Dimensional Systems Research Articles

Disassembling one-dimensional chains in molybdenum oxides

Abstract The dimensionality of quantum materials strongly affects their physical properties. Although many emergent phenomena, such as charge-density wave and Luttinger liquid behavior, are well understood in one-dimensional (1D) systems, the generalization to explore them in higher dimensional systems is still a challenging task. In this study, we aim to bridge this gap by systematically investigating the crystal and electronic structures of molybdenum-oxide family compounds, where the contexture of 1D chains facilitates rich emergent properties. While the quasi-1D chains in these materials share general similarities, such as the motifs made up of MoO6 octahedrons, they exhibit vast complexity and remarkable tunability. We disassemble the 1D chains in molybdenum oxides with different dimensions and construct effective models to excellently fit their low-energy electronic structures obtained by ab initio calculations. Furthermore, we discuss the implications of such chains on other physical properties of the materials and the practical significance of the effective models. Our work establishes the molybdenum oxides as simple and tunable model systems for studying and manipulating the dimensionality in quantum systems.

Modulating the Electrical Transport in Superconducting NbC Crystals by Fractal Morphology.

The self-similar fractal morphology mediated by nonequilibrium processes is widely observed in low-dimensional materials grown by various techniques. Understanding how these fractal geometries affect the physical and chemical properties of materials and devices is crucial for both fundamental studies and various applications. In particular, the interplay between superconducting phase fluctuations and disorder can give rise to intriguing phenomena depending on the dimensionality. However, current experimental studies on low-dimensional superconductors are limited to two- and one-dimensional systems, leaving fractional dimensional systems largely unexplored. Here, we use chemical vapor deposition to successfully synthesize ultrathin NbC crystals with a well-defined fractal geometry at the nanoscale. By performing electrical transport measurements, we find that both the superconducting and normal-state properties are strongly affected in the fractal samples, where the intrinsic and geometric disorder is induced. In contrast to the 2D crystal, the fractal NbC crystals show a significant low-temperature resistive upturn before the onset of superconducting transition, which can be attributed to the disorder-enhanced electron-electron interaction effect. From transport data analysis, we demonstrate that the superconducting transition in NbC is correlated to the strength of disorder and the fractional dimensions, revealing that nanoscale fractal structures can significantly modify the electronic properties of low-dimensional superconductors. Our work paves the way for the explorations of mesoscopic transport and intriguing superconducting phenomena in fractional dimensions.

Dynamics of high-dimensional quantum systems coupled to a harmonic bath. General theory and implementation via multiconfigurational wave packets and truncated hierarchical equations for the mean-fields.

Modeling the dynamics of a quantum system coupled to a dissipative environment becomes particularly challenging when the system's dimensionality is too high to permit the computation of its eigenstates. This problem is addressed by introducing an eigenstate-free formalism, where the open quantum system is represented as a mixture of high-dimensional, time-dependent wave packets governed by coupled Schrödinger equations, while the environment is described by a multi-component quantum master equation. An efficient computational implementation of this formalism is presented, employing a variational mixed Gaussian/multiconfigurational time-dependent Hartree (G-MCTDH) ansatz for the wave packets and propagating the environment dynamics via hierarchical equations, truncated at the first or second level of the hierarchy. The effectiveness of the proposed methodology is demonstrated on a 61-dimensional model of phonon-driven vibrational relaxation of an adsorbate. G-MCTDH calculations on 4- and 10-dimensional reduced models, combined with truncated hierarchical equations for the mean fields, nearly quantitatively replicate the full-dimensional quantum dynamical results on vibrational relaxation while significantly reducing the computational time. This approach thus offers a promising quantum dynamical method for modeling complex system-bath interactions, where a large number of degrees of freedom must be explicitly considered.

