Nonintegrable Systems Research Articles

Ensemble dependence of information-theoretic contributions to the entropy production.

The entropy production of an open system coupled to a reservoir initialized in a canonical state can be expressed as a sum of two microscopic information-theoretic contributions: the system-bath mutual information and the relative entropy measuring the displacement of the environment from equilibrium. We investigate whether this result can be generalized to situations where the reservoir is initialized in a microcanonical or in a certain pure state (e.g., an eigenstate of a nonintegrable system), such that the reduced dynamics and thermodynamics of the system are the same as for the thermal bath. We show that while in such a case the entropy production can still be expressed as a sum of the mutual information between the system and the bath and a properly redefined displacement term, the relative weight of those contributions depends on the initial state of the reservoir. In other words, different statistical ensembles for the environment predicting the same reduced dynamics for the system give rise to the same total entropy production but to different information-theoretic contributions to the entropy production.

Cis-regulatory atlas of primary human CD4+ T cells

Cis-regulatory elements (CRE) are critical for coordinating gene expression programs that dictate cell-specific differentiation and homeostasis. Recently developed self-transcribing active regulatory region sequencing (STARR-Seq) has allowed for genome-wide annotation of functional CREs. Despite this, STARR-Seq assays are only employed in cell lines, in part, due to difficulties in delivering reporter constructs. Herein, we implemented and validated a STARR-Seq–based screen in human CD4+ T cells using a non-integrating lentiviral transduction system. Lenti-STARR-Seq is the first example of a genome-wide assay of CRE function in human primary cells, identifying thousands of functional enhancers and negative regulatory elements (NREs) in human CD4+ T cells. We find an unexpected difference in nucleosome organization between enhancers and NRE: enhancers are located between nucleosomes, whereas NRE are occupied by nucleosomes in their endogenous locations. We also describe chromatin modification, eRNA production, and transcription factor binding at both enhancers and NREs. Our findings support the idea of silencer repurposing as enhancers in alternate cell types. Collectively, these data suggest that Lenti-STARR-Seq is a successful approach for CRE screening in primary human cell types, and provides an atlas of functional CREs in human CD4+ T cells.

Prominent quantum many-body scars in a truncated Schwinger model

The high level of control and precision achievable in current synthetic quantum matter setups has enabled first attempts at quantum-simulating various intriguing phenomena in condensed matter physics, including those probing thermalization or its absence in closed quantum systems. In a recent work [Desaules \textit{et al.} [arXiv:2203.08830], we have shown that quantum many-body scars -- special low-entropy eigenstates that weakly break ergodicity in nonintegrable systems -- arise in spin-$S$ quantum link models that converge to $(1+1)-$D lattice quantum electrodynamics (Schwinger model) in the Kogut--Susskind limit $S\to\infty$. In this work, we further demonstrate that quantum many-body scars exist in a truncated version of the Schwinger model, and are qualitatively more prominent than their counterparts in spin-$S$ quantum link models. We illustrate this by, among other things, performing a finite-$S$ scaling analysis that strongly suggests that scarring persists in the truncated Schwinger model in the limit $S\to\infty$. Although it does not asymptotically converge to the Schwinger model, the truncated formulation is relevant to synthetic quantum matter experiments, and also provides fundamental insight into the nature of quantum many-body scars, their connection to lattice gauge theories, and the thermalization dynamics of the latter. Our conclusions can be readily tested in current cold-atom setups.

Generation and Controllability of High-Dimensional Rogue Waves in an Electromagnetically Induced Transparent Medium

We propose a scheme to generate and control high-dimensional rogue waves in a coherent three-level Λ-type atomic system via electromagnetically induced transparency (EIT). Under EIT conditions, the probe field envelopes obey the non-integrable nonlinear Schrödinger equations (NLSE) with or without the external potential, which result from the stark (Zeeman) effect contributed by an electric (magnetic) field. By adjusting the amplitude and width of the initial pulse, we can generate the high-dimensional rogue waves and obtain the phase-transition curves of high-dimensional rogue waves. In the system, the far-detuned electric field, the random weak magnetic field, and the Gauss weak magnetic field are not conducive to the excitation of high-dimensional rogue waves. The results not only provide a theoretical basis for the experimental realization or prevention of the high-dimensional rogue waves, but also prove the possibility of generating and controlling the rogue waves in other high-dimensional non-integrable systems.

