Location and thermal evolution of the pseudogap due to spin fluctuations

We study pseudogap behavior in a metal near a spin density wave (SDW) instability due to thermal magnetic fluctuations. We consider the $t-t'$ Hubbard model on a square lattice at a finite doping, at intermediate coupling strength, and analyze the thermal evolution of the electron spectral function between a SDW ordered state at low temperatures and a normal Fermi liquid at high temperatures. We argue that for proper description of the pseudogap one needs to sum up infinite series of diagrams for both the fermionic self-energy and the SDW order parameter in the SDW state or the magnetic correlation length in the paramagnetic state. We use eikonal approach to sum up an infinite series of diagrammatic contributions from thermal fluctuations. Earlier studies found that in the SDW state, the spectral function $A_{\bf k} (\omega)$ of a hot fermion at a finite $T$ is exponentially small below the energy scale $\Delta (T)$, which scales with SDW order and vanishes at the ordering temperature $T_N$, and has a hump at a larger frequency $\Delta_{\rm pg}$, comparable to the zero-temperature SDW gap $\Delta (T=0)$. We argue that the hump, which we associate with the pseudogap, survives in some $T$ range above $T_N$. We show that this range is split by regions of strong and weak pseudogap behavior. In the first region, $\Delta_{\rm pg}$ is weakly temperature dependent, despite that it comes from thermal fluctuations. Such a behavior has been seen in numerical studies of the Hubbard model. We show that to obtain it, one needs to go beyond the one-loop approximation and sum up the infinite series of diagrams. In the second regime, $\Delta_{\rm pg}$ decreases with increasing $T$ and eventually vanishes. We further argue that a magnetic pseudogap at a finite $T$ emerges only if the ground state is magnetically ordered. We present the phase diagram and apply the results to high-$T_c$ cuprates.Comment: 22+3 pages, 16 figure

Performance Analysis of Discrete-Phase-Shifter IRS-aided Amplify-and-Forward Relay Network

As a new technology to reconfigure wireless communication environment by signal reflection controlled by software, intelligent reflecting surface (IRS) has attracted lots of attention in recent years. Compared with conventional relay system, the relay system aided by IRS can effectively reduce the cost and energy consumption, and significantly enhance the system performance. However, the phase quantization error generated by IRS with discrete phase shifter may degrade the receiving performance of the receiver. To analyze the performance loss caused by IRS phase quantization error, based on the law of large numbers and Rayleigh distribution, the closed-form expressions for the signal-to-noise ratio (SNR) performance loss and achievable rate of the IRS-aided amplify-and-forward (AF) relay network, which are related to the number of phase shifter quantization bits, are derived under the line-of-sight (LoS) channels and Rayleigh channels, respectively. Moreover, their approximate performance loss closed-form expressions are also derived based on the Taylor series expansion. Simulation results show that the performance losses of SNR and achievable rate decrease with the number of quantization bits increases gradually. When the number of quantization bits is larger than or equal to 3, the SNR performance loss of the system is smaller than 0.23dB, and the achievable rate loss is less than 0.04bits/s/Hz, regardless of the LoS channels or Rayleigh channels

Three Efficient Beamforming Methods for Hybrid IRS plus AF Relay-aided Metaverse

In this paper, an optimization problem is formulated to maximize signal-to-noise ratio (SNR) by jointly optimizing the beamforming matrix at AF relay and the reflecting coefficient matrices at IRS subject to the constraints of transmit power budgets at the base station (BS)/AF relay/hybrid IRS and that of unit-modulus for passive IRS phase shifts. To achieve high rate performance and extend the coverage range, a high-performance method based on semidefinite relaxation and fractional programming (HP-SDR-FP) algorithm is presented. Due to its extremely high complexity, a low-complexity method based on successive convex approximation and FP (LC-SCA-FP) algorithm is put forward. To further reduce the complexity, a lower-complexity method based on whitening filter, general power iterative and generalized Rayleigh-Ritz (WF-GPI-GRR) is proposed, where different from the above two methods, it is assumed that the amplifying coefficient of each active IRS element is equal, and the corresponding analytical solution of the amplifying coefficient can be obtained according to the transmit powers at AF relay and hybrid IRS. Simulation results show that the proposed three methods can greatly improve the rate performance compared to the existing technology-aided metaverse, such as the passive IRS plus AF relay-aided metaverse and only AF relay-aided metaverse. In particular, a 50.0% rate gain over the existing technology-aided metaverse is approximately achieved in the high power budget region of hybrid IRS. Moreover, it is verified that the proposed three efficient beamforming methods have an increasing order in rate performance: WF-GPI-GRR, LC-SCA-FP and HP-SDR-FP

Treating depressive disorders with the unified protocol: A preliminary randomized evaluation.

OBJECTIVES: This study aims to examine the efficacy of the Unified Protocol for Transdiagnostic Treatment of Emotional Disorders (UP) for individuals diagnosed with a depressive disorder. METHOD: Participants included 44 adults who met criteria for major depressive disorder, persistent depressive disorder, or another specified depressive disorder according to the Anxiety Disorder Interview Schedule (ADIS). These individuals represent a subset of patients from a larger clinical trial comparing the UP to single-disorder protocols (SDPs) for discrete anxiety disorders and a waitlist control (WLC) condition (Barlow et al., 2017); inclusion criteria for the parent study required participants to have a principal anxiety disorder. RESULTS: Significant reductions in depressive symptoms were observed within the UP condition across clinician-rated and self-report measures of depression from baseline to post-treatment, as well as to the 12-month follow-up assessment. Compared to the WLC group, individuals in the UP condition demonstrated significantly lower levels on our continuous, clinician-rated measure of depressive symptoms at post-treatment. There were no differences between the UP and SDP conditions on depressive symptoms at post-treatment or at the 12-month follow-up timepoint. CONCLUSIONS: In this exploratory set of analyses, the UP evidenced efficacy for reduction of depressive symptoms, adding to the growing support for its utility in treating depression.R01 MH090053 - NIMH NIH HHSAccepted manuscrip