Gaussian Environment Research Articles

Implementation of frozen density embedding in CP2K and OpenMolcas: CASSCF wavefunctions embedded in a Gaussian and plane wave DFT environment.

Most chemical processes happen at a local scale where only a subset of molecular orbitals is directly involved and only a subset of covalent bonds may be rearranged. To model such reactions, Density Functional Theory (DFT) is often inadequate, and the use of computationally more expensive correlated wavefunction (WF) methods is required for accurate results. Mixed-resolution approaches backed by quantum embedding theory have been used extensively to approach this imbalance. Based on the frozen density embedding freeze-and-thaw algorithm, we describe an approach to embed complete active space self-consistent field simulations run in the OpenMolcas code in a DFT environment calculated in CP2K without requiring any external tools. This makes it possible to study a local, active part of a chemical system in a larger and relatively static environment with a computational cost balanced between the accuracy of a WF method and the efficiency of DFT, which we test on environment-subsystem pairs. Finally, we apply the implementation to an oxygen molecule leaving an aluminum (111) surface and a ruthenium(IV) oxide (110) surface.

Spin relaxation dynamics with a continuous spin environment: The dissipaton equation of motion approach.

We investigate the quantum dynamics of a spin coupling to a bath of independent spins via the dissipaton equation of motion (DEOM) approach. The bath, characterized by a continuous spectral density function, is composed of spins that are independent level systems described by the su(2) Lie algebra, representing an environment with a large magnitude of anharmonicity. Based on the previous work by Suarez and Silbey [J. Chem. Phys. 95, 9115 (1991)] and by Makri [J. Chem. Phys. 111, 6164 (1999)] that the spin bath can be mapped to a Gaussian environment under its linear response limit, we use the time-domain Prony fitting decomposition scheme to the bare-bath time correlation function (TCF) given by the bosonic fluctuation-dissipation theorem to generate the exponential decay basis (or pseudo modes) for DEOM construction. The accuracy and efficiency of this strategy have been explored by a variety of numerical results. We envision that this work provides new insights into extending the hierarchical equations of motion and DEOM approach to certain types of anharmonic environments with arbitrary TCF or spectral density.

A Gaussian interval type-2 fuzzy characterization method based on heterogeneous big data and its application in forest ecological assessment

The under-forest economy is a new agricultural and forestry production mode. It can improve the utilization efficiency of forest land and make full use of forest resources, forest space, and forest ecological environment through different forms of industries such as understory planting and breeding. The under-forest economy has important ecological and economic benefits, significant to rural revitalization and industrial structure adjustment. It has been widely discussed by people in recent years. The forest ecological security level is a core factor to be considered in selecting sites for the under-forest economy. In practice, some forest ecological security evaluation indexes usually show heterogeneous forms. To comprehensively evaluate the level of forest ecological security, this study constructs a new multi-indicator fuzzy evaluation method based on heterogeneous big data. Firstly, a new linguistic scale function is defined to realize the consistent conversion of multi-granularity linguistic information. A Gaussian interval type-2 fuzzy aggregation formula for heterogeneous large-scale data is proposed. This formula is used to describe the differences in evaluation information between individuals caused by different knowledge backgrounds of evaluators. Then, the Gaussian interval type-2 fuzzy cross-entropy is defined, and it is verified to satisfy the excellent properties. This cross-entropy is applied to determine the objective weights of evaluation indexes. Considering the risk-averse psychology of experts and combining the prospect theory, the MULTIMOORA method in the Gaussian interval type-2 fuzzy environment is proposed. Finally, the applicability of the constructed Gaussian interval type-2 fuzzy comprehensive evaluation method (GIT2FCE) is verified through a case study conducted on the site selection of the under-forest economic industry.

