Arbitrary System Research Articles

Classifying Two-Body Hamiltonians for Quantum Darwinism

Quantum Darwinism is a paradigm to understand how classically objective reality emerges from within a fundamentally quantum universe. Despite the growing attention that this field of research has been enjoying, it is currently not known what specific properties a given Hamiltonian describing a generic quantum system must have to allow the emergence of classicality. Therefore, in the present work, we consider a broadly applicable generic model of an arbitrary finite-dimensional system interacting with an environment formed from an arbitrary collection of finite-dimensional degrees of freedom via an unspecified, potentially time-dependent Hamiltonian containing at most two-body interaction terms. We show that such models support quantum Darwinism if the set of operators acting on the system which enter the Hamiltonian satisfy a set of commutation relations with a pointer observable and with one other. We demonstrate our results by analyzing a wide range of example systems: a qutrit interacting with a qubit environment, a qubit-qubit model with interactions alternating in time, and a series of collision models including a minimal model of a quantum Maxwell demon. Published by the American Physical Society 2024

Managing singular kernels and logarithmic corrections in the staggered six-vertex model

In this paper, we investigate the spectral properties of the staggered six-vertex model with Z2 symmetry for arbitrary system sizes L using non-linear integral equations (NLIEs). Our study is motivated by two key questions: what is the accuracy of results based on the ODE/IQFT correspondence in the asymptotic regime of large system sizes, and what is the optimal approach based on NLIE for analyzing the staggered six-vertex model?We demonstrate that the quantization conditions for low-lying primary and descendant states, derived from the ODE/IQFT approach in the scaling limit, are impressively accurate even for relatively small system sizes. Specifically, in the anisotropy parameter range π/4 < γ < π/2, the difference between NLIE and ODE/IQFT results for energy and quasi-momentum eigenvalues is of order OL−2.Furthermore, we present a unifying framework for NLIEs, distinguishing between versions with singular and regular kernels. We provide a compact derivation of NLIE with a singular kernel, followed by an equivalent set with a regular kernel. We address the stability issues in numerical treatments and offer solutions to achieve high-accuracy results, validating our approach for system sizes ranging from L = 2 to L = 1024.Our findings not only validate the ODE/IQFT approach for finite system sizes but also enhance the understanding of NLIEs in the context of the staggered six-vertex model. We hope the insights gained from this study have significant implications for resolving the spectral problem of other lattice systems with emergent non-compact degrees of freedom and provide a foundation for future research in this domain.

Generalized representative structures for atomistic systems.

A new method is presented to generate atomic structures that reproduce the essential characteristics of arbitrary material systems, phases, or ensembles. Previous methods allow one to reproduce the essential characteristics (e.g., the chemical disorder) of a large random alloy within a small crystal structure. The ability to generate small representations of random alloys, along with the restriction to crystal systems, results from using the fixed-lattice cluster correlations to describe structural characteristics. A more general description of the structural characteristics of atomic systems is obtained using complete sets of atomic environment descriptors. These are used within for generating representative atomic structures without restriction to fixed lattices. A general data-driven approach is provided here utilizing the atomic cluster expansion (ACE) basis. TheN-body ACE descriptors are a complete set of atomic environment descriptors that span both chemical and spatial degrees of freedom and are used within for describing atomic structures. The generalized representative structure (GRS) method presented within generates small atomic structures that reproduce ACE descriptor distributions corresponding to arbitrary structural and chemical complexity. It is shown that systematically improvable representations of crystalline systems on fixed parent lattices, amorphous materials, liquids, and ensembles of atomic structures may be produced efficiently through optimization algorithms. With the GRS method, we highlight reduced representations of atomistic machine-learning training datasets that contain similar amounts of information and small 40-72 atom representations of liquid phases. The ability to use GRS methodology as a driver for informed novel structure generation is also demonstrated. The advantages over other data-driven methods and state-of-the-art methods restricted to high-symmetry systems are highlighted.

