Phonon effects on the current noise spectra and the ac conductance of a single molecular junction

By using nonequilibrium Green's functions and the equation of motion method, we formulate a self-consistent field theory for the electron transport through a single molecular junction (SMJ) coupled with a vibrational mode. We show that the nonequilibrium dynamics of the phonons in strong electron-phonon coupling regime can be taken into account appropriately in this self-consistent perturbation theory, and the self-energy of phonons is connected with the current fluctuations in the molecular junction. We calculate the finite-frequency nonsymmetrized noise spectra and the ac conductance, which reveal a wealth of inelastic electron tunneling characteristics on the absorption and emission properties of this SMJ. In the presence of a finite bias voltage and the electron tunneling current, the vibration mode of the molecular junction is heated and driven to an unequilibrated state. The influences of unequilibrated phonons on the current and the noise spectra are investigated.Comment: 12 pages, 8 figure

Finite frequency current fluctuations and the self-consistent perturbation theory for electron transport through quantum dot

We have formulated the problem of electron transport through interacting quantum dot system in the framework of self-consistent perturbation theory, and show that the current conservation condition is guaranteed due to the gauge invariant properties of the Green's functions and the generalized Ward identity. By using a generating functional for the statistics of the nonequilibrium system, we have obtained general formulae for calculating the current and the current fluctuations in the presence of arbitrary time-dependent potentials. As demonstration of application, we have studied the interaction effects on the finite frequency noise for electron resonant tunneling through an Anderson impurity, and obtained an analytical equation for the interaction effect on the finite frequency current noise within the Hartree approximation, which is an extension of the previous results obtained by Hershfield on zero frequency shot noise.Comment: 9 pages, 3 figure

A note on closedness of the sum of two closed subspaces in a Banach space

Let $X$ be a Banach space, and $M,N$ be two closed subspaces of $X$. We present several necessary and sufficient conditions for the closedness of $M+N$ ($M+N$ is not necessarily direct sum)

Scale-free power spectrums in the delayed cosmology

The delayed cosmology [JCAP 02(2012)046] assumes that the evolution of geometries is delayed relative to that of matter and/or energies. This idea allows inflation occur without inflaton fields or vacuum energies of any kind as drivings. We considered the production and evolution of primordial perturbations in this model. The results indicate that, with delaying, we could get a nearly scale-free power spectrum of perturbations starting from a radiation dominated early universe.Comment: basic ideas remain the same, numerical results improved remarkabl

Occlusion-Adaptive Deep Network for Robust Facial Expression Recognition

Recognizing the expressions of partially occluded faces is a challenging computer vision problem. Previous expression recognition methods, either overlooked this issue or resolved it using extreme assumptions. Motivated by the fact that the human visual system is adept at ignoring the occlusion and focus on non-occluded facial areas, we propose a landmark-guided attention branch to find and discard corrupted features from occluded regions so that they are not used for recognition. An attention map is first generated to indicate if a specific facial part is occluded and guide our model to attend to non-occluded regions. To further improve robustness, we propose a facial region branch to partition the feature maps into non-overlapping facial blocks and task each block to predict the expression independently. This results in more diverse and discriminative features, enabling the expression recognition system to recover even though the face is partially occluded. Depending on the synergistic effects of the two branches, our occlusion-adaptive deep network significantly outperforms state-of-the-art methods on two challenging in-the-wild benchmark datasets and three real-world occluded expression datasets

On completeness of the space of weighted pseudo almost automorphic functions

In this paper, we prove that for every $\rho\in \mathbb{U}_{\infty}$, the space of weighted pseudo almost automorphic functions is complete under the supremum norm. This gives an affirmative answer to a key and fundamental problem for weighted pseudo almost automorphic functions, and fills a gap in the proof of [J. Funct. Anal. 258, No. 1, 196-207 (2010)].Comment: 8 page

