Complex Time Evolution Research Articles

Dynamical correlation functions from complex time evolution

Dynamical correlation functions from complex time evolution

Statistical mechanics from relational complex time with a pure state

Thermodynamics and its quantum counterpart are traditionally described with statistical ensembles. Canonical typicality has related statistical mechanics for a system to ensembles of global energy eigenstates of a system and its environment, analyzing their cardinality. We show that the canonical density for a system emerges from a maximally entangled global state of system and environment through relational complex time evolution between system and environment without the need to maximize the entropy or to count states. Published by the American Physical Society 2024

Complex time evolution in tensor networks and time-dependent Green's functions

Complex time evolution in tensor networks and time-dependent Green's functions

Quantitative Analysis of the Complex Time Evolution of a Camphor Boat

The motion of a camphor boat on the water’s surface is a long-studied example of the direct transformation of chemical energy into a mechanical one. Recent experimental papers have reported a complex character of boat motion depending on the location of the camphor source. If the source is close to the stern, the boat moves at a constant speed. When it is shifted towards the boat center, oscillations of speed are observed. When the source is close to the boat center, pulses of speed followed by oscillations appear. Here, we focus on numerical simulations of camphor boat motion. We discuss approximations that allow us to reduce the numerical complexity of the problem and formulate a model in which the equation for boat velocity is coupled with a one-dimensional reaction–diffusion equation for camphor surface concentration. We scanned the phase space of model parameters and found the values that give qualitative agreement with the experiments. The model predicts all types of boat motion (continuous, oscillating, and pulsating) observed in experiments. Moreover, the model with selected parameter values shows that for specific locations of the camphor source, a spike in speed is followed by transient oscillations, which are an inherent part of speed relaxation.

Time evolution of spread complexity in quenched Lipkin–Meshkov–Glick model

We use the spread complexity (SC) of a time-evolved state after a sudden quantum quench in the Lipkin–Meshkov–Glick (LMG) model prepared in the ground state as a probe of the quantum phase transition when the system is quenched toward the critical point. By studying the growth of the effective number of elements of the Krylov basis that contributes to the SC more than a preassigned cutoff, we show how the two phases of the LMG model can be distinguished. We also explore the time evolution of spread entropy after both non-critical and critical quenches. We show that the sum contributing to the spread entropy converges slowly in the symmetric phase of the LMG model compared to that in the broken phase, and for a critical quench, the spread entropy diverges logarithmically at late times.

Time evolution of spread complexity and statistics of work done in quantum quenches

Time evolution of spread complexity and statistics of work done in quantum quenches

A dynamic factor model to predict homicides with firearm in the United States

PurposeResearch on temporal dynamics of crime in the United States is growing. Yet, mathematical tools to reliably predict homicides with firearm are still lacking, due to delays in the release of official data lagging up to almost two years. This study takes a critical step in this direction by establishing a reliable statistical tool to predict homicides with firearm at a monthly resolution, combining official data and easy-to-access explanatory variables. MethodWe propose a dynamic factor model to predict homicides with firearm from 1999 to 2020 using official monthly data released yearly by the Centers for Disease Control and Prevention, provisional quarterly data from the same agencies, media output from newspapers, and crowdsourced information from the Guns Violence Archive. ResultsStatistical findings demonstrate that the dynamic factor model outperforms state-of-the-art techniques (AI and classical autoregressive models). The dynamic factor model offers improved ability to backcast, nowcast, and forecast homicides with firearm, and can anticipate sudden changes in the time-series. ConclusionsBy decomposing the time-series of homicides with firearm on common and idiosyncratic components, the dynamic factor model successfully captures their complex time-evolution. This approach offers a vantage point to policymakers and practitioners, allowing for timely predictions, otherwise unfeasible.

Hawkes Processes With Stochastic Exogenous Effects for Continuous-Time Interaction Modelling.

Continuous-time interaction data is usually generated under time-evolving environment. Hawkes processes (HP) are commonly used mechanisms for the analysis of such data. However, typical model implementations (such as e.g., stochastic block models) assume that the exogenous (background) interaction rate is constant, and so they are limited in their ability to adequately describe any complex time-evolution in the background rate of a process. In this paper, we introduce a stochastic exogenous rate Hawkes process (SE-HP) which is able to learn time variations in the exogenous rate. The model affiliates each node with a piecewise-constant membership distribution with an unknown number of changepoint locations, and allows these distributions to be related to the membership distributions of interacting nodes. The time-varying background rate function is derived through combinations of these membership functions. We introduce a stochastic gradient MCMC algorithm for efficient, scalable inference. The performance of the SE-HP is explored on real world, continuous-time interaction datasets, where we demonstrate that the SE-HP strongly outperforms comparable state-of-the-art methods.