A Local Macroscopic Conservative (LoMaC) Low Rank Tensor Method for the Vlasov Dynamics

In this paper, we propose a novel Local Macroscopic Conservative (LoMaC) low rank tensor method for simulating the Vlasov-Poisson (VP) system. The LoMaC property refers to the exact local conservation of macroscopic mass, momentum and energy at the discrete level. This is a follow-up work of our previous development of a conservative low rank tensor approach for Vlasov dynamics (arXiv:2201.10397). In that work, we applied a low rank tensor method with a conservative singular value decomposition to the high dimensional VP system to mitigate the curse of dimensionality, while maintaining the local conservation of mass and momentum. However, energy conservation is not guaranteed, which is a critical property to avoid unphysical plasma self-heating or cooling. The new ingredient in the LoMaC low rank tensor algorithm is that we simultaneously evolve the macroscopic conservation laws of mass, momentum and energy using a flux-difference form with kinetic flux vector splitting; then the LoMaC property is realized by projecting the low rank kinetic solution onto a subspace that shares the same macroscopic observables by a conservative orthogonal projection. The algorithm is extended to the high dimensional problems by hierarchical Tuck decomposition of solution tensors and a corresponding conservative projection algorithm. Extensive numerical tests on the VP system are showcased for the algorithm’s efficacy.

Index Concepts for Linear Differential-Algebraic Equations in Infinite Dimensions

Different index concepts for regular linear differential-algebraic equations are defined and compared in the general Banach space setting. For regular finite dimensional linear differential-algebraic equations, all these indices exist and are equivalent. For infinite dimensional systems, the situation is more complex. It is proven that although some indices imply others, in general they are not equivalent. The situation is illustrated with a number of examples.

Fermi's golden rule in tunneling models with quantum waveguides perturbed by Kato class measures

Abstract In this paper we consider two dimensional quantum system with an infinite waveguide of the width $d$ and a transversally invariant profile. Furthermore, we assume that at a distant $\rho$ there is a perturbation defined by the Kato measure. We show that, under certain conditions, the resolvent of the Hamiltonian has the second sheet pole which reproduces the resonance at $z(\rho)$ with the asymptotics $z(\rho)=\mathcal E_{\beta ; n}+\mathcal O \Big(\frac{ \exp(-\sqrt{2 |\mathcal E_{\beta ;n}| } \rho )}{\rho }\Big)$ for $\rho$ large and with the resonant energy $\mathcal E_{\beta ;n}$. Moreover, we show that the imaginary component of $z(\rho)$ satisfies Fermi's golden rule which we explicitly derive.

Decomposition and equivalence of general nonlinear dynamical control systems

AbstractProjection and equivalence concepts have been widely studied in the literature. In the present paper two nonlinear systems with the same number of inputs, but not the same number of state variables, are considered. Under mild assumptions, necessary and sufficient conditions are given for the existence of a submersion such that the higher dimensional system projects locally onto the other one. The solution to this problem has relevant applications, for instance in robotics. It includes as a special case the equivalence of nonlinear systems with no particular structure.

Learning quantum properties from short-range correlations using multi-task networks

Characterizing multipartite quantum systems is crucial for quantum computing and many-body physics. The problem, however, becomes challenging when the system size is large and the properties of interest involve correlations among a large number of particles. Here we introduce a neural network model that can predict various quantum properties of many-body quantum states with constant correlation length, using only measurement data from a small number of neighboring sites. The model is based on the technique of multi-task learning, which we show to offer several advantages over traditional single-task approaches. Through numerical experiments, we show that multi-task learning can be applied to sufficiently regular states to predict global properties, like string order parameters, from the observation of short-range correlations, and to distinguish between quantum phases that cannot be distinguished by single-task networks. Remarkably, our model appears to be able to transfer information learnt from lower dimensional quantum systems to higher dimensional ones, and to make accurate predictions for Hamiltonians that were not seen in the training.

