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A new variational method for studying the equilibrium states of an interacting particles system has been proposed. The statistical description of the system is realized by means of a density matrix. This method is used for description of…
We study the effect of surface scattering on transport properties in many-mode conducting channels (electron waveguides). Assuming a strong roughness of the surface profiles, we show that there are two independent control parameters that…
This work deals with the average scattering entropy of quantum graphs. We explore this concept in several distinct scenarios that involve periodic, aperiodic and random distribution of vertices of distinct degrees. In particular, we compare…
We study spectral and transport properties of one-dimensional tight-binding $\mathcal{PT}$-symmetric chains with alternating couplings. Based on the transfer matrix method, we have analytically developed the expressions for the transmission…
In this paper, we consider a one-dimensional random geometric graph process with the inter-nodal gaps evolving according to an exponential AR(1) process, which may serve as a mobile wireless network model. The transition probability matrix…
We consider the scattering matrix approach to quantum electron transport in meso- and nano-conductors. This approach is an alternative to the more conventional kinetic equation and Green's function approaches, and often is more efficient…
In this research work, roll-to-roll chemical vapor deposited graphene device electronic transport properties are benchmarked to elucidate and comprehend mobility degradation in the real-world commercial application of graphene devices.…
The main features of the conductivity of doped single layer graphene are analyzed, and models for different scattering mechanisms are presented.
By decoupling the geometric from the dynamical contributions in the scattering processes, we develop a method to compute the scattering matrix of electrons in a one-dimensional coherent conductor connected to two electrodes. In particular,…
This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for…
We have applied the Numerical Renormalization Group method to study a mesoscopic system consisting of two samples of metal separated by an insulating barrier, with nanometer dimensions, which allows the tunnelling of a single electron from…
Direct transport processes play an important role in wireless communications where an ideal setup uses microwave fields to establish reliable communication channels between transmitter and receiver. But it is inherent to the problem that…
Statistical properties of coherent radiation propagating in a quasi - 1D random media is studied in the framework of random matrix theory. Distribution functions for the total transmission coefficient and the angular transmission…
Scattering transforms are non-trainable deep convolutional architectures that exploit the multi-scale resolution of a wavelet filter bank to obtain an appropriate representation of data. More importantly, they are proven invariant to…
We study diffusion of information packets on several classes of structured networks. Packets diffuse from a randomly chosen node to a specified destination in the network. As local transport rules we consider random diffusion and an…
The scattering transform is a multilayered wavelet-based deep learning architecture that acts as a model of convolutional neural networks. Recently, several works have introduced generalizations of the scattering transform for non-Euclidean…
The intrinsic dynamical complexity of classically chaotic systems enforces a universal description of the transport properties of their wave-mechanical analogues. These universal rules have been established within the framework of linear…
The influence of electron-electron scattering on the distribution function and transport characteristics of intrinsic monolayer graphene is investigated via an ensemble Monte Carlo simulation. Due to the linear dispersion relation in the…
A geometric view of the possible outcomes of elastic collisions of two massive bodies is developed that integrates laboratory, center of mass, and relative body frames in a single diagram. From these diagrams all the scattering properties…
We consider the distribution of the transmission coefficients, i.e. the singular values of the modal transmission matrix, for 2D random media with periodic boundary conditions composed of a large number of point-like non-absorbing…