Numerical model of N-level cascade systems for atomic Radio Frequency sensing applications

A ready-to-use numerical model has been developed for the atomic ladder (cascade) systems which are widely exploited in Rydberg Radio Frequency (RF) sensors. The model has been explicitly designed for user convenience and to be extensible to arbitrary N-level non-thermal systems. The versatility and adaptability of the model is validated up to 4-level atomic systems by direct comparison with experimental results from the prior art. The numerical model provides a good approximation to the experimental results and provides experimentalists with a convenient ready-to-use model to optimise the operation of an N-level Rydberg RF sensor. Current sensors exploit the 4-level atomic systems based on alkali metal atoms which require visible frequency lasers and these can be expensive and also suffer from high attenuation within optical fiber. The ability to quickly and simply explore more complex N-level systems offers the potential to use cheaper and lower-loss near-infrared lasers.

Reverse-Bent Modular Coil Structure with Enhanced Output Stability in DWPT for Arbitrary Linear Transport Systems.

Dynamic wireless power transfer (DWPT) systems with segmented transmitters suffer from output pulsations during the moving process. Although numerous coil structures have been developed to mitigate this fluctuation, the parameter design process is complicated and restricted by specific working conditions (e.g., air gaps). To solve these problems, a novel reverse-bent modular transmitter structure is proposed for DWPT in industrial automatic application scenarios such as linear transport systems. Considering the heterogeneous current density distribution in the adjacent region between two coils which causes a drop in magnetic field, the proposed coil structure attempts to eliminate the effects of the adjacent region by bending the terminal parts of each coil reversely to the ferrite layer for shielding. Compared to traditional planar couplers, this structure array can generate a uniform magnetic field over various air gaps. A 100 W laboratory prototype was built to verify the feasibility of the proposed system. The experimental results show that the proposed system achieved a constant output voltage, and the output pulsation was within ±2.3% in the dynamic powering process. The average efficiency was about 88.29%, with a 200 mm transfer distance. When the air gap varied from 20 mm to 30 mm, the system could still retain constant voltage output characteristics.

Representing turbulent statistics with partitions of state space. Part 1. Theory and methodology

This is the first of a two-part paper. We formulate a data-driven method for constructing finite-volume discretizations of an arbitrary dynamical system's underlying Liouville/Fokker–Planck equation. A method is employed that allows for flexibility in partitioning state space, generalizes to function spaces, applies to arbitrarily long sequences of time-series data, is robust to noise and quantifies uncertainty with respect to finite sample effects. After applying the method, one is left with Markov states (cell centres) and a random matrix approximation to the generator. When used in tandem, they emulate the statistics of the underlying system. We illustrate the method on the Lorenz equations (a three-dimensional ordinary differential equation) saving a fluid dynamical application for Part 2 (Souza, J. Fluid Mech., vol. 997, 2024, A2).

A Virtual Reality Tool for Accuracy Assessment of 3D Models in an Immersive Virtual Environment

Abstract. Accurate validation and assessment techniques are essential for ensuring the reliability of spatial reconstructions derived from photogrammetry, enabling well-informed decision-making across diverse domains. This study presents a Virtual Reality (VR) based accuracy assessment tool tailored for evaluating the accuracy and quality of 3D models generated by Unmanned Aerial Vehicles (UAVs). Leveraging the Unity game engine platform, our workflow entails three key steps: aligning real-world coordinates with an arbitrary Unity coordinate system, transforming the positions of Ground Control Points (GCPs) from field survey to the arbitrary system using a reference GCP, and marking observed points on the 3D models. Absolute and Relative Root Mean Square Errors (RMSE), Mean Errors (ME), and Standard Deviation of errors (SD) are computed within the virtual environment via the game object transform properties. The error distributions around each GCP are visually depicted using Unity game engine components for enhanced interaction and comprehension. The efficacy of the tool is validated through experimentation on four 3D models generated from varying camera angles during UAV data capture. The tool provides the opportunity to directly interact with the 3D models and visualize the errors, which is quite distinct from traditional methods. Using the developed tool, results were obtained to indicate that configurations employing camera angles of 60° + 75º exhibit notable performance in terms of relative and absolute accuracy.