Geometry of Kirkwood–Dirac classical states: a case study based on discrete Fourier transform

Abstract The characterization of Kirkwood-Dirac (KD) classicality or non-classicality is very important in quantum information processing. In general, the set of KD classical states with respect to two bases is not a convex polytope[J. Math. Phys. \textbf{65} 072201 (2024)], which makes us interested in finding out in which circumnstances they do form a polytope. In this paper, we focus on the characterization of KD classicality of mixed states for the case where the transition matrix between two bases is a discrete Fourier transform (DFT) matrix in Hilbert space with dimensions $p^2$ and $pq$, respectively, where $p, q$ are prime. For the two particular cases we investigate, the sets of extremal points are finite, implying that the set of KD classical states we characterize forms a convex polytope. We show that for $p^2$ dimensional system, the set $\rm{KD}_{\mathcal{A},\mathcal{B}}^+$ is a convex hull of the set $\rm {pure}({\rm {KD}_{\mathcal{A},\mathcal{B}}^+})$ based on DFT, where $\rm{KD}_{\mathcal{A},\mathcal{B}}^+$ is the set of KD classical states with respect to two bases and $\rm {pure}({\rm {KD}_{\mathcal{A},\mathcal{B}}^+})$ is the set of all the rank-one projectors of KD classical pure states with respect to two bases. In $pq$ dimensional system, we believe that this result also holds. Unfortunately, we do not completely prove it, but some meaningful conclusions are obtained about the characterization of KD classicality.

Stabilization of Continuous Two Dimensional Fractional order Positive Takagi-Sugeno Fuzzy Systems with Delays

Stabilization of Continuous Two Dimensional Fractional order Positive Takagi-Sugeno Fuzzy Systems with Delays

A Dynamic Principal-Agent Problem with One-Sided Commitment

In this paper, we consider a principal-agent problem where the agent is allowed to quit by incurring a cost. When the current agent quits the job, the principal will hire a new one, possibly with a different type. We characterize the principal’s dynamic value function, which could be discontinuous at the boundary, as the (unique) minimal solution of an infinite dimensional system of Hamilton-Jacobi-Bellman equations, parameterized by the agent’s type. This dynamic problem is time consistent in a certain sense. Some interesting findings are worth mentioning. First, self-enforcing contracts are typically suboptimal. The principal would rather let the agent quit and hire a new one. Next, the standard contract for a committed agent may also be suboptimal because of the presence of different types of agents in our model. The principal may prefer no commitment from the agent; then, the principal can hire a cheaper one from the market at a later time by designing the contract to induce the current agent to quit. Moreover, because of the cost incurred to the agent, the principal will see only finitely many quittings. Funding: J. Zhang is supported in part by the NSF [Grants DMS-1908665 and DMS-2205972]. Z. Zhu is supported by The Hong Kong University of Science and Technology (Guangzhou) Start-Up Fund [Grant G0101000240] and the Guangzhou-HKUST(GZ) Joint Funding Program [Grant 2024A03J0630].

Optimality of the Howard-Vala T-gate in stabilizer quantum computation

In a remarkable work [Phys. Rev. A 86 022316 (2012)], Howard and Vala introduced a qudit version of the qubit T-gate (i.e., π/8-gate) for any prime dimensional system. This non-Clifford gate is a key ingredient of the paradigm ‘Clifford +T’, which are widely employed in the stabilizer formalism of universal and fault-tolerant quantum computation. Considering the applications and significance of the T-gate, it is desirable to characterize it from various angles. Here we prove that in any prime dimensional system, the Howard-Vala T-gate is optimal, among all diagonal gates, for generating magic resources from stabilizer states when the magic is quantified via the L 1-norm of characteristic functions (Fourier transforms) of quantum states. The quadratic Gaussian sum in number theory plays a key role in establishing this optimality. This highlights an extreme feature of the Howard-Vala T-gate. We further reveal an intrinsic relation between the Howard-Vala T-gate and the Watson-Campbell-Anwar-Browne T-gate [Phys. Rev. A 92 022312 (2015)] for any prime dimensional system.

Optical Extinction-Based 3D Nano-Imaging of WS2 on Gold.

Broadband nanoextinction images recorded in tip-enhanced optical spectroscopy geometry track the 3D topography of a single layer of WS2 on Au substrate. The described nano-optical method is complementary to conventional atomic force microscopy and offers additional information about the buried material-metal interface that is not accessible using conventional topographic imaging. Beyond 3D optical imaging, we observe large variations in the junction plasmon resonance on the nanoscale. The latter is important to understand and account for in tip-enhanced Raman and photoluminescence studies that target low-dimensional materials specifically. Our observations and (coherent) optical scattering-based method are also relevant to emerging efforts aimed at exploring strong coupling and Fano interferences in hybrid plasmonic-low dimensional quantum material systems.