Disordered Collective Motion in Dense Assemblies of Persistent Particles.

We explore the emergence of nonequilibrium collective motion in disordered nonthermal active matter when persistent motion and crowding effects compete, using simulations of a two-dimensional model of size polydisperse self-propelled particles. In stark contrast with monodisperse systems, we find that polydispersity stabilizes a homogeneous active liquid at arbitrary large persistence times, characterized by remarkable velocity correlations and irregular turbulent flows. For all persistence values, the active fluid undergoes a nonequilibrium glass transition at large density. This is accompanied by collective motion, whose nature evolves from near-equilibrium spatially heterogeneous dynamics at small persistence, to a qualitatively different intermittent dynamics when persistence is large. This latter regime involves a complex time evolution of the correlated displacement field.

The complex time and energy evolution of quasi-periodic eruptions in eRO-QPE1

Quasi-periodic eruptions (QPEs) are recurrent X-ray bursts found in the nuclei of low-mass galaxies. Their trigger mechanism is still unknown, but recent models involving one or two stellar-mass companions around the central massive (≈105 − 106 M⊙) black hole have gathered significant attention. While these models have been compared only qualitatively with observations, the phenomenology of QPEs is developing at a fast pace, and has the potential to reveal new insights. Here we report two new observational results found in eRO-QPE1, the brightest QPE source discovered so far. First, the eruptions in eRO-QPE1 sometimes occur as single isolated bursts, and at others as chaotic mixtures of multiple overlapping bursts with very different amplitudes. Second, we confirm that QPEs peak at later times and are broader at lower energies than at higher energies, while we find for the first time that QPEs also start earlier at lower energies. Furthermore, eruptions appear to undergo a counterclockwise hysteresis cycle in a plane of hardness ratio versus total count rate. The first behavior has not been found in any other QPE source, and implies that if a common trigger mechanism is in place for all QPEs, it must be able to produce both types of timing properties, regular and complex. The second result implies that the X-ray emitting component does not have an achromatic evolution even during the start of QPEs, and that the rise is harder than the decay at a given total count rate. This specific energy dependence could be qualitatively compatible with inward radial propagation during the rise within a compact accretion flow, the presence of which is suggested by the stable quiescence spectrum observed in general for QPE sources.

Complexity in a moving mirror model

In a two-dimensional conformal field theory with a moving mirror, known as a moving mirror model, the time evolution of the entanglement entropy shows a Page like curve. This implies that the moving mirror model is useful to understand the island formula. In this paper, we study the time evolution of the subregion CV complexity in the moving mirror model for a better understanding of the island formula of the complexity. In contrast to the entanglement entropy, the subregion CV complexity shows a peculiar behaviour. We discuss this behaviour in more detail.

Nonlinear complexification of periodic orbits in the generalized Landau scenario.

We have found a way for penetrating the space of the dynamical systems toward systems of arbitrary dimension exhibiting the nonlinear mixing of a large number of oscillation modes through which extraordinarily complex time evolutions may arise. The system design is based on assuring the occurrence of a number of Hopf bifurcations in a set of fixed points of a relatively generic system of ordinary differential equations, in which the main peculiarity is that the nonlinearities appear through functions of a linear combination of the system variables. The paper outlines the design procedure and presents a selection of numerical simulations with a variety of designed systems whose dynamical behaviors are really rich and full of unknown features. For concreteness, the presentation is focused on illustrating the oscillatory mixing effects on the periodic orbits, through which the harmonic oscillation born in a Hopf bifurcation becomes successively enriched with the intermittent incorporation of other oscillation modes of higher frequencies while the orbit remains periodic and without the necessity of bifurcating instabilities. Even in the absence of a proper mathematical theory covering the nonlinear mixing mechanisms, we find enough evidence to expect that the oscillatory scenario be truly scalable concerning the phase-space dimension, the multiplicity of involved fixed points, and the range of time scales so that extremely complex but ordered dynamical behaviors could be sustained through it.