Modeling the unphysical pseudomode model with physical ensembles: Simulation, mitigation, and restructuring of non-Markovian quantum noise

The influence of a Gaussian environment on a quantum system can be described by effectively replacing the continuum with a discrete set of ancillary quantum and classical degrees of freedom. This defines a pseudomode model which can be used to classically simulate the reduced system dynamics. Here we consider an alternative point of view and analyze the potential benefits of an analog or digital quantum simulation of the pseudomode model itself. Superficially, such a direct experimental implementation is, in general, impossible due to the unphysical properties of the effective degrees of freedom involved. However, we show that the effects of the unphysical pseudomode model can still be reproduced using measurement results over an ensemble of physical systems involving ancillary harmonic modes and an optional stochastic driving field. This is done by introducing an extrapolation technique whose efficiency is limited by stability against imprecision in the measurement data. We examine how such a simulation would allow us to (i) perform a quantum simulation of the effects of complex nonperturbative and non-Markovian environments in regimes that are challenging for classical simulation; (ii) conversely, mitigate potential unwanted non-Markovian noise present in quantum devices; and (iii) restructure some of the properties of a given physical bath, such as its temperature. Published by the American Physical Society 2024

Open Quantum System Dynamics from Infinite Tensor Network Contraction.

Approaching the long-time dynamics of non-Markovian open quantum systems presents a challenging task if the bath is strongly coupled. Recent proposals address this problem through a representation of the so-called process tensor in terms of a tensor network. We show that for Gaussian environments highly efficient contraction to a matrix product operator (MPO) form can be achieved with infinite MPO evolution methods, leading to significant computational speed-up over existing proposals. The result structurally resembles open system evolution with carefully designed auxiliary degrees of freedom, as in hierarchical or pseudomode methods. Here, however, these degrees of freedom are generated automatically by the MPO evolution algorithm. Moreover, the semigroup form of the resulting propagator enables us to explore steady-state physics, such as phase transitions.

Amplification of the anomalous scaling in the Kazantsev-Kraichnan model with finite-time correlations and spatial parity violation.

By using the field theoretic renormalization group technique together with the operator product expansion, simultaneous influence of the spatial parity violation and finite-time correlations of an electrically conductive turbulent environment on the inertial-range scaling behavior of correlation functions of a passively advected weak magnetic field is investigated within the corresponding generalized Kazantsev-Kraichnan model in the second order of the perturbation theory (in the two-loop approximation). The explicit dependence of the anomalous dimensions of the leading composite operators on the fixed point value of the parameter that controls the presence of finite-time correlations of the turbulent field as well as on the parameter that drives the amount of the spatial parity violation (helicity) in the system is found even in the case with the presence of the large-scale anisotropy. In accordance with the Kolmogorov's local isotropy restoration hypothesis, it is shown that, regardless of the amount of the spatial parity violation, the scaling properties of the model are always driven by the anomalous dimensions of the composite operators near the isotropic shell. The asymptotic (inertial-range) scaling form of all single-time two-point correlation functions of arbitrary order of the passively advected magnetic field is found. The explicit dependence of the corresponding scaling exponents on the helicity parameter as well as on the parameter that controls the finite-time velocity correlations is determined. It is shown that, regardless of the amount of the finite-time correlations of the given Gaussian turbulent environment, the presence of the spatial parity violation always leads to more negative values of the scaling exponents, i.e., to the more pronounced anomalous scaling of the magnetic correlation functions. At the same time, it is shown that the stronger the violation of spatial parity, the larger the anomalous behavior of magnetic correlations.

Generalized system-bath entanglement theorem for Gaussian environments.

The entanglement between system and bath often plays a pivotal role in complex systems spanning multiple orders of magnitude. A system-bath entanglement theorem was previously established for Gaussian environments in J. Chem. Phys. 152, 034102 (2020) regarding linear response functions. This theorem connects the entangled responses to the local system and bare bath properties. In this work, we generalize it to correlation functions. Key steps in derivations involve using the generalized Langevin dynamics for hybridizing bath modes and the Bogoliubov transformation that maps the original finite-temperature reservoir to an effective zero-temperature vacuum by employing an auxiliary bath. The generalized theorem allows us to evaluate the system-bath entangled correlations and the bath mode correlations in the total composite space, as long as we know the bare-bath statistical properties and obtain the reduced system correlations. To demonstrate the cross-scale entanglements, we utilize the generalized theorem to calculate the solvation free energy of an electron transfer system with intramolecular vibrational modes.

