Transmission through a Quantum Dynamical Delta Barrier

Abstract

We discuss electron scattering in a one-dimensional delta barrier potential with either a time-dependent coupling constant (classical model) or a coupling constant that is linear in a boson coordinate (quantum model). We find an exact continued fraction solution and Fano like resonances in the transmission coefficient. In the quantum model, energies for perfect transmission exist below the first sideband threshold. Introduction and ModelSimple models for the interaction between fermions and bosons continue to be fascinating, as often very non-trivial results can be obtained from even the most primitive Hamiltonians. Exactly solvable models for the interaction of photons or phonons with electrons in quantum dots [1] or quasi-one-dimensional systems [2, 3] provide the best examples, as they often provide a deep insight into rich and complex physics.In this contribution, we re-consider a simple model for a single electron of mass m in one dimension that interacts with a delta-barrier through a coupling parameter that itself is a dynamical quantity. The Hamiltonian is written as

Correlated electron systems periodically driven out of equilibrium:Floquet+DMFTformalism

“…The idea of FGFM was first introduced by Faisal, 8 followed by several groups. [9][10][11] In this section we give another way to define a Floquet matrix form of Green's function, which we shall use in this paper.…”

“…We can readily check that definition ͑7͒ is equivalent to the one given by Refs. [8][9][10][11]. The Floquet representation is used during calculations, while the Wigner representation is used when we interpret the result since the Wigner representation has a clear physical interpretation that G n is the nth oscillating mode in t av of G͑t , tЈ͒.…”

Electron-phonon bound states and impurity band formation in quantum wells

“…However, in the presence of inelastic scattering channels resonance features in the form of spikes and dips in T (E) occur at energies slightly below the local oscillator levels. They indicate the formation of bound states [15,19,26], manifested by Fano features which for attractive potentials can completely suppress electron transmission right below the resonance energy (red line in Fig. 1(a)).…”

Efeitos de canais inelásticos no transporte eletrônico: um exemplo além do formalismo de Landauer

“…Esteé o caso do potencial delta de Dirac acoplado a uma coordenada harmônica. Desde os trabalhos pioneiros, acerca de suas versões atrativa 16 e repulsiva 17 , verificamos seu aparecimento frequente na literatura [18][19][20][21] . Costuma-se explorar a obtenção das amplitudes e o comportamento ressonante das probabilidades de transmissão.…”

“…Os resultados mostrados no presente capítulo não são de todo originais, tendo sido explorados anteriormente. [16][17][18][19][20][21]42 O diferencial do qué e apresentado neste tratabalho como um todo, com relação a essas referências, está no cálculo da corrente elétrica. Isto será feito via um formalismo que vai além de Landauer, para a contabilização correta de processos inelásticos no espalhamento, num sistema em que a amostra real pode ser descrita pelo potencial delta acoplado.…”