractals. Each class has its own imprint on the scattering intensity, and although one cannot uniquely identify the structure of a fractal based solely on SAS data, one can differentiate between various classes to which they belong. This has important practical applications in correlating their structural properties with physical ones. The article reviews SAS from several fractal models with an emphasis on describing which information can be extracted from each class, and how this can be performed experimentally. To illustrate this procedure and to validate the theoretical models, numerical simulations based on Monte Carlo methods are performed.

show abstract

Section: Introductionmentioning

confidence: 99%

Small-Angle Scattering from Fractals: Differentiating between Various Types of Structures

Anitas

2020

Symmetry

View full text Add to dashboard Cite

show abstract

“…Thus, for the plane graphene sheet the full set of the operatorŜ t consists of the wave functions in Equations (18) and (19). These wave functions contain the equal mixture of the spin up and down states, associated with electrons that move in opposite directions of our structure.…”

Section: The Operatorŝ T = τ Y ⊗ Iσ Y Cmentioning

confidence: 99%

“…Let us analyse this situation in details. One can readily see that the eigenfunctions in Equations (18) and (19), associated with the flat graphene piece, are common eigenstates for the both operators:…”

Section: The Relation Between the Operatorsŝ T Andŝ Chmentioning

confidence: 99%

See 1 more Smart Citation

On Symmetry Properties of The Corrugated Graphene System

2020

View full text Add to dashboard Cite

The properties of the ballistic electron transport through a corrugated graphene system are analysed from the symmetry point of view. The corrugated system is modelled by a curved surface (an arc of a circle) connected from both sides to flat sheets. The spin–orbit couplings, induced by the curvature, give rise to equivalence between the transmission (reflection) probabilities of the transmitted (reflected) electrons with the opposite spin polarisation, incoming from opposite system sides. We find two integrals of motion that explain the chiral electron transport in the considered system.

show abstract

“…At the microscopic level, this corresponds to electrically neutral molecules or clusters of molecules. Problems related to formation and structure of these quantities [4] are beyond the scope of this article.…”

Section: Introductionmentioning

confidence: 99%

Symmetry Breaking in Stochastic Dynamics and Turbulence

2019

View full text Add to dashboard Cite

Symmetries play paramount roles in dynamics of physical systems. All theories of quantum physics and microworld including the fundamental Standard Model are constructed on the basis of symmetry principles. In classical physics, the importance and weight of these principles are the same as in quantum physics: dynamics of complex nonlinear statistical systems is straightforwardly dictated by their symmetry or its breaking, as we demonstrate on the example of developed (magneto)hydrodynamic turbulence and the related theoretical models. To simplify the problem, unbounded models are commonly used. However, turbulence is a mesoscopic phenomenon and the size of the system must be taken into account. It turns out that influence of outer length of turbulence is significant and can lead to intermittency. More precisely, we analyze the connection of phenomena such as behavior of statistical correlations of observable quantities, anomalous scaling, and generation of magnetic field by hydrodynamic fluctuations with symmetries such as Galilean symmetry, isotropy, spatial parity and their violation and finite size of the system.

show abstract

From Chaos to Order in Mesoscopic Systems

Cited by 4 publications

References 55 publications

Small-Angle Scattering from Fractals: Differentiating between Various Types of Structures

Small-Angle Scattering from Fractals: Differentiating between Various Types of Structures

On Symmetry Properties of The Corrugated Graphene System

Symmetry Breaking in Stochastic Dynamics and Turbulence

Contact Info

Product

Resources

About