Transient currents of a single molecular junction with a vibrational mode

By using a propagation scheme for current matrices and an auxiliary mode expansion method, we investigate the transient dynamics of a single molecular junction coupled with a vibrational mode. Our approach is based on the Anderson-Holstein model and the dressed tunneling approximation for the electronic self-energy in the polaronic regime. The time-dependent currents after a sudden switching on the tunneling to leads and an abrupt upward step bias pulse are calculated. We show that the strong electron-phonon interaction greatly influences the nonlinear response properties of the system, and gives rise to interesting characteristics on the time traces of transient currents.Comment: 8 pages, 5 figure

Velocity-determined anisotropic behaviors of RKKY interaction in 8-\textit{Pmmn} borophene

As a new two-dimensional Dirac material, 8-\textit{Pmmn} borophene hosts novel anisotropic and tilted massless Dirac fermions (MDFs) and has attracted increasing interest. However, the potential application of 8-\textit{Pmmn} borophene in spin fields has not been explored. Here, we study the long-range RKKY interaction mediated by anisotropic and tilted MDFs in magnetically-doped 8-\textit{Pmmn} borophene. To this aim, we carefully analyze the unique real-space propagation of anisotropic and tilted MDFs with noncolinear momenta and group velocities. As a result, we analytically demonstrate the anisotropic behaviors of long-range RKKY interaction, which have no dependence on the Fermi level but are velocity-determined, i.e., the anisotropy degrees of oscillation period and envelop amplitude are determined by the anisotropic and tilted velocities. The velocity-determined RKKY interaction favors to fully determine the characteristic velocities of anisotropic and tilted MDFs through its measurement, and has high tunability by engineering velocities shedding light on the application of 8-\textit{Pmmn} borophene in spin fields.Comment: 8 pages, 5 figure

Computational Study on Hysteresis of Ion Channels: Multiple Solutions to Steady-State Poisson--Nernst--Planck Equations

The steady-state Poisson-Nernst-Planck (ssPNP) equations are an effective model for the description of ionic transport in ion channels. It is observed that an ion channel exhibits voltage-dependent switching between open and closed states. Different conductance states of a channel imply that the ssPNP equations probably have multiple solutions with different level of currents. We propose numerical approaches to study multiple solutions to the ssPNP equations with multiple ionic species. To find complete current-voltage (I-V ) and current-concentration (I-C) curves, we reformulate the ssPNP equations into four different boundary value problems (BVPs). Numerical continuation approaches are developed to provide good initial guesses for iteratively solving algebraic equations resulting from discretization. Numerical continuations on V , I, and boundary concentrations result in S-shaped and double S-shaped (I-V and I-C) curves for the ssPNP equations with multiple species of ions. There are five solutions to the ssPNP equations with five ionic species, when an applied voltage is given in certain intervals. Remarkably, the current through ion channels responds hysteretically to varying applied voltages and boundary concentrations, showing a memory effect. In addition, we propose a useful computational approach to locate turning points of an I-V curve. With obtained locations, we are able to determine critical threshold values for hysteresis to occur and the interval for V in which the ssPNP equations have multiple solutions. Our numerical results indicate that the developed numerical approaches have a promising potential in studying hysteretic conductance states of ion channels

Prediction of Extraordinary Magnetoresistance in Janus Monolayer MoTeB2

Based on first-principles calculations, we studied the geometric configuration, stability and electronic structure of the two-dimensional Janus MoTeB2. The MoTeB2 monolayer is semimetal, and its attractive electronic structure reveals the perfect electron-hole compensation. Moreover, the electron-type and hole-type bands of the MoTeB2 monolayer are easily adjustable by external stain and charge doping, such as the switch of carrier polarity by charge doping, and the metal-semiconductor transition under tensile stain. These properties allow the MoTeB2 monolayer to be a controllable two-dimensional material with extraordinary large magnetoresistance in magnetic field.Comment: 16 pages, 6 figure