Global and local spreading rate estimation in forced plumes

A new methodology is proposed to study turbulent axisymmetric plume behaviour based on the analysis of dye forced plume images. The methodology is based on the plume geometrical information deduced from the frames and allows us to obtain measurements in all the axial and radial extensions of the plume (vertical and radial profiles) and its use in a sequence of consecutive frames allows the analysis of the time evolution of the vertical and radial measurements.The time evolution of the vertical and radial measurements allows us to study the spreading rate coefficient in detail. We define the concept of the local spreading rate (βlocal) and its maximum value frequently used in the studies reported in the literature and named here the classical spreading rate (βclassic).As a case study, two experiments were carried out, with two values of Atwood number (0.001 and 0.01) and a fixed source distance Ho(2 cm). The results confirm the variability of the spreading rate with distance from the source (axial evolution) and show a complex time evolution depending on the z-coordinate. In addition, an asymptotic trend was observed but the asymptotic behaviour was not a constant value also depending on the z-coordinate.This methodological approach has the advantage of being noninvasive and easily exportable and requires only the recording of fluid flows (for example, volcanic plumes). Generally, it is not possible to directly control and/or measure a real fluid flow (a geophysical or pollution flow) and the only thing that can be done is its recording and analysis it, which our method allows.

Holographic complexity for black branes with momentum relaxation

We employ the "complexity equals action" conjecture to investigate the action growth rate for the charged and neutral AdS black branes of a holographic toy model consisting of Einstein-Maxwell theory in $d + 1$-dimensional bulk spacetime with $d - 1$ massless scalar fields which is called Einstein-Maxwell-Axion (EMA) theory. From the holographic point of view, the scalar fields source a spatially dependent field theory with momentum relaxation on the boundary, which is dual to the homogeneous and isotropic black branes. We find that the growth rate of the holographic complexity within the Wheeler-DeWitt (WDW) patch saturates the corresponding Lloyd's bound at the late time limit. Especially for the neutral AdS black branes, it will be shown that the complexity growth rate at late time vanishes for a particular value of relaxation parameter $\beta_{max}$ where the temperature of the black hole is minimal. Then, we investigate the transport properties of the holographic dual theory in the minimum temperature. A non-linear contribution of the axion field kinetic term in the context of k-essence model in the four-dimensional spacetime is considered as well. We also study the time evolution of the holographic complexity for the dyonic AdS black branes in this model.

Complexity and uncomplexity during energy injection

We consider a strongly coupled field theory with a critical point and nonzero chemical potential at finite temperature, which is dual to an asymptotically AdS charged black hole. We study the evolution of the rescaled holographic subregion complexity near and far from the critical point. We explain two distinct concepts of complexity in this theory and discuss that the state under study is complex based on how much information is needed to specify the state and is simple according to how many operations have to be done to reach the state. It has been reported before that time evolution of holographic subregion complexity contradicts the second law of complexity in these AdS-Vaidya-like geometries, but we try to provide a compatible interpretation. We justify decreasing of complexity using an increasing number of microstates of the mixed state and speculate about the description of the relative complexity of the initial state and the final state as a resource. We propose that in this process complexity of the mixed state decreases and complexity of the environment increases. We also observe that in this model, the rescaled holographic subregion complexity is a good observable for probing the dynamical critical exponent.

Superradiance from nonideal initial states: A quantum trajectory approach

Collective emission behavior is usually described by the decay dynamics of the completely symmetric Dicke states. To study a more realistic scenario, we investigate alternative initial states inducing a more complex time evolution. Superposition states of the fully inverted Dicke state and the Dicke ground state with unequal mutual weights are studied as examples as well as superradiance stemming from atoms in clusters separated by more than one wavelength. The Monte Carlo wave function method serves as framework to study the dynamics of quantum states, which is determined by quantum jumps on the one hand and continuous evolution dynamics on the other hand. We compare this method with the classical picture of a system of rate equations written for the diagonal components of the density matrix.

