Related papers: Quantum conductance problems and the Jacobi ensemb…
In this work we exploit the integrability of the two-lead Anderson model to compute transport properties of a quantum dot, in and out of equilibrium. Our method combines the properties of integrable scattering together with a…
We bring together the semiclassical approximation, matrix integrals and the theory of symmetric polynomials in order to solve a long standing problem in the field of quantum chaos: to compute transport moments when tunnel barriers are…
Transport phenomena in parallel coupled scatterers are studied by transfer matrix formulism. We derive a simple recurrence relation for transfer matrix of one-dimensional two-terminal systems consisting of $N$ arbitrary scattering unit…
The rarely used Hamilton-Jacobi equation has been utilized as an elegant way to find the trajectories of mechanical systems and to derive symplectic maps. Further, the exact solution in kick approximation of Hamilton's equations of motion…
This is a comprehensive review of the random-matrix approach to the theory of phase-coherent conduction in mesocopic systems. The theory is applied to a variety of physical phenomena in quantum dots and disordered wires, including universal…
A wide range of physical problems can be described by randomly-oriented linear trajectories, including any system of objects, organisms, particles, or rays that follow a linear path. Dependent upon the particular random variables that…
The linear response conductance coefficients are calculated in the scattering approach at finite frequency, damping and magnetic field for a microstructure in which the reservoirs are modeled as quantum wire leads of infinite length but…
The scattering properties of quantum particles on fractal potentials at different stages of fractal growth are obtained by means of the transfer matrix method. This approach can be easily adopted for project assignments in introductory…
The Jacobi system with matrix-valued coefficients and with the spectral parameter depending on a matrix-valued weight factor is considered on the full-line lattice. The scattering from the full-line lattice is expressed in terms of the…
We give a simple example of non-uniqueness in the inverse scattering for Jacobi matrices: roughly speaking $S$-matrix is analytic. Then, multiplying a reflection coefficient by an inner function, we repair this matrix in such a way that it…
In the framework of the random matrix approach, we apply the theory of Selberg's integral to problems of quantum transport in chaotic cavities. All the moments of transmission eigenvalues are calculated analytically up to the fourth order.…
We describe the application of the quantum mechanical bootstrap to the solution of one-dimensional scattering problems. By fixing a boundary and modulating the Robin parameter of the boundary conditions we are able to extract the reflection…
In high-energy physics experiments, the trajectories of charged particles are reconstructed using track reconstruction algorithms. Such algorithms need to both identify the set of measurements from a single charged particle and to fit the…
In the customary random matrix model for transport in quantum dots with $M$ internal degrees of freedom coupled to a chaotic environment via $N\ll M$ channels, the density $\rho$ of transmission eigenvalues is computed from a specific…
The calculation of transport profiles from experimental measurements belongs in the category of inverse problems which are known to come with issues of ill-conditioning or singularity. A reformulation of the calculation, the matricial…
One-dimensional scattering problem admitting a complex, PT-symmetric short-range potential V(x) is considered. Using a Runge-Kutta-discretized version of Schroedinger equation we derive the formulae for the reflection and transmission…
General dynamical transport of classical particles in disordered quasi-1D samples is viewed in the framework of scattering approach. Simple equation for the transfer-matrix is obtained within this unified picture. In the case of diffusive…
Coherent electron transport through a quantum channel in the presence of a general extended scattering potential is investigated using a T-matrix Lippmann-Schwinger approach. The formalism is applied to a quantum wire with Gaussian type…
We develop a statistical theory that describes quantum-mechanical scattering of a particle by a cavity when the geometry is such that the classical dynamics is chaotic. This picture is relevant to a variety of physical systems, ranging from…
The six Painlev\'e transcendants which originally appeared in the studies of ordinary differential equations have been found numerous applications in physical problems. The well-known examples among which include symmetry reduction of the…