Fat‐tailed DSGE models: A survey and new results

AbstractWe review recent advances in dynamic stochastic general equilibrium theory concerned with the emergence of fat‐tailed time‐series distributions. Focusing on mechanisms that are firmly grounded in structural equilibrium models, we provide a common reference framework to organize existing contributions according to whether they entail extreme business cycle swings as an endogenous response to small and short‐lived shocks (“thin in, fat out”), or rather as an automatic consequence of large and/or heteroskedastic exogenous impulses (“fat in, fat out”). Within the former class, non‐Gaussian features of equilibrium patterns can endogenously emerge in fully rational, Gaussian environments. Using an empirically plausible real business cycle framework, we also report novel simulation‐based evidence that helps reconcile theoretical predictions with the documented higher‐order properties of time‐series data for output measures.

The q-gradient LMS spline adaptive filtering algorithm and its variable step-size variant

In this study, an innovation q-gradient least-mean-square (LMS) spline adaptive filtering (S-AF) algorithm (SAF-qLMS) on the basis of the theory of q-derivative is proposed. The q-calculus confronts the issue of slow convergence by mitigating the over-reliance of LMS-type algorithms on the diffusion of eigenvalues in the input correlation matrix. Compared to conventional derivatives, the SAF-qLMS exploits q-calculus to compute the secant of the cost function, enabling it to take larger steps in the search direction for q>1. Furthermore, for balancing the convergence rate and steady-state error of SAF-qLMS and solving the deficiency of the fixed step-size, the SAF-VqLMS based on variable step-size is further proposed. Finally, the convergence conditions of the SAF-qLMS are discussed. Simulations in a correlated Gaussian input environment confirm the outstanding performance of the proposed algorithms for nonlinear system identification.

On the Unraveling of Open Quantum Dynamics

It is well known that the state operator of an open quantum system can be generically represented as the solution of a time-local equation — a quantum master equation. Unraveling in quantum trajectories offers a picture of open system dynamics dual to solving master equations. In the unraveling picture, physical indicators are computed as Monte Carlo averages over a stochastic process valued in the Hilbert space of the system. This approach is particularly adapted to simulate systems in large Hilbert spaces. We show that the dynamics of an open quantum system generically admits an unraveling in the Hilbert space of the system described by a Markov process generated by ordinary stochastic differential equations for which rigorous concentration estimates are available. The unraveling can be equivalently formulated in terms of norm-preserving state vectors or in terms of linear “ostensible” processes trace preserving only on average. We illustrate the results in the case of a two level system in a simple boson environment. Next, we derive the state-of-the-art form of the Diósi-Gisin-Strunz Gaussian random ostensible state equation in the context of a model problem. This equation provides an exact unraveling of open systems in Gaussian environments. We compare and contrast the two unravelings and their potential for applications to quantum error mitigation.

Quantum-Classical Decomposition of Gaussian Quantum Environments: A Stochastic Pseudomode Model

Quantum-Classical Decomposition of Gaussian Quantum Environments: A Stochastic Pseudomode Model

A Generalized Robust Logarithmic Family-Based Adaptive Filtering Algorithms

In recent years, algorithms based on the Maximum Versoria Criterion (MVC) and a relative logarithmic cost function have gained the attention of researchers because they improve the filtering accuracy and robustness towards non-Gaussian/impulsive noises. To further enhance the steady-state convergence behavior of these aforementioned algorithms in impulsive noise scenarios, we introduce a generalized, robust logarithmic family (GRLF) framework that underlies the relative logarithmic cost function and MVC, and the corresponding GRLF-based adaptive filters called least mean square based-GRLF (GRLF-LMS) and least absolute difference based-GRLF (GRLF-LAD) algorithms are designed. With an approximate solution using Taylors expansion, the steady-state behavior of the GRLF-LMS and GRLF-LAD methods is presented. Then, algorithms are used in practical simulation studies in system identification to compare the performance of GRLF-LMS and GRLF-LAD filtering in Gaussian and non-Gaussian impulsive environments in terms of accuracy and robustness to that of their competitors.