Numerical analysis of resonant axion-photon mixing

Many present-day axion searches attempt to probe the mixing of axions and photons, which occurs in the presence of an external magnetic field. While this process is well understood in a number of simple and idealized contexts, a strongly varying or highly inhomogeneous background can impact the efficiency and evolution of the mixing in a nontrivial manner. In an effort to develop a generalized framework for analyzing axion-photon mixing in arbitrary systems, we focus in this work on directly solving the axion-modified form of Maxwell’s equations across a simulation domain with a spatially varying background. We concentrate specifically on understanding resonantly enhanced axion-photon mixing in a highly magnetized plasma, which is a key ingredient for developing precision predictions of radio signals emanating from the magnetospheres of neutron stars. After illustrating the success and accuracy of our approach for simplified limiting cases, we compare our results with a number of analytic solutions recently derived to describe mixing in these systems. We find that our numerical method demonstrates a high level of agreement with one, but only one, of the published results. Interestingly, our method also recovers the mixing between the axion and magnetosonic-t and Alfvén modes; these modes cannot escape from the regions of dense plasma but could nontrivially alter the dynamics in certain environments. Future work will focus on extending our calculations to study resonant mixing in strongly variable backgrounds, mixing in generalized media (beyond the strong magnetic field limit), and the mixing of photons with other light bosonic fields, such as dark photons. Published by the American Physical Society 2024

Aspect ratio-dependent volume resistivity in unidirectional composites: Insights from electrical conduction behavior

The electrical properties of carbon fibers serve as the foundation for the multifunctional applications of carbon fiber-reinforced composite structures. In scenarios that exploit the electrical characteristics of materials, accurate estimation of electrical resistivity stands as a critical factor. This study endeavors to elucidate the electrical conduction behaviors in unidirectional composites with different fiber orientation angles (0°, 15°, 30°, 45°, 60°, 75°, and 90°) and aspect ratios, thereby deriving the volume resistivity within an arbitrary Cartesian coordinate system. Employing thermal infrared imaging technology and finite element analysis, we identified distinctive electrical conduction behaviors associated with aspect ratios in carbon fiber composite plates. Notably, a critical aspect ratio exists wherein the diagonal yarn is the only conductive path between two electrodes. Below this critical threshold, no direct conductive path exists, and current flows through the shortest distance between parallel yarns. Conversely, beyond the critical aspect ratio value, multiple yarns form conductive paths between the two electrodes. Based on the electrical conduction behavior of unidirectional composites under different angles and aspect ratios, the volume resistivity with finite boundaries was derived and examined under an arbitrary Cartesian coordinate basis.

Improving the convergence of an iterative algorithm for solving arbitrary linear equation systems using classical or quantum binary optimization

Improving the convergence of an iterative algorithm for solving arbitrary linear equation systems using classical or quantum binary optimization

On determinant representations of Hermite–Padé polynomials

In this work we introduce new concepts: weakly normal index, weakly perfect system of functions. With these concepts for an arbitrary system of power series we formulate and prove criteria for the uniqueness of solutions to two Hermite–Padé problems, and obtain explicit determinant representations of Hermite–Padé types 1 and 2 polynomials. Proven statements complement well-known results in Hermite–Padé approximation theory.

Clifford orbits and stabilizer states

Abstract Stabilizer states serve as “classical objects” in the stabilizer formalism of quantum theory, and play an important role in quantum error correction, fault-tolerant quantum computation, and quantum communication. They provide an efficient description of many basic features of quantum theory and exhibit a rich structure. For prime dimensional systems, they may be defined by two quite different yet equivalent ways: The first is via stabilizer groups (maximal Abelian subgroups of the discrete Heisenberg-Weyl group). The second is via the orbits of the Clifford group acting on any computational basis state. However, in a general dimensional system, this equivalence breaks down, and consequently, it is desirable to classify the difference and relation between the above two approaches to stabilizer states. In this work, we show that these two approaches are equivalent if and only if the system dimension is square-free (i.e., has no square factor). Furthermore, we completely clarify the relation between the Cli&amp;amp;amp;#64256;ord orbits and stabilizer states in an arbitrary dimensional system, derive the explicit expressions of the Clifford orbits and determine their cardinalities.&amp;#xD;