Reprogramming of human peripheral blood mononuclear cells into induced mesenchymal stromal cells using non-integrating vectors

Mesenchymal stromal cells (MSCs) have great value in cell therapies. The MSC therapies have many challenges due to its inconsistent potency and limited quantity. Here, we report a strategy to generate induced MSCs (iMSCs) by directly reprogramming human peripheral blood mononuclear cells (PBMCs) with OCT4, SOX9, MYC, KLF4, and BCL-XL using a nonintegrating episomal vector system. While OCT4 was not required to reprogram PBMCs into iMSCs, omission of OCT4 significantly impaired iMSC functionality. The omission of OCT4 resulted in significantly downregulating MSC lineage specific and mesoderm-regulating genes, including SRPX, COL5A1, SOX4, SALL4, TWIST1. When reprogramming PBMCs in the absence of OCT4, 67 genes were significantly hypermethylated with reduced transcriptional expression. These data indicate that transient expression of OCT4 may serve as a universal reprogramming factor by increasing chromatin accessibility and promoting demethylation. Our findings represent an approach to produce functional MSCs, and aid in identifying putative function associated MSC markers.

Establishment of an induced pluripotent stem cell (SIAISi016-A) line from a 62-years old Chinese Han patient with Alzheimer's disease

A 62-years old Alzheimer's disease (AD) male patient donated his Peripheral blood mononuclear cells. The non-integrating episomal vector system used to reprogram PBMCs with Oct3/4, Klf4, Sox2 and c-Myc transcription factors. The pluripotency of transgene-free pluripotent stem cell (iPSC) was confirmed by immunocytochemistry for pluripotency markers-SOX2, NANOG, OCT3/4, SSEA4, TRA1-60, and TRA1-81. The differentiation capacity of the iPSCs into endoderm, mesoderm and ectoderm was assessed by AFP, SMA and βIII-TUBULIN, respectively. In addition, the iPSC line displayed a normal karyotype. This iPSC line might offer a good cell model to explore the pathological mechanisms and treatment strategies for AD.

A Novel Photo-Thermal-Electric Conversion System with an Integrated Support Material.

In conventional photo-thermal-electric conversion systems, the photo-thermal conversion module is coupled to a thermoelectric conversion module. However, the physical contact interface between the modules causes serious energy loss. In order to solve this problem, a novel photo-thermal-electric conversion system with an integrated support material has been developed, with a photo-thermal conversion component at the top, an inside thermoelectric conversion component, and a cooling component at the bottom, surrounded by a water conduction component. The supporting materials of each part are polydimethylsiloxane (PDMS), and there is no apparent physical interface between each part. This integrated support material reduces the heat loss caused by the mechanically coupled interfaces in traditional components. In addition, the confined edge 2D water transport path effectively reduces the heat loss due to water convection. Under 1 sun irradiation, the water evaporation rate and open-circuit voltage of the integrated system reach 2.46 kg m-2 h-1 and 30 mV, respectively, and are nearly 1.4 times and 5.8 times higher than those of non-integrated systems.

Non-Abelian Eigenstate Thermalization Hypothesis.

The eigenstate thermalization hypothesis (ETH) explains why nonintegrable quantum many-body systems thermalize internally if the Hamiltonian lacks symmetries. If the Hamiltonian conserves one quantity ("charge"), the ETH implies thermalization within a charge sector-in a microcanonical subspace. But quantum systems can have charges that fail to commute with each other and so share no eigenbasis; microcanonical subspaces may not exist. Furthermore, the Hamiltonian will have degeneracies, so the ETH need not imply thermalization. We adapt the ETH to noncommuting charges by positing a non-Abelian ETH and invoking the approximate microcanonical subspace introduced in quantum thermodynamics. Illustrating with SU(2) symmetry, we apply the non-Abelian ETH in calculating local operators' time-averaged and thermal expectation values. In many cases, we prove, the time average thermalizes. However, we find cases in which, under a physically reasonable assumption, the time average converges to the thermal average unusually slowly as a function of the global-system size. This work extends the ETH, a cornerstone of many-body physics, to noncommuting charges, recently a subject of intense activity in quantum thermodynamics.