Improving the sensitivity of distributed phase estimation under noisy Gaussian environment with noiseless linear amplification

The deterioration of precision caused by quantum decoherence in dissipative environments is a longstanding problem in the development of distributed quantum metrology. Therefore, it is significant to effectively overcome the entanglement-distribution loss and channel noise of dissipative environments and improve the measurement-sensitivity. Here, we introduce noiseless linear amplifier (NLA) based on photon catalysis into distributed phase estimation to mitigate the loss and noise. Through utilizing a series of reduction and equivalence relations to simplify the problem of distributed phase estimation to a single-parameter estimation situation, our results show that Photon catalysis (PC)-NLAs can effectively mitigate the loss and noise of dissipative environments, and greatly improve the measurement-sensitivity. More interestingly, we find that adding thermal photons of environment has positive contributions on the measurement-sensitivity under certain circumstances. Our scheme should prove valuable for the global wide-area quantum sensor network.

Dissipatons as generalized Brownian particles for open quantum systems: Dissipaton-embedded quantum master equation.

Dissipaton theory had been proposed as an exact, nonperturbative approach to deal with open quantum system dynamics, where the influence of the Gaussian environment is characterized by statistical quasi-particles, named dissipatons. In this work, we revisit the dissipaton equation of motion theory and establish an equivalent dissipaton-embedded quantum master equation (DQME) that gives rise to dissipatons as generalized Brownian particles. As explained in this work, the DQME supplies a direct approach to investigate the statistical characteristics of dissipatons and, thus, the physically supporting hybrid bath modes. Numerical demonstrations are carried out on the electron transfer model, exhibiting the transient statistical properties of the solvation coordinate.

A Distributed Underwater Multi-Target Tracking Algorithm Based on Two-Layer Particle Filter

Underwater multi-target tracking is one of the key technologies for military missions, including patrol and combat in the crucial area. Since the underwater environment is complex and targets’ trajectories may intersect when they are in a dense area, it is challenging to guarantee the precision of observed information. In order to provide high-precision underwater localization and tracking services over an underwater monitoring network, a dynamic network resource allocation mechanism and an underwater multi-target tracking algorithm based on a two-layer particle filter with distributed probability fusion (TLPF-DPF) are proposed. The position estimation model based on geometric constraints and the dynamic allocation mechanism of network resources based on prior position estimation are designed. Using the improved filtering algorithm with known initial states, the reliable tracking of multiple targets with trajectory intersection in a small area under complex noises is achieved. In the non-Gaussian environment, the average positioning error of TLPF-DPF is less by nearly 30% than alternative algorithms. When switching from a Gaussian environment to a non-Gaussian environment, the performance degradation of TLPF-DPF is less than 12%, which exhibits stability compared with other algorithms when targets are close to each other with crossing trajectories.

Natural Intelligence as the Brain of Intelligent Systems

This article discusses the concept and applications of cognitive dynamic systems (CDS), which are a type of intelligent system inspired by the brain. There are two branches of CDS, one for linear and Gaussian environments (LGEs), such as cognitive radio and cognitive radar, and another one for non-Gaussian and nonlinear environments (NGNLEs), such as cyber processing in smart systems. Both branches use the same principle, called the perception action cycle (PAC), to make decisions. The focus of this review is on the applications of CDS, including cognitive radios, cognitive radar, cognitive control, cyber security, self-driving cars, and smart grids for LGEs. For NGNLEs, the article reviews the use of CDS in smart e-healthcare applications and software-defined optical communication systems (SDOCS), such as smart fiber optic links. The results of implementing CDS in these systems are very promising, with improved accuracy, performance, and lower computational costs. For example, CDS implementation in cognitive radars achieved a range estimation error that is as good as 0.47 (m) and a velocity estimation error of 3.30 (m/s), outperforming traditional active radars. Similarly, CDS implementation in smart fiber optic links improved the quality factor by 7 dB and the maximum achievable data rate by 43% compared to those of other mitigation techniques.

A Robust Hierarchical Estimation Scheme for Vehicle State Based on Maximum Correntropy Square-Root Cubature Kalman Filter