Genuine entanglement detection via projection map in multipartite systems

We present a formalism to detect genuine multipartite entanglement by considering projection map which is a positive but not completely positive map. Projection map has been motivated by the no-pancake theorem which repudiates the existence of a quantum operation that maps the Bloch sphere onto a disk along its equator. The not-complete positivity feature of projection map is explored to investigate genuine multipartite entanglement in arbitrary N-qubit quantum systems. Our proposed framework can detect some important classes of genuinely entangled states in tripartite and quadripartite scenarios. We provide illustrative example to show the efficacy of our formalism to detect a class of tripartite PPT bound entangled states. Finally, we construct a suitable witness operator based on projection map to certify genuine tripartite entanglement, which is likely to be feasible experimentally.

GPTFF: A high-accuracy out-of-the-box universal AI force field for arbitrary inorganic materials

This study introduces a novel artificial intelligence (AI) force field, namely a graph-based pre-trained transformer force field (GPTFF), which can simulate arbitrary inorganic systems with good precision and generalizability. Harnessing a large trove of the data and the attention mechanism of transformer algorithms, the model can accurately predict energy, atomic force, and stress with mean absolute error (MAE) values of 32 meV/atom, 71 meV/Å, and 0.365 GPa, respectively. The dataset used to train the model includes 37.8 million single-point energies, 11.7 billion force pairs, and 340.2 million stresses. We also demonstrated that the GPTFF can be universally used to simulate various physical systems, such as crystal structure optimization, phase transition simulations, and mass transport. The model is publicly released with this paper, enabling anyone to use it immediately without needing to train it.

Shi arrangements and low elements in Coxeter groups

AbstractGiven an arbitrary Coxeter system and a non‐negative integer , the ‐Shi arrangement of is a subarrangement of the Coxeter hyperplane arrangement of . The classical Shi arrangement () was introduced in the case of affine Weyl groups by Shi to study Kazhdan–Lusztig cells for . As two key results, Shi showed that each region of the Shi arrangement contains exactly one element of minimal length in and that the union of their inverses form a convex subset of the Coxeter complex. The set of ‐low elements in were introduced to study the word problem of the corresponding Artin–Tits (braid) group and they turn out to produce automata to study the combinatorics of reduced words in . In this article, we generalize and extend Shi's results to any Coxeter system for any : (1) the set of minimal length elements of the regions in a ‐Shi arrangement is precisely the set of ‐low elements, settling a conjecture of the first and third authors in this case; (2) the union of the inverses of the (0‐)low elements form a convex subset in the Coxeter complex, settling a conjecture by the third author, Nadeau and Williams.

Infinite Order Hydrodynamics: An Analytical Example.

We construct a kinetic model for matter-radiation interactions whose hydrodynamic gradient expansion can be computed analytically up to infinite order in derivatives, in the fully nonlinear regime, and for arbitrary flows. The frequency dependence of the opacity of matter is chosen to mimic the relaxation time of a self-interacting scalar field. In this way, the transient sector simulates that of a realistic quantum field theory. The gradient series is found to diverge for most flows, in agreement with previous findings. We identify, for the model at hand, the mechanism at the origin of the divergence, and we provide a successful regularization scheme. Additionally, we propose a universal qualitative framework for predicting the breakdown of the gradient expansion of an arbitrary microscopic system undergoing a given flow. This framework correctly recovers all previously known instances of gradient expansion divergence. As a new prediction, we show that the gradient expansion diverges when the energy-dependent mean free path is unbounded above.