Measure rigidity of Anosov flows via the factorization method

Using the factorization method, a method pioneered by Eskin and Mirzakhani in their groundbreaking work about measure classification over the moduli space of translation surfaces, we show that generalized $u$-Gibbs states over quantitatively non-integrable Anosov systems are absolutely continuous with respect to the whole unstable manifold.

Simulation and Exergoeconomic Analysis of a Trigeneration System Based on Biofuels from Spent Coffee Grounds

Biofuels have become a source of renewable energy to offset the use of fossil fuels and meet the demand for electricity, heat, and cooling in the industrial sector. This study aims to (a) develop a simulation of a trigeneration system based on a gas turbine cycle and an absorption chiller unit, using biomass and syngas from spent coffee grounds (SCGs) to replace the conventional system currently supplying the energy requirements of an instant coffee plant located in Guayaquil, Ecuador, and (b) carry out an exergoeconomic analysis of the simulated system to compare the effects of different fuels. The results showed an increase in the exergetic efficiency from 51.9% to 84.5% when using a trigeneration system based on biomass instead of the conventional non-integrated system. Furthermore, the biomass-based system was found to have the lowest operating costs ($154.7/h) and the lowest heating, cooling, and power costs ($10.3/GJ, $20.2/GJ, and $23.4/GJ, respectively). Therefore, the results of this analysis reveal that using SCGs as biofuel in this instant coffee plant is feasible for producing steam, chilled water, and power.

Deep Reinforcement Learning for Preparation of Thermal and Prethermal Quantum States

We propose a method based on deep reinforcement learning that efficiently prepares a quantum many-body pure state in thermal or prethermal equilibrium. The main physical intuition underlying the method is that the information on the equilibrium states can be efficiently encoded/extracted by focusing on only a few local observables, relying on the typicality of equilibrium states. Instead of resorting to the expensive preparation protocol that adopts global features such as the quantum state fidelity, we show that the equilibrium states can be efficiently prepared only by learning the expectation values of local observables. We demonstrate our method by preparing two illustrative examples: Gibbs ensembles in non-integrable systems and generalized Gibbs ensembles in integrable systems. Pure states prepared solely from local observables are numerically shown to successfully encode the macroscopic properties of the equilibrium states. Furthermore, we find that the preparation errors, with respect to the system size, decay exponentially for Gibbs ensembles and polynomially for generalized Gibbs ensembles, which are in agreement with the finite-size fluctuation within thermodynamic ensembles. Our method paves a path toward studying the thermodynamic and statistical properties of quantum many-body systems in quantum hardware.

Chaotic string motion in a near pp-wave limit

We revisit classical string motion in a near pp-wave limit of AdS5 × S5. It is known that the Toda lattice models are integrable. But if the exponential potential is truncated at finite order, then the system may become non-integrable. In particular, when the exponential potential in a three-particle periodic Toda chain is truncated at the third order of the dynamical variables, the resulting system becomes a well-known non-integrable system, Henon-Heiles model. The same thing may happen in a near pp-wave limit of AdS5 × S5, on which the classical string motion becomes chaotic.

Kardar–Parisi–Zhang Equation from Long-Range Exclusion Processes

We prove here that the height function associated to non-simple exclusion processes with arbitrary jump-length converges to the solution of the Kardar–Parisi–Zhang SPDE under suitable scaling and renormalization. This extends the work of Dembo and Tsai (Commun Math Phys 341(1):219–261, 2016) for arbitrary jump-length and Goncalves and Jara (Stoch Process Appl 127(12):4029–4052, 2017) for the non-stationary regime. Thus we answer a "Big Picture Question" from the AIM workshop on KPZ and also expand on the almost empty set of non-integrable and non-stationary particle systems for which weak KPZ universality is proven. We use an approximate microscopic Cole-Hopf transform like in Dembo and Tsai (2016) but we develop tools to analyze local statistics of the particle system via local equilibrium and work of Goncalves and Jara (2017). Local equilibrium is done via the one-block step in Guo et al. (Commun Math Phys 118:31, 1988) for path-space/dynamic statistics.

