Related papers: A transfer matrix method for the analysis of fract…
A pair of scattering potentials are called $\alpha$-equivalent if they have identical scattering properties for incident plane waves with wavenumber $k\leq\alpha$ (energy $k^2\leq\alpha^2$.) We use a recently developed multidimensional…
Quantum transmissions of a free particle passing through a rectangular potential barrier with dissipation are studied using a path decomposition technique. Dissipative processes strongly suppress the transmission probability at resonance…
The problem of one-dimensional quantum wire along which a moving particle interacts with a linear array of N delta-function potentials is studied. Using a quantum waveguide approach, the transfer matrix is calculated to obtain the…
Several matrix approaches were developed to control light propagation through multiple scattering media under illumination of ultrashort pulses of light. These matrices can be recorded either with spectral or temporal resolution. Thanks to…
In this paper, we consider a nonlinear integral eigenvalue problem, which is a reformulation of the transmission eigenvalue problem arising in the inverse scattering theory. The boundary element method is employed for discretization, which…
The scattering of massless fermions on a one-dimensional Q-ball is studied both analytically and numerically in the background field approximation. The wave functions of the fermionic scattering states are found in analytical form. General…
We introduce a new transfer matrix method for calculating the thermodynamic properties of random-tiling models of quasicrystals in any number of dimensions, and describe how it may be used to calculate the phason elastic properties of these…
A 1-dimensional model for coherent quantum energy transfer through a complex of compressible boxes is investigated by numerical integration of the time-dependent Schr\"odinger equation. Energy is communicated from one box to the next by the…
The fractal character of some quantum properties has been shown for systems described by continuous variables. Here, a definition of quantum fractal states is given that suits the discrete systems used in quantum information processing,…
Radial Bragg gratings are commonly used to enhance light extraction from quantum emitters, but lack a well-suited, fast simulation method for optimization beyond periodic designs. To overcome this limitation, we propose and demonstrate an…
In this paper we study scattering of two-dimensional massless Dirac fermions by a potential that depends on a single Cartesian variable. Depending on the energy of the incoming particle and its angle of incidence, there are three different…
A quantum scattering theory is developed for Fock states scattered by two-level systems in the free space. Compared to existing scattering theories that treat incident light semi-classically, the theory fully quantizes the incident light as…
The transfer matrix formalism is implemented in the form of the multiple collision technique to account for dissipative transmission processes by using complex potentials in several models of atomic chains. The absorption term is rigorously…
Modeling the propagation of cracks at the microscopic level is fundamental to understand the effect of the microstructure on the fracture process. Nevertheless, microscopic propagation is often unstable and when using phase field fracture…
Because of a formal equivalence with the partition function of an Ising chain, the semiclassical traces of the quantum baker map can be calculated using the transfer-matrix method. We analyze the transfer matrices associated with the baker…
A scattering transform defines a locally translation invariant representation which is stable to time-warping deformations. It extends MFCC representations by computing modulation spectrum coefficients of multiple orders, through cascades…
The transfer matrix formalism is widely used in modeling heat diffusion in layered structures.Due to an intrinsic numerical instability issue, which has not yet drawn enough attention to the heat transfer community,this formalism fails at…
Using the tools of random matrix theory we develop a statistical analysis of the transport properties of thermoelectric low-dimensional systems made of two electron reservoirs set at different temperatures and chemical potentials, and…
Scaling properties in financial fluctuations are reviewed from the standpoint of statistical physics. We firstly show theoretically that the balance of demand and supply enhances fluctuations due to the underlying phase transition…
The Fraunhofer diffraction of quantum particles from materials with sharp electron-density edges or symmetric bond structures is ubiquitous. In contrast, diffraction from atoms with characteristic asymptotically-diffused electron…