Nonlocality activation using local filtering operations based on CGLMP inequality

Entanglement is necessary but not sufficient to demonstrate nonlocality as there exist local entangled states which do not violate any Bell inequality. In recent years, the activation of nonlocality (known as hidden nonlocality) by using local filtering operations has gained considerable interest. In the original proposal of Popescu [Phys. Rev. Lett. 74, 2619 (1995)] the hidden nonlocality was demonstrated for the Werner class of states in d ≥ 5. In this paper, we demonstrate the hidden nonlocality for a class of mixed entangled states (convex mixture of a pure state and color noise) in an arbitrary d-dimensional system using suitable local filtering operations. For our demonstration, we consider the quantum violation of Collins-Linden-Gisin-Masser-Popescu (CGLMP) inequality which has hitherto not been considered for this purpose. We show that when the pure state in the aforementioned mixed entangled state is a maximally entangled state, the range of the mixing parameter for revealing hidden nonlocality increases with increasing the dimension of the system. Importantly, we find that for d ≥ 8, hidden non-locality can be revealed for the whole range of mixing parameter. Further, by considering another pure state, the maximally CGLMP-violating state, we demonstrate the activation of nonlocality by using the same local filtering operation. We have also shown the activation of quantum fidelity for mixed entangled states using the same local filtering operator.

Trade-off between bagging and boosting for quantum separability-entanglement classification

Certifying whether an arbitrary quantum system is entangled or not, is, in general, an NP-hard problem. Though various necessary and sufficient conditions have already been explored in this regard for lower-dimensional systems, it is hard to extend them to higher dimensions. Recently, an ensemble bagging and convex hull approximation (CHA) approach (together, BCHA) was proposed and it strongly suggests employing a machine learning technique for the separability-entanglement classification problem. However, BCHA does only incorporate the balanced dataset for classification tasks which results in lower average accuracy. In order to solve the data imbalance problem in the present literature, an exploration of the boosting technique has been carried out, and a trade-off between the boosting and bagging-based ensemble classifier is explored for quantum separability problems. For the two-qubit and two-qutrit quantum systems, the pros and cons of the proposed random under-sampling boost CHA (RUSBCHA) for the quantum separability problem are compared with the state-of-the-art CHA and BCHA approaches. As the data are highly unbalanced, performance measures such as overall accuracy, average accuracy, F-measure, and G-mean are evaluated for a fair comparison. The outcomes suggest that RUSBCHA is an alternative to the BCHA approach. Also, for several cases, performance improvements are observed for RUSBCHA since the data are imbalanced.

Amplitude equations for wave bifurcations in reaction–diffusion systems

A wave bifurcation is the counterpart to a Turing instability in reaction–diffusion systems, but where the critical wavenumber corresponds to a pure imaginary pair rather than a zero temporal eigenvalue. Such bifurcations require at least three components and give rise to patterns that are periodic in both space and time. Depending on boundary conditions, these patterns can comprise either rotating or standing waves. Restricting to systems in one spatial dimension, complete formulae are derived for the evaluation of the coefficients of the weakly nonlinear normal form of the bifurcation up to order five, including those that determine the criticality of both rotating and standing waves. The formulae apply to arbitrary n-component systems ( n⩾3 ) and their evaluation is implemented in software which is made available as supplementary material. The theory is illustrated on two different versions of three-component reaction–diffusion models of excitable media that were previously shown to feature super- and subcritical wave instabilities and on a five-component model of two-layer chemical reaction. In each case, two-parameter bifurcation diagrams are produced to illustrate the connection between complex dispersion relations and different types of Hopf, Turing, and wave bifurcations, including the existence of several codimension-two bifurcations.

Star exponentials from propagators and path integrals

In this paper we address the relation between the star exponentials emerging within the Deformation Quantization formalism and Feynman’s path integrals associated with propagators in quantum dynamics. In order to obtain such a relation, we start by visualizing the quantum propagator as an integral transform of the star exponential by means of the symbol corresponding to the time evolution operator and, thus, we introduce Feynman’s path integral representation of the propagator as a sum over all the classical histories. The star exponential thus constructed has the advantage that it does not depend on the convergence of formal series, as commonly understood within the context of Deformation Quantization. We include some basic examples to illustrate our findings, recovering standard results reported in the literature. Further, for an arbitrary finite dimensional system, we use the star exponential introduced here in order to find a particular representation of the star product which may be recognized as the one encountered in the context of the quantum field theory for a Poisson sigma model.