Dynamics of the coherent structure for incompressible fluid flow in turbulent boundary layers

We consider the nonlinear interaction system of waves to identify discrete clusters of resonant triads, which are classified on the basis of the resonance condition. This study is conducted to investigate the coherent structure of incompressible fluid flow in the turbulent boundary layer. The discrete wave turbulence is characterised by weakly nonlinear interaction modes for amplitude Tollmien Schlichting in a single-mode approximation. Within the framework of multiple-scale analysis, the coherent part of the amplitude equation is defined in the case of multiple three-wave resonance. The resonance condition is defined from the dispersion relation of these amplitudes, which are determined from solving the spectral problem of Orr–Sommerfeld equation by the Chebyshev collocation method. The spectral characteristics of these amplitudes are investigated to define the condition of multiple three-wave resonance. This condition is also defined for a resonant cluster made out of triads sharing a common mode, where all triads satisfy the resonance condition. The coherent amplitudes are represented dynamically by an autonomous system of ordinary differential equations. Non-integrable system of a single triad and a cluster of triads is noted, where the interaction coefficients in the given system do not have the same complex phase. The obtained dynamical system admits a number of invariants, similar to the classical Manley–Rowe invariants but of a different nature. One of these invariants is called the energy invariant manifold that represents the sum of modules square amplitudes of the dynamical system, this invariant is normalised to be defined on the unit sphere. Therefore, Birkhoff–Khinchin theory is applied to calculate the time average of square harmonic and sub harmonic amplitudes. Moreover, this paper is also focused on studying the numerical solutions of both simple and complex structure of the dynamical system by using Runge–Kutta method with random initial conditions. The solution of the dynamical system is examined at different signs of the weight factors, where the bounded solutions of this system are found at both positive and negative signs. However, in another study of a dynamical system, an explosive instability is noted at a negative sign for only one of the weight factors, where all study cases are related to the choice of wave vectors. The random initial conditions are applied to both simple and complex dynamical system to study the behaviour of system solutions. The coupling different triads within the dynamical system lead to chaotic turbulence regime.

CONCEPTUAL BASIS OF MANAGEMENT OF ENTERPRISE ASSETS UNDER CONDITIONS OF UNCERTAINTY AND RISK

The article is devoted to the current problems of the development of the conceptual foundations of enterprise asset management in the conditions of modern challenges. Asset management is viewed by most organizations as a simple business operation, however, the modern era requires sophisticated methodologies to meet business needs in optimizing asset management. A review of international standards on asset management was conducted. British Standards have made a significant contribution by publishing their PAS 55 standard on asset management. In January 2014, the International Organization for Standardization released the ISO 55000 series of standards, which are mainly based on PAS 55. The purpose of the standardization was to unite organizations around the world under a common asset management system. The needs for the formation of asset management programs based on standardized definitions of the concept of "enterprise asset", types of assets, and in conditions of uncertainty were noted. The authors analyzed the problems of the forecasting paradigm, which is marked by huge uncertainty, and formed the factors for ensuring correct forecasts in the models. The primary goal of an effective asset management program is to ensure that assets maximize value for all stakeholders in the value chain throughout their lifecycle. Empirical evidence shows that accurate forecasting in the economic and business world is quite difficult due to significant uncertainty, since practically all types of economic and business activity depend on events that we cannot predict in principle. In this context, a high-level model is proposed, which provides an integrated approach to the management of individual or complex assets. The proposed global model contains six sub-models: Market and revenue sub-model, A sub-model of factors of reliability, availability and serviceability, A sub-model of operations and operational constraints, Cost submodel, Organizational submodel A sub-model of influence taking into account other influence factors. The models of this plan provide a comprehensive approach to the management of individual or complex assets. It can help organizations overcome challenges associated with aging infrastructure or human assets, as well as isolated or disconnected systems. An integrated approach can help align operations with overall business goals by breaking down multiple non-standard, non-integrated systems. This integrated approach can also support long-term and short-term planning, use preventive maintenance and asset-based maintenance methods, help manage suppliers by supporting a full range of contracts and fully support service agreement management, etc.