Nanoflare Theory Revisited

Abstract At any scale l in the turbulent inertial range, the magnetic field can be divided up into a large-scale component and a small-scale, high spatial frequency component which undergoes magnetic reversals. Such local reconnections, i.e., on any inertial scale l, seem to be an inseparable part of magnetohydrodynamic (MHD) turbulence, whose collective outcome can lead to global reconnection with a rate independent of the small-scale physics dominant at dissipative scales. We show that this picture, known as stochastic reconnection, is intimately related to nanoflare theory, proposed long ago to explain solar coronal heating. We argue that, due to stochastic flux freezing, a generalized version of magnetic flux freezing in turbulence, the field follows the flow in a statistical sense. Turbulence bends and stretches the field, increasing its spatial complexity. Strong magnetic shears associated with such a highly tangled field can trigger local reversals and field annihilations on a wide range of inertial scales which convert magnetic energy into kinetic and thermal energy. The former may efficiently enhance turbulence and the latter heat generation. We support this theoretical picture using scaling laws of MHD turbulence and also recent analytical and numerical studies which suggest a statistical correlation between magnetic spatial complexity and energy dissipation. Finally, using an MHD numerical simulation, we show that the time evolution of the magnetic complexity is statistically correlated with the rate of kinetic energy injection and/or magnetic-to-thermal energy conversion, in agreement with our proposed theoretical picture.

Neural Decoding of Multi-Modal Imagery Behavior Focusing on Temporal Complexity.

Mental imagery behaviors of various modalities include visual, auditory, and motor behaviors. Their alterations are pathologically involved in various psychiatric disorders. Results of earlier studies suggest that imagery behaviors are correlated with the modulated activities of the respective modality-specific regions and the additional activities of supramodal imagery-related regions. Additionally, despite the availability of complexity analysis in the neuroimaging field, it has not been used for neural decoding approaches. Therefore, we sought to characterize neural oscillation related to multimodal imagery through complexity-based neural decoding. For this study, we modified existing complexity measures to characterize the time evolution of temporal complexity. We took magnetoencephalography (MEG) data of eight healthy subjects as they performed multimodal imagery and non-imagery tasks. The MEG data were decomposed into amplitude and phase of sub-band frequencies by Hilbert–Huang transform. Subsequently, we calculated the complexity values of each reconstructed time series, along with raw data and band power for comparison, and applied these results as inputs to decode visual perception (VP), visual imagery (VI), motor execution (ME), and motor imagery (MI) functions. Consequently, intra-subject decoding with the complexity yielded a characteristic sensitivity map for each task with high decoding accuracy. The map is inverted in the occipital regions between VP and VI and in the central regions between ME and MI. Additionally, replacement of the labels into two classes as imagery and non-imagery also yielded better classification performance and characteristic sensitivity with the complexity. It is particularly interesting that some subjects showed characteristic sensitivities not only in modality-specific regions, but also in supramodal regions. These analyses indicate that two-class and four-class classifications each provided better performance when using complexity than when using raw data or band power as input. When inter-subject decoding was used with the same model, characteristic sensitivity maps were also obtained, although their decoding performance was lower. Results of this study underscore the availability of complexity measures in neural decoding approaches and suggest the possibility of a modality-independent imagery-related mechanism. The use of time evolution of temporal complexity in neural decoding might extend our knowledge of the neural bases of hierarchical functions in the human brain.

Weakly intrusive time homogenization technique to deal with pseudo-cyclic coupled thermomechanical problems with uncertainties

This article is dedicated to the analysis of visco-plastic and damageable structures submitted to thermomechanical loadings embedding some uncertain parameters. In particular, complex time evolutions of the loadings are considered, at two different time scales. An homogenized-in-time model is used to provide kind of a surrogate model for damage evolution analysis. Then a stochastic analysis using polynomial chaos expansion with collocation can be performed. Indeed, though this is a non-intrusive approach, it belongs to the category of many-query problems, so the surrogate model allows to reduce the computational cost in order to be affordable. Focus is herein on the complex time evolutions, the considered test case is mono-dimensional, but up to 300 000 cycles are used.

Dynamic levitation behavior of a radial-type SMB under axial load condition

Due to the external disturbances or the time-variable load, it is necessary to study the dynamic levitation behavior in order to guarantee the stable levitation of superconducting magnetic bearing (SMB). This paper investigates the dynamic levitation behaviors of a radial-type SMB under axial load condition. By adopting the Power-law E-J relation, the simplified H-formulation finite element model of a radial-type SMB was established to calculate the axial dynamic levitation behavior with the aid of the PDE module and ODE module in software COMSOL. The experimental measurements of the axial levitation force were performed in the field cooling condition so as to validate the model. Then, the dynamic levitation behaviors of the radial-type SMB were discussed when the PM rotor suffers from the external disturbances including the axial constant load with different initial velocities and the sinusoidal time-variable loads. The results show that both the load size and the initial velocity drift the work point of PM rotor. And the sinusoidal load leads to a complex time-evolution of the levitation behavior. The study is useful to predict the effects of external disturbances on the dynamic levitation behaviors in the practical applications of the SMB.