The resonant state of the open quantum system is studied from the viewpoint of the outgoing momentum flux. We show that the number of particles is conserved for a resonant state, if we use an expanding volume of integration in order to take account of the outgoing momentum flux; the number of particles would decay exponentially in a fixed volume of integration. Moreover, we introduce new numerical methods of treating the resonant state with the use of the effective potential. We first give a numerical method of finding a resonance pole in the complex energy plane. The method seeks an energy eigenvalue iteratively. We found that our method leads to a super-convergence, the convergence exponential with respect to the iteration step. The present method is completely independent of commonly used complex scaling. We also give a numerical trick for computing the time evolution of the resonant state in a limited spatial area. Since the wave function of the resonant state is diverging away from the scattering potential, it has been previously difficult to follow its time evolution numerically in a finite area.
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.
The electronic conduction in mesoscopic systems has been studied extensively in recent years. A theoretically interesting feature of the problem is the fact that the system in question is an open quantum system with semi-infinite leads. The open quantum system intrinsically has resonant states, which can strongly affect the electronic conduction. 1 A popular way of treating the semi-infinite leads is to contract the leads to the self-energy.The self-energy of leads is a useful way of computing the conductance as well as obtaining resonant states. In this note, we propose a new method of calculating the self-energy of the leads. The self-energy Σ(E) was originally defined in 2for sites x and x ′ inside the central conductor, where H c is the Hamiltonian of the central conductor and H is the total Hamiltonian including semi-infinite leads attached to the conductor. The self-energy has been calculated by various methods. The method that we present here is much easier than previous methods. The main claim of this note is that the self-energy is equivalent to the boundary conditions for resonant states.We consider the Hamiltonian of a conductor with semi-infinite leads attached to it: H = H c + α H α , where H c is a one-body Hamiltonian of a finite-size conductor, while H α describes a semi-infinite lead given by the tight-binding modelThis includes the hopping between a site x α = 0 on the conductor and the lead α. (Note that, if we have hopping between the conductor and a lead with the amplitude different from −t, we include it in H c .)Equation (1) suggests that the eigenvalues of the effective Hamiltonian H eff (E) ≡ H c + Σ(E) are the poles (bound states and resonant states) of the total Hamiltonian H on the complex E plane. Therefore, we seek discrete and generally complex eigenvalues E n of resonant *
The preparation of lamellar type mesoporous silica (MPS) compact through the spark plasma sintering (SPS) and the adsorption/desorption of protein onto MPS compact are reported to be compared with those onto 2d‐hexagonal and 3d‐cubic type MPS compacts. A lamellar‐type MPS powder (MPS‐la) was prepared using triblock copolymer, PEO 5 PPO 68 PEO 5 , and was compacted in a carbon die and heated at 500°C for 5 min under uniaxial pressure. The products are referred to as MPS‐la‐500. The MPS compacts keep the lamellar type mesoporous configuration. The adsorbed amount of protein onto MPS‐la‐500 was 100 mg/g, while that on MPS‐la was 130 mg/g, and the former decreased by 23%. However, its decreasing ratio of the protein adsorption on MPS‐la‐500 was less than those of 2d‐hexagonal and 3d‐cubic type MPS compacts, which were 73 and 34%, respectively. The released amount of protein into PBS solution from MPS‐la‐500, which was soaked in the protein solution for 48 h, increased with the soaking time, while those from 2d‐ and 3d‐type MPS compacts reached to plateau for 4 h of soaking. The lamellar type MPS compact was found to be easier to absorb and release proteins, which may be due to the large aperture of the mesoporous configuration.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.