Accurate acquisition of vehicle dynamics state information is essential for vehicle active safety control systems. However, these states cannot be easily measured, and the measurement is expensive. Conventional Kalman filters perform well for vehicle state estimation in Gaussian environments but exhibit low accuracy and robustness under practical non-Gaussian noise. Vehicle model parameter ingestion, inaccurate tire force calculation, and non-Gaussian noise from on-board sensors cause great challenges to the estimation of vehicle driving states. Therefore, this paper presents a robust hierarchical estimation scheme for vehicle driving state based on the maximum correntropy square-root cubature Kalman filter (MCSCKF) using easily measurable on-board sensor information. First, the vehicle mass is dynamically updated based on the recursive least squares (FRLS) method with a forgetting factor. Then, an adaptive sliding mode observer (ASMO) is designed to estimate the longitudinal and lateral tire forces. Ultimately, the vehicle states are estimated based on the MCSCKF under non-Gaussian noise. Two typical operating situations are carried out to verify the validity of the proposed estimation scheme. The results prove that the proposed estimation scheme can estimate the vehicle's driving state accurately compared to other common methods. And the MCSCKF algorithm has better accuracy and robustness than the traditional Kalman filters for vehicle state estimation in non-Gaussian situations.

A Gaussian Type-2 Fuzzy Programming Approach for Multicrowd Congestion-Relieved Evacuation Planning

Large-scale emergencies occur frequently around the world, causing serious casualties. Emergency evacuation is one of the top priorities after a disaster. Due to the uncertain and complex evacuation processes, evacuation plans obtained in a deterministic context may not meet the requirements of practical engineering applications. This research considers a multi-crowd congestion-relieved evacuation problem in Gaussian Type-2 fuzzy environments. A path-based one destination network flow (P-ODNF) model is developed for the problem formulation. To relieve the traffic congestion, a multi-point diversion evacuation strategy is employed in the model’s construction. The uncertainties associated with the evacuation process are expressed as Gaussian Type-2 fuzzy variables. A critical value-based defuzzification technique is adopted to handle the Type-2 fuzziness. Based on the credibility measure, the uncertain P-ODNF model is transformed into its deterministic counterpart. An efficient adaptive chaos particle swarm optimization algorithm (A-CPSO) is designed for model solving. Several numerical experiments are performed to demonstrate the proposed methodology. A sensitivity analysis is performed to illustrate the logical correctness of the proposed defuzzification process. The computational results show that A-CPSO is competitive in both its effectiveness and efficiency. The proposed methodology can coordinate multiple simultaneous evacuation processes to relieve congestion and improves the overall evacuation efficiency.

Using the Environment to Understand non-Markovian Open Quantum Systems

Tracing out the environmental degrees of freedom is a necessary procedure when simulating open quantum systems. While being an essential step in deriving a tractable master equation it represents a loss of information. In situations where there is strong interplay between the system and environmental degrees of freedom this loss makes understanding the dynamics challenging. These dynamics, when viewed in isolation, have no time-local description: they are non-Markovian and memory effects induce complex features that are difficult to interpret. To address this problem, we here show how to use system correlations, calculated by any method, to infer any correlation function of a Gaussian environment, so long as the coupling between system and environment is linear. This not only allows reconstruction of the full dynamics of both system and environment, but also opens avenues into studying the effect of a system on its environment. In order to obtain accurate bath dynamics, we exploit a numerically exact approach to simulating the system dynamics, which is based on the construction and contraction of a tensor network that represents the process tensor of this open quantum system. Using this we are able to find any system correlation function exactly. To demonstrate the applicability of our method we show how heat moves between different modes of a bosonic bath when coupled to a two-level system that is subject to an off-resonant drive.

2D and 3D Angles-Only Target Tracking Based on Maximum Correntropy Kalman Filters.

In this paper, angles-only target tracking (AoT) problem is investigated in the non Gaussian environment. Since the conventional minimum mean square error criterion based estimators tend to give poor accuracy in the presence of large outliers or impulsive noises in measurement, a maximum correntropy criterion (MCC) based framework is presented. Accordingly, three new estimation algorithms are developed for AoT problems based on the conventional sigma point filters, termed as MC-UKF-CK, MC-NSKF-GK and MC-NSKF-CK. Here MC-NSKF-GK represents the maximum correntropy new sigma point Kalman filter realized using Gaussian kernel and MC-NSKF-CK represents realization using Cauchy kernel. Similarly, based on the unscented Kalman filter, MC-UKF-CK has been developed. The performance of all these estimators is evaluated in terms of root-mean-square error (RMSE) in position and % track loss. The simulations were carried out for 2D as well as 3D AoT scenarios and it was inferred that, the developed algorithms performed with improved estimation accuracy than the conventional ones, in the presence of non Gaussian measurement noise.