Multiplicative noise induced bistability and stochastic resonance

Abstract Stochastic resonance is a well established phenomenon, which proves relevant for a wide range of applications, of broad trans-disciplinary breath. Consider a one dimensional bistable stochastic system, characterized by a deterministic double well potential and shaken by an additive noise source. When subject to an external periodic drive, and for a proper choice of the noise strength, the system swings regularly between the two existing deterministic fixed points, with just one switch for each oscillation of the imposed forcing term. This resonant condition can be exploited to unravel weak periodic signals, otherwise inaccessible to conventional detectors. Here, we will set to revisit the stochastic resonance concept by operating in a modified framework where bistability is induced by the nonlinear nature of the multiplicative noise. A candidate model is in particular introduced which fulfils the above requirements while allowing for analytical progress to be made. Working with reference to this case study, we elaborate on the conditions for the onset of the generalized stochastic resonance mechanism. As a byproduct of the analysis, a novel resonant regime is also identified which displays no lower bound for the frequencies that can be resolved, at variance with the traditional setting.

First principles design of two dimensional TiSSe Janus drug delivery system for nitrosourea.

In this paper, we delved into the exploration of a novel drug delivery platform for nitrosourea, leveraging a Janus-structured two-dimensional material, TiSSe, as the carrier. Our approach was grounded in a comprehensive application of first-principles computational methods. By evaluating the adsorption energies across a spectrum of potential configurations, we demonstrated the favorable attributes of TiSSe as a carrier for nitrosourea. Our in-depth examination of the electronic structure unveiled intriguing insights. The Janus nature of TiSSe imparts distinct adsorption profiles to nitrosourea molecules at the sulfur (S) and selenium (Se) terminated surfaces. This disparity in electronic properties not only facilitates precise detection but also helps the design of more intriguing two-dimensional materials.

Detailed cellular and spatial characterization of chronic lung allograft dysfunction using imaging mass cytometry

Long-term survival after lung transplantation remains limited by chronic lung allograft dysfunction (CLAD), with two main phenotypes: bronchiolitis obliterans syndrome (BOS) and restrictive allograft syndrome (RAS). We aimed to assess CLAD lung allografts using imaging mass cytometry (IMC), a high dimensional tissue imaging system allowing a multiparametric in situ exploration at a single cell level. 4 BOS, 4 RAS, and 4 control lung samples were stained with 35 heavy metal-tagged antibodies selected to assess structural and immune proteins of interest. We identified 50 immune and non-immune cell clusters. CLAD lungs had significantly reduced club cells. A Ki67-high basal cell population was mostly present in RAS and in proximity to memory T cells. Memory CD8+ T cells were more frequent in CLAD lungs, regulatory T cells more prominent in RAS. IMC is a powerful technology for detailed cellular analysis within intact organ structures that may shed further light on CLAD mechanisms.

Conversion mechanisms and transformed waves for the (3 + 1)-dimensional nonlinear equation

In this paper, we focus on investigating the (3 + 1)-dimensional nonlinear equation which is used to describe the propagation of waves in the shallow water. The study begins with the application of the Hirota bilinear method to obtain N-soliton solution. Building on this foundation, the research delves into the construction of first-order breather wave by imposing complex conjugate constraints on the parameters of two solitons. Further analysis of the characteristic lines of breathers leads to the derivation of conversion conditions. Under this specific condition, a series of nonlinear transformed waves are presented, including quasi-kink solitons, W-shaped kink solitons, oscillation W-shaped kink solitons, multipeaks solitons, quasi-periodic waves, and line rogue waves. Each of these transformed waves exhibits unique structural and dynamic properties, enriching the understanding of wave behavior in higher-dimensional nonlinear systems. The study also explores the nonlinear superposition mechanism between solitary wave and periodic wave. This mechanism elucidates the formation process of nonlinear waves, explaining how their locality and oscillatory characteristics emerge from the superposition of different wave components. Moreover, the geometric properties of the two characteristic lines of the waves are analyzed to understand the time-varying nature of the transformed waves. This temporal analysis is crucial for predicting the evolution and interaction of these waves over time. Finally, the research extends to the higher-order breather wave and explores the interactions among various waves. These interactions reveal the complex dynamics that may arise in the (3 + 1)-dimensional nonlinear systems and provide deeper insights into the interactions among different wave structures.

