Nonequilibrium transport on a quantum molecular chain in terms of the complex Liouvillian spectrum

The transport process in a molecular chain in a nonequilibrium stationary state is theoretically investigated. The molecule is interacting at both ends with thermal baths of different temperatures, while no dissipation mechanism is contained inside the molecular chain. We have first obtained the nonequilibrium stationary state outside the Hilbert space in terms of the complex spectral representation of Liouvillian. The nonequilibrium stationary state is obtained as an eigenstate of the Liouvillian, which is constructed through the collision invariant of the kinetic equation. The eigenstate of the Liouvillian contains information on the spatial correlation between the molecular chain and the thermal baths. While energy flow in the nonequilibrium state which is due to the first-order correlation can be described by the Landauer formula, the particle current due to the second-order correlation cannot be described by the Landauer formula. The present method provides a simple way to evaluate the energy transport in a molecular chain in a nonequilibrium situation.Ministry of Education, Science, Sports, and Culture of JapanYukawa International Program for Quark-Hadron Sciences YIPQSPhysic

Non-divergent representation of non-Hermitian operator near the exceptional point with application to a quantum Lorentz gas

We propose a non-singular representation for a non-Hermitian operator even if the parameter space contains exceptional points (EPs), at which the operator cannot be diagonalized and the usual spectral representation ceases to exist. Our representation has a generalized Jordan block form and is written in terms of extended pseudo-eigenstates. Our method is free from a divergence in the spectral representation at EPs, at which multiple eigenvalues and eigenvectors coalesce and the eigenvectors cannot be normalized. Our representation improves the accuracy of numerical calculations of physical quantities near EPs. We also find that our method is applicable to various problems related to EPs in the parameter space of non-Hermitian operators. We demonstrate the usefulness of our representation by investigating Boltzmann's collision operator in a one-dimensional quantum Lorentz gas in the weak coupling approximation

Tunable Bound States in Continuum by Optical Frequency

We demonstrate the existence of tunable bound-states in continuum (BIC) in a 1-dimensional quantum wire with two impurities induced by an intense monochromatic radiation field. We found that there is a new type of BIC due to the Fano interference between two optical transition channels, in addition to the ordinary BIC due to a geometrical interference between electron wave functions emitted by impurities. In both cases the BIC can be achieved by tuning the frequency of the radiation field.Comment: 5 figure

Harmonic oscillator model for the atom-surface Casimir-Polder interaction energy

In this paper we consider a quantum harmonic oscillator interacting with the electromagnetic radiation field in the presence of a boundary condition preserving the continuous spectrum of the field, such as an infinite perfectly conducting plate. Using an appropriate Bogoliubov-type transformation we can diagonalize exactly the Hamiltonian of our system in the continuum limit and obtain non-perturbative expressions for its ground-state energy. From the expressions found, the atom-wall Casimir-Polder interaction energy can be obtained, and well-know lowest-order results are recovered as a limiting case. Use and advantage of this method for dealing with other systems where perturbation theory cannot be used is also discussed.Comment: 6 page

Enhanced resonant force between two entangled identical atoms in a photonic crystal

We consider the resonant interaction energy and force between two identical atoms, one in an excited state and the other in the ground state, placed inside a photonic crystal. The atoms, having the same orientation of their dipole moment, are supposed prepared in their symmetrical state and interact with the quantum electromagnetic field. We consider two specific models of photonic crystals: a one-dimensional model and an isotropic model. We show that in both cases the resonant interatomic force can be strongly enhanced by the presence of the photonic crystal, as a consequence of the modified dispersion relation and density of states, in particular if the transition frequency of the atoms is close to the edge of a photonic gap. Differences between the two models considered of photonic crystal are discussed in detail, as well as comparison with the analogous system of two impurity atoms in a quantum semiconductor wire. A numerical estimate of the effect in a realistic situation is also discussed.Comment: 8 page