Reconstructing the graviton

We reconstruct the Lorentzian graviton propagator in asymptotically safe quantum gravity from Euclidean data. The reconstruction is applied to both the dynamical fluctuation graviton and the background graviton propagator. We prove that the spectral function of the latter necessarily has negative parts similar to, and for the same reasons, as the gluon spectral function. In turn, the spectral function of the dynamical graviton is positive. We argue that the latter enters cross sections and other observables in asymptotically safe quantum gravity. Hence, its positivity may hint at the unitarity of asymptotically safe quantum gravity.

The probe particle scattering cross-section off the many-fermion systems in the impulse approximation

In this work, we study the differential scattering cross-section (DSCS) in the first-order Born approximation. It is not difficult to show that the DSCS can be simplified in terms of the system response function. Also, the system response function has this property to be written in terms of the spectral function and the momentum distribution function in the impulse approximation (IA) scheme. Therefore, the DSCS in the IA scheme can be formulated in terms of the spectral function and the momentum distribution function. On the other hand, the DSCS for an electron off the [Formula: see text] and [Formula: see text] nuclei is calculated in the harmonic oscillator shell model. The obtained results are compared with the experimental data, too. The most important result derived from this study is that the calculated DSCS in terms of the spectral function has a high agreement with the experimental data at the low-energy transfer, while the obtained DSCS in terms of the momentum distribution function does not. Therefore, we conclude that the response of a many-fermion system to a probe particle in IA must be written in terms of the spectral function for getting accurate theoretical results in the field of collision. This is another important result of our study.

Effective field theory of the Higgs mode in a two-dimensional dilute Bose gas

In this paper, we investigate the spectral function of the Higgs mode in a two-dimensional Bose gas by using the effective field theory in the zero-temperature limit. Our approach explains the experimental feature that the peak of the spectral function is a soft continuum rather than a sharp peak, broadens and vanishes in the superfluid phase, which cannot be explained in terms of the [Formula: see text] model. We also find that the scalar susceptibility is the same as the longitudinal susceptibility.

Dynamics of string-like states of a hole in a quantum antiferromagnet: A diagrammatic Monte Carlo simulation

The dynamics of a hole motion in a quantum antiferromagnet has been studied in the past three decade because of its relationship to models related to superconductivity in cuprates. The same problem has received significant attention because of its connection to very recent experiments of the dynamics of ultra-cold atoms in optical lattices where models of strongly correlated electrons can be simulated. In this paper we apply the diagrammatic Monte Carlo method to calculate the single-hole Green's function in the t-J model, where the $J$ term is linearized, in a wide range of imaginary-time with the aim to examine the polaron formation and in particular the details of the contribution of the so-called {\it string excitations} found in such recent experiments. We calculate the single-hole spectral function by analytic continuation from imaginary to real time and study the various aspects that constitute the string picture, such as, the energy-momentum dependence of the main quasiparticle peak and its residue, the {\it internal excitations} of the string which appear as multiple peaks in the spectral function as well as their momentum dependence. We find that the earlier analysis of the spectral function based on a mobile-hole connected with a string of overturn spins and the contribution of the internal string excitations as obtained from the non-crossing approximation is accurate.

Photoemission Spectra from the Extended Koopman’s Theorem, Revisited

The Extended Koopman’s Theorem (EKT) provides a straightforward way to compute charged excitations from any level of theory. In this work we make the link with the many-body effective energy theory (MEET) that we derived to calculate the spectral function, which is directly related to photoemission spectra. In particular, we show that at its lowest level of approximation the MEET removal and addition energies correspond to the so-called diagonal approximation of the EKT. Thanks to this link, the EKT and the MEET can benefit from mutual insight. In particular, one can readily extend the EKT to calculate the full spectral function, and choose a more optimal basis set for the MEET by solving the EKT secular equation. We illustrate these findings with the examples of the Hubbard dimer and bulk silicon.

Equation-of-Motion Coupled-Cluster Cumulant Green’s Function for Excited States and X-Ray Spectra

Green’s function methods provide a robust, general framework within many-body theory for treating electron correlation in both excited states and x-ray spectra. Conventional methods using the Dyson equation or the cumulant expansion are typically based on the GW self-energy approximation. In order to extend this approximation in molecular systems, a non-perturbative real-time coupled-cluster cumulant Green’s function approach has been introduced, where the cumulant is obtained as the solution to a system of coupled first order, non-linear differential equations. This approach naturally includes non-linear corrections to conventional cumulant Green’s function techniques where the cumulant is linear in the GW self-energy. The method yields the spectral function for the core Green’s function, which is directly related to the x-ray photoemission spectra (XPS) of molecular systems. The approach also yields very good results for binding energies and satellite excitations. The x-ray absorption spectrum (XAS) is then calculated using a convolution of the core spectral function and an effective, one-body XAS. Here this approach is extended to include the full coupled-cluster-singles (CCS) core Green’s function by including the complete form of the non-linear contributions to the cumulant as well as all single, double, and triple cluster excitations in the CC amplitude equations. This approach naturally builds in orthogonality and shake-up effects analogous to those in the Mahan-Noizeres-de Dominicis edge singularity corrections that enhance the XAS near the edge. The method is illustrated for the XPS and XAS of NH3.

On the difference between FOPT and CIPT for hadronic tau decays

In this article we review the results of our recent work on the difference between the Borel representations of $$\tau $$ τ hadronic spectral function moments obtained with the CIPT and FOPT methods. For the presentation of the theoretical results we focus on the large-$$\beta _0$$ β 0 approximation, where all expressions can be written down in closed form, and we comment on the generalization to full QCD. The results may explain the discrepancy in the behavior of the FOPT and CIPT series that has been the topic of intense discussions in previous literature and which represents a major part of the theoretical uncertainties in current strong coupling determinations from hadronic $$\tau $$ τ decays. The findings also imply that the OPE corrections for FOPT and CIPT differ and that the OPE corrections for CIPT do not have standard form.

Insights into the Multilevel Structural Characterization and Adsorption Mechanism of Sinogastromyzon szechuanensis Sucker on the Rough Surface

The present study investigates the adsorption performance and adsorption mechanism of Sinogastromyzon szechuanensis on different rough surfaces. The different positions of the sucker surface of Sinogastromyzon szechuanensis were observed by adopting the stereomicroscope and SEM. The observed results showed that the sucker of Sinogastromyzonszechuanensis had a multilevel structure of villi and groove. The anterior and posterior of Sinogastromyzonszechuanensis had different microscopic morphologies. The surface roughness of the adsorption substrate ranged from 7 μm to 188 μm. Adsorption strength of Sinogastromyzonszechuanensis and the conventional sucker on different rough surfaces were measured by a purposely designed device. The results showed that the back of Sinogastromyzonszechuanensis mainly provided the adsorption strength. The adsorption strength of the conventional sucker gradually decreased with surface roughness increasing, but the adsorption strength of Sinogastromyzon szechuanensis had not changed significantly. Based on the experimental results, the adsorption mechanism of Sinogastromyzonszechuanensis on the surface with different roughness was analyzed by the spectral function. The Sinogastromyzonszechuanensis sucker with a multilevel structure worked well on the rough surface, which led to Sinogastromyzonszechuanensis with a good sealing on the rough surface. The present work could help to develop a new type of sucker with effective adsorption performance on a rough surface to meet the needs of the engineering field.