Related papers: A Novel Transfer Matrix Framework for Multiple Dir…
Dirac delta function of matrix argument is employed frequently in the development of diverse fields such as Random Matrix Theory, Quantum Information Theory, etc. The purpose of the article is pedagogical, it begins by recalling detailed…
We make a relativistic extension of the one-dimensional J-matrix method of scattering. The relativistic potential matrix is a combination of vector, scalar, and pseudo-scalar components. These are non-singular short-range potential…
We consider tunnelling of a non-relativistic particle across a potential barrier. It is shown that the barrier acts as an effective beam splitter which builds up the transmitted pulse from the copies of the initial envelope shifted in the…
We address the problem of barrier tunneling in the two-dimensional T_3 lattice (dice lattice). In particular we focus on the low-energy, long-wavelength approximation for the Hamiltonian of the system, where the lattice can be described by…
Photon-assisted charge transport through a double barrier structure under a time periodic field in graphene is studied. Within the framework of the Floquet formalism and using the transfer matrix method, the transmission probabilities for…
Dirac particles can undergo perfect transmission through a sufficiently high potential barrier in the Klein zone. Although the perfect Klein tunneling (often referred to as the Klein paradox) is similar to the non-relativistic resonant…
Exact reflection and transmission coefficients for supersymmetric shape-invariant potentials barriers are calculated by an analytical continuation of the asymptotic wave functions obtained via the introduction of new generalized ladder…
We propose a new method to construct a four parameter family of quantum-mechanical point interactions in one dimension, which is known as all possible self-adjoint extensions of the symmetric operator $T=-\Delta \lceil C^{\infty}_{0}({\bf…
Quantum tunneling across multiple barriers as yet is an unsolved problem for barrier numbers greater than five. The complexity of the mathematical analysis even for small number of barriers pushed it into the realms of Numerical Analysis.…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…
We show that engineering of tunnel barriers forming at the interfaces of a one-dimensional spin valve provides a viable path to a strong gate-voltage tunability of the magnetoresistance effect. In particular, we investigate theoretically 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…
The formalism of the scattering matrix is applied to describe the transmission properties of multilayered structures with deep variations of the refractive index and arbitrary arrangements of the layers. We show that there is an exact…
The physical interpretation of the appearance of resonant transmission through single-point barriers is discussed on the basis of a double-layer heterostructure in the squeezing limit as both the thickness of the layers and the distance…
By directly integrating the Schroedinger starting in the transmission region and working backwards through the barrier, the tunneling probability can be determined for arbitrary potential barriers. The method employs techniques familiar to…
Earlier, in the CINT program at Los Alamos National Laboratory, we focused ultrafast mode-locked lasers on the tip-sample junction of a scanning tunneling microscope to generate currents at hundreds of harmonics of the laser pulse…
A semiclassical method for the calculation of tunneling exponent in systems with many degrees of freedom is developed. We find that corresponding classical solution as function of energy form several branches joint by bifurcation points. A…
We study the tunneling through an oscillating delta barrier. Using time periodicity of the model, the time-dependent Schr\"odinger equation is reduced to a simple but infinite matrix equation. Employing Toeplitz matrices methods, the…
The transfer matrix is a powerful technique that can be applied to statistical mechanics systems as, for example, in the calculus of the entropy of the ice model. One interesting way to study such systems is to map it onto a 3-color…
For the wave representing particle traveling through any layer system we calculate appropriate phase shifts comparing two methods. One bases on the standard scattering theory and is well known another uses unimodular but not unitary…