Gonzalo Ordonez

Resonant Spectrum Analysis of the Conductance of an Open Quantum System and Three Types of Fano Parameter

We explain the Fano peak (an asymmetric resonance peak) as an interference effect involving resonant states. We reveal that there are three types of Fano asymmetry according to their origins: the interference between a resonant state and an anti-resonant state, that between a resonant state and a bound state, and that between two resonant states. We show that the last two show the asymmetric energy dependence given by Fano, but the first one shows a slightly different form. In order to show the above, we analytically and microscopically derive a formula where we express the conductance purely in terms of the summation over all discrete eigenstates including resonant states and anti-resonant states, without any background integrals. We thereby obtain microscopic expressions of the Fano parameters that describe the three types of the Fano asymmetry. One of the expressions indicates that the corresponding Fano parameter becomes complex under an external magnetic field.

Time-Reversal Symmetric Resolution of Unity without Background Integrals in Open Quantum Systems

We present a new complete set of states for a class of open quantum systems, to be used in expansion of the Green’s function and the time-evolution operator. A remarkable feature of the complete set is that it observes time-reversal symmetry in the sense that it contains decaying states (resonant states) and growing states (anti-resonant states) parallelly. We can thereby pinpoint the occurrence of the breaking of time-reversal symmetry at the choice of whether we solve Schrodinger equation as an initial-condition problem or a terminal-condition problem. Another feature of the complete set is that in the subspace of the central scattering area of the system, it consists of contributions of all states with point spectra but does not contain any background integrals. In computing the time evolution, we can clearly see contribution of which point spectrum produces which time dependence. In the whole infinite state space, the complete set does contain an integral but it is over unperturbed eigenstates of the environmental area of the system and hence can be calculated analytically. We demonstrate the usefulness of the complete set by computing explicitly the survival probability and the escaping probability as well as the dynamics of wave packets. The origin of each term of matrix elements is clear in our formulation, particularly, the exponential decays due to the resonance poles.

Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects

It has been reported in the literature that the survival probability

Existence and nonexistence of an intrinsic tunneling time

P(t)

Resonant-state Expansion of the Green’s Function of Open Quantum Systems

near an exceptional point where two eigenstates coalesce should generally exhibit an evolution

Impurity-directed transport within a finite disordered lattice

P(t) \sim t^2 e^{-\Gamma t}

Irreversibility and the breaking of resonance-antiresonance symmetry

, in which

Universal electric current of interacting resonant-level models with asymmetric interactions: An extension of the Landauer formula

\Gamma

Exact scattering eigenstates in double quantum-dot systems with an interdot Coulomb interaction

is the decay rate of the coalesced eigenstate; this has been verified in a microwave billiard experiment [B. Dietz, et al, Phys. Rev. E 75, 027201 (2007)]. However, the heuristic effective Hamiltonian that is usually employed to obtain this result ignores the possible influence of the continuum threshold on the dynamics. By contrast, in this work we employ an analytical approach starting from the microscopic Hamiltonian representing two simple models in order to show that the continuum threshold has a strong influence on the dynamics near exceptional points in a variety of circumstances. To report our results, we divide the exceptional points in Hermitian open quantum systems into two cases: at an EP2A two virtual bound states coalesce before forming a resonance, anti-resonance pair with complex conjugate eigenvalues, while at an EP2B two resonances coalesce before forming two different resonances. For the EP2B, which is the case studied in the microwave billiard experiment, we verify the survival probability exhibits the previously reported modified exponential decay on intermediate timescales, but this is replaced with an inverse power law on very long timescales. Meanwhile, for the EP2A the influence from the continuum threshold is so strong that the evolution is non-exponential on all timescales and the heuristic approach fails completely. When the EP2A appears very near the threshold we obtain the novel evolution

Electron trapping in a one-dimensional semiconductor quantum wire with multiple impurities

P(t) \sim 1 - C_1 \sqrt{t} + D_1 t