Structure results for the integral set of a submanifold with respect to a non-integrable exterior differential system

Structure results for the integral set of a submanifold with respect to a non-integrable exterior differential system

Avoiding Small Denominator Problems by Means of the Homotopy Analysis Method

The so-called ``small denominator problem'' was a fundamental problem of dynamics, as pointed out by Poincar\'{e}. Small denominators appear most commonly in perturbative theory. The Duffing equation is the simplest example of a non-integrable system exhibiting all problems due to small denominators. In this paper, using the forced Duffing equation as an example, we illustrate that the famous ``small denominator problems'' never appear if a non-perturbative approach based on the homotopy analysis method (HAM), namely ``the method of directly defining inverse mapping'' (MDDiM), is used. The HAM-based MDDiM provides us great freedom to directly define the inverse operator of an undetermined linear operator so that all small denominators can be completely avoided and besides the convergent series of multiple limit-cycles of the forced Duffing equation with high nonlinearity are successfully obtained. So, from the viewpoint of the HAM, the famous ``small denominator problems'' are only artifacts of perturbation methods. Therefore, completely abandoning perturbation methods but using the HAM-based MDDiM, one would be never troubled by ``small denominators''. The HAM-based MDDiM has general meanings in mathematics and thus can be used to attack many open problems related to the so-called ``small denominators''.

Relaxation Exponents of OTOCs and Overlap with Local Hamiltonians.

OTOC has been used to characterize the information scrambling in quantum systems. Recent studies have shown that local conserved quantities play a crucial role in governing the relaxation dynamics of OTOC in non-integrable systems. In particular, the slow scrambling of OTOC is seen for observables that have an overlap with local conserved quantities. However, an observable may not overlap with the Hamiltonian but instead with the Hamiltonian elevated to an exponent larger than one. Here, we show that higher exponents correspond to faster relaxation, although still algebraic, and such exponents can increase indefinitely. Our analytical results are supported by numerical experiments.

Eigenstate thermalization and disappearance of quantum many-body scar states in weakly interacting fermion systems

The recent discovery of quantum many-body scar states has revealed the possibility of having states with low entanglement that violate the eigenstate thermalization hypothesis in nonintegrable systems. Such states with low entanglement entropy are rare but naturally exist in the integrable system of free fermions. Here, we demonstrate analytically that these atypical states would be always eliminated when an arbitrary weak interaction is introduced between the fermions. In particular, we show that the probability of having a many-body scar state with entanglement entropy satisfying a sub-volume scaling law decreases double exponentially as the system size. Thus, our results provide a quantitative argument for the disappearance of scar states in interacting fermion systems.

Feedback stabilization of quasi nonintegrable Hamiltonian systems under combined Gaussian and Poisson white noise excitations

A procedure for designing a feedback control to asymptotic Lyapunov stability with probability one of quasi nonintegrable Hamiltonian systems under combined Gaussian and Poisson white noise excitations is proposed. First, a one dimensional partially averaged Itô stochastic differential equation for controlled Hamiltonian is derived from the motion equations of the system by using the stochastic averaging method. Second, the dynamical programming equation for the ergodic control problem of the averaged system with undetermined cost function is set up based on the dynamical programming principle and the jump–diffusion chain stochastic differential rules. The optimal control law is obtained by solving the dynamical programming equation. Third, the analytical expression for the largest Lyapunov exponent of the averaged system is derived. Finally, the asymptotic Lyapunov stability with probability one of the originally controlled system is analyzed approximately by using the largest Lyapunov exponent. The cost function and optimal control forces are determined by the requirements of stabilizing the system. An example is worked out in detail to illustrate the effectiveness of the proposed method for stabilization control, and the control effect of the proposed feedback stabilization varies with the change of parameters is also studied in this paper, such as, the greater the excitation intensity of Gaussian and Poisson white noise, the better the stabilization control effect.