Electron and spin transport in the presence of a complex absorbing potential

Abstract

We examine the impact of a complex absorbing potential on electron transport both in the continuum and on a lattice. This requires the use of non-Hermitian Hamiltonians; the required formalism is briefly outlined. The lattice formulation allows us to study the interesting problem of an electron interacting with a stationary spin and the subsequent time evolution of the electron and spin properties as the electron is absorbed after the initial interaction. Remarkably, the properties of the localized spin are affected "at a distance" by the interaction of the ͑now entangled͒ electron with a complex potential.

Invisibility in non-Hermitian tight-binding lattices

“…(6), (7), (15) and from the assumed asymptotic behavior of κ (1) n and V (1) n as n → ±∞, it follows that |ψ E is a proper (improper) eigenfunction of H 2 in the same way as |ψ E is a proper (improper) eigenfunction of H 1 . In a similar way, one can show that any eigenvalue E of H 2 , belonging to its continuous or to its point spectrum, is also an eigenvalue of H 1 provided that E = µ 1 .…”

“…Therefore, | ψE is an eigenfunction of H 2 corresponding to the energy E. Also, from Eqs. ( 6), ( 7), (15) and from the assumed asymptotic behavior of κ…”

“…It is the aim of this work to show that fully invisibility of localized defects can be realized in non-Hermitian tight-binding lattices, which are synthesized by iterated application of the intertwining operator technique (Darboux transformation) to a defect-free tight-binding Hermitian lattice. The study of non-Hermitian tightbinding lattices has received in recent years a great attention (see, e.g., [14][15][16][17][18][19] and references therein); such previous studies have been mainly focused to lattices possessing parity-time (PT ) symmetry and were framed in the context of non-Hermitian quantum mechanics [17][18][19][20], however the possibility to realize invisibility in a non-Hermitian lattice was not investigated in such previous works [21]. It should be noted that the class of non-Hermtian lattices synthesized in the present work by application of the Darboux transformation and showing the property of invisibility are not PT -symmetric.…”

Non-Hermitian bidirectional robust transport

“…Transport, localization and scattering of quantum or classical waves in systems described by effective non-Hermitian Hamiltonians are of major interest in different areas of science , ranging from the physics of open quantum systems to mesoscopic solid-state structures [2,13,14,17,20,23,25], atomic and molecular physics [1,34], optics and photonics [18,29,31,36,37,39,40,43], acoustics [48,52], magnetic and spin systems [21,28,32,33,35,46,47], quantum computing [26,27,42], and biological systems [7,50]. Several important signatures of non-Hermitian transport have been revealed, including non-Hermitian delocalization in disordered lattices [3][4][5][6][7][8][9][10][11][12], one-way scattering [15,16], transition from ballistic to diffusive transport [29], hyperballistic transport [30], invisibility of defects…”

Emerging nonequilibrium bound state in spin-current–local-spin scattering

“…The scenario of an incoming (electron) spin, often modeled as a wave packet, whose spin degree of freedom is coupled with local spins, has been advanced by a number of workers [24,25,26,27,28,29]. The coupling between the incoming spin and the local spins is Kondo-like, while the local spins are themselves ferromagnetically coupled via a Heisenberg exchange interaction.…”