Bayesian Estimation of Muscle Mechanisms and Therapeutic Targets Using Variational Autoencoders.

Cardiomyopathies, often caused by mutations in genes encoding muscle proteins, are traditionally treated by phenotyping hearts and addressing symptoms post irreversible damage. With advancements in genotyping, early diagnosis is now possible, potentially introducing earlier treatment. However, the intricate structure of muscle and its myriad proteins make treatment predictions challenging. Here we approach the problem of estimating therapeutic targets for a mutation in mouse muscle using a spatially explicit half sarcomere muscle model. We selected 9 rate parameters in our model linked to both small molecules and cardiomyopathy-causing mutations. We then randomly varied these rate parameters and simulated an isometric twitch for each combination to generate a large training dataset. We used this dataset to train a Conditional Variational Autoencoder (CVAE), a technique used in Bayesian parameter estimation. Given simulated or experimental isometric twitches, this machine learning model is able to then predict the set of rate parameters which are most likely to yield that result. We then predict the set of rate parameters associated with twitches from control mice with the cardiac Troponin C (cTnC) I61Q variant and control twitches treated with the myosin activator Danicamtiv, as well as model parameters that recover the abnormal I61Q cTnC twitches.

Approximation identification for the stochastic time-delayed dynamical system

This paper addresses the challenges of analyzing stochastic dynamical systems with a single time-delay within a data-driven framework. The presence of time-delay introduces non-Markovian characteristics to the system, complicating the analysis of its dynamic behavior using traditional approaches. Drawing inspiration from the small delay approximation, we apply a sparse identification technique to approximate the non-Markovian process with a Markovian one. This innovative method circumvents limitations associated with the system's dimensionality and the complexity of delayed diffusion terms, offering a versatile tool for investigating the dynamics of stochastic time-delayed systems. Our approach begins by establishing a connection between the system's coefficients and simulated data using the Kramers-Moyal formula, which captures the essential statistical properties of the system. We then leverage sparse identification to extract a concise model of the stochastic dynamical system, effectively eliminating the time-delay from consideration. The practicality and efficacy of our method are substantiated through a series of illustrative examples that showcase its application and validate its performance. By introducing this method, we aim to provide a novel analytical framework for stochastic time-delayed systems, advancing the current capabilities for modeling and understanding such complex dynamics.

The P300 and hierarchical dimensions of psychopathology.

The Hierarchical Taxonomy of Psychopathology (HiTOP) framework offers the potential to better understand how neurobiological mechanisms relate to psychopathology. The P300 is an event-related potential component that indexes attention, stimulus evaluation, and categorization. A blunted P300 has been associated with psychiatric disorders across externalizing, internalizing, and thought disorder domains. However, there has been little research investigating whether the P300 is related to higher-order dimensions of psychopathology. In a sample of 225 adults aged 18-35 years (Mage = 23.09, SD = 3.83, 82.2% female) who were oversampled for psychopathology, the present study examined the associations between the P300 and both psychopathology spectra and a general factor. Participants completed multiple experimental tasks, while electroencephalography was recorded to measure the P300 elicited by auditory, tactile, and visual stimuli. Participants also completed the self-report Comprehensive Assessment of Traits Relevant to Personality Disorder to assess pathological personality dimensions. We used structural equation modeling to examine the relationship between a latent P300 factor and both psychopathology spectra (negative emotionality, detachment, psychoticism, disinhibition, and antagonism) and a general factor. The results indicated that the P300 was inversely related to the general factor. Further analyses revealed no relationships between the P300 and any individual spectrum when accounting for the general factor. Overall, the present study indicates that the P300 is associated with the general factor of psychopathology, which might explain its association with multiple categorical disorders. The study also demonstrates the potential importance of neuroscience-informed dimensional systems to understand clinical phenomena. (PsycInfo Database Record (c) 2024 APA, all rights reserved).