Temperature Chaos Research Articles

Chaos Raman distributed optical fiber sensing

The physics principle of pulse flight positioning is the main theoretical bottleneck that restricts the spatial resolution of the existing Raman distributed optical fiber sensing scheme. Owing to the pulse width of tens of nanoseconds, the spatial resolution of the existing Raman distributed optical fiber sensing scheme with kilometer-level sensing distance is limited to the meter level, which seriously restricts the development of the optical time-domain reflection system. In this paper, a chaos laser is proposed in the context of the physical principle of the Raman scattering effect, and a novel theory of chaos Raman distributed optical fiber sensing scheme is presented. The scheme reveals the characteristics of chaos Raman scattering light excited by a chaotic signal on the sensing fiber. Further, the chaos time-domain compression demodulation mechanism between the temperature variation information and chaos correlation peak is demonstrated. Then, the position of the temperature variation signal is precisely located using the delay time of the chaos correlation peak combined with the chaos pulse flight time. Based on this novel optical sensing mechanism, an experiment with 10 cm spatial resolution and 1.4 km sensing distance was conducted, and the spatial resolution was found to be independent of the sensing distance. Within the limit of the existing spatial resolution theory, the spatial resolution of the proposed scheme is 50 times higher than that of the traditional scheme. The scheme also provides a new research direction for optical chaos and optical fiber sensing.

Analysis of chaos-coherence peculiarities within the chaotic phenomena of fluid at finite temperature

In this distinctive research, I explored the influence of temperature and momentum-dependent coherence and chaos radiations on particles emanated fluid with quantum correlations. The equations are elucidated by using the interferometry technique to prevail in perspicuous aphorism for the coherence-chaotic field. Chaotic parameter examines the coherence through boson femtoscopy within an evolving boson gas model and probes significant parameters within the produced fluid characterization for the potential of harmonics oscillators. The proportion of condensate of identical bosons, densities distribution, and the correlations functions for the expansion of boson gas are investigated. The findings suggest that the particular temperatures in the relativistic smashing possess the hadronic phase and the resulting sources at that phase containing hundreds of analogous boson particles divulge the robustness of quantum coherence. The correlations are delineated to analyze the coherence and source peculiarities with certain temperature ranges, particles number, and particle pairs averaging momentum. At small pair momenta, the finite condensation reduces the correlations in pion interferometry observations and strives for an insignificant effect at high particles pair momenta. As shown in the plots the graphical interpretations of the density distribution, correlations and chaotic profile against assorted apropos parameters have been demonstrated for pertinent physical reasons. The significant results divulged that the density distributions possession enhance at higher coherent