Positivity Preserving non-Markovian Master Equation for Open Quantum System Dynamics: Stochastic Schr\"{o}dinger Equation Approach

Positivity preservation is naturally guaranteed in exact non-Markovian master equations for open quantum system dynamics. However, in many approximated non-Markovian master equations, the positivity of the reduced density matrix is not guaranteed. In this paper, we provide a general class of time-local, perturbative and positivity-preserving non-Markovian master equations generated from stochastic Schrodinger equations, particularly quantum-state-diffusion equations. Our method has an expanded range of applicability for accommodating a variety of non-Markovian environments. We show the positivity-preserving master equation for a three-level system coupled to a dissipative bosonic environment as a particular example to exemplify our general approach. We illustrate the numerical simulations with an analysis explaining why the previous approximated non-Markovian master equations cannot guarantee positivity. Our work provides a consistent master equation for studying the non-Markovian dynamics in ultrafast quantum processes and strong-coupling systems.Comment: 9 pages, 4 figure

Decentralized Federated Reinforcement Learning for User-Centric Dynamic TFDD Control

The explosive growth of dynamic and heterogeneous data traffic brings great challenges for 5G and beyond mobile networks. To enhance the network capacity and reliability, we propose a learning-based dynamic time-frequency division duplexing (D-TFDD) scheme that adaptively allocates the uplink and downlink time-frequency resources of base stations (BSs) to meet the asymmetric and heterogeneous traffic demands while alleviating the inter-cell interference. We formulate the problem as a decentralized partially observable Markov decision process (Dec-POMDP) that maximizes the long-term expected sum rate under the users' packet dropping ratio constraints. In order to jointly optimize the global resources in a decentralized manner, we propose a federated reinforcement learning (RL) algorithm named federated Wolpertinger deep deterministic policy gradient (FWDDPG) algorithm. The BSs decide their local time-frequency configurations through RL algorithms and achieve global training via exchanging local RL models with their neighbors under a decentralized federated learning framework. Specifically, to deal with the large-scale discrete action space of each BS, we adopt a DDPG-based algorithm to generate actions in a continuous space, and then utilize Wolpertinger policy to reduce the mapping errors from continuous action space back to discrete action space. Simulation results demonstrate the superiority of our proposed algorithm to benchmark algorithms with respect to system sum rate

Mirror symmetry decomposition in double-twisted multilayer graphene systems

Due to the observed superconductivity, the alternating twisted trilayer graphene (ATTLG) has drawn great research interest very recently, in which three monolayer graphene (MLG) are stacked in alternating twist way. If one or several of the MLG in ATTLG are replaced by a multilayer graphene, we get a double twisted multilayer graphene (DTMLG). In this work, we theoretically illustrate that, if the DTMLG has a mirror symmetry along z direction like the ATTLG, there exists a mirror symmetry decomposition (MSD), by which the DTMLG can be exactly decoupled into two subsystems with opposite parity. The two subsystems are either a twisted multilayer graphene (single twist) or a multilayer graphene, depending on the stacking configuration. Such MSD can give a clear interpretation about all the novel features of the moir\'{e} band structures of DTMLG, e.g. the fourfold degenerate flat bands and the enlarged magic angle. Meanwhile, in such DTMLG, the parity becomes a new degree of freedom of the electrons, so that we can define a parity resolved Chern number for the moir\'{e} flat bands. More importantly, the MSD implies that all the novel correlated phases in the twisted multilayer graphene should also exist in the corresponding DTMLGs, since they have the exact same Hamiltonian in form. Specifically, according to the MSD, we predict that the superconductivity should exist in the (1+3+1)-DTMLG.Comment: 12 pages, 6 figure

Mechanism of crack propagation for K9 glass

In order to study the mechanism of crack propagation, the varied cutting-depth scratch experiment is carried out and smoothed particle hydrodynamics (SPH) simulation method is used to assistant the investigation. The SPH simulation results reveal that crack will propagate in the direction where stress concentration exceeds the fracture toughness of K9 glass. The initial crack length in critical transition depth is calculated by combining the critical stress of fracture and the fracture toughness of K9 glass. Based on the effective plastic strain, the relation between scratching depth and crack depth is obtained. The recovery of crack tip is found and explained from the relationship between cutting depth and crack depth. Using the energy balance theory of Griffith, the variation of material internal energy is revealed. Comparing the scratching forces obtained from experiment and simulation, the validity of simulation results is verified. The phenomenon of crack delayed propagation is found in both experiment and simulation. The explanation of mechanism is given

Observation of strong-coupling pairing with weakened Fermi-surface nesting at optimal hole doping in Ca0.33_{0.33}Na0.67_{0.67}Fe2_2As2_2

We report an angle-resolved photoemission investigation of optimally-doped Ca$_{0.33}$Na$_{0.67}$Fe$_2$As$_2$. The Fermi surface topology of this compound is similar to that of the well-studied Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ material, except for larger hole pockets resulting from a higher hole concentration per Fe atoms. We find that the quasi-nesting conditions are weakened in this compound as compared to Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$. As with Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ though, we observe nearly isotropic superconducting gaps with Fermi surface-dependent magnitudes. A small variation in the gap size along the momentum direction perpendicular to the surface is found for one of the Fermi surfaces. Our superconducting gap results on all Fermi surface sheets fit simultaneously very well to a global gap function derived from a strong coupling approach, which contains only 2 global parameters.Comment: 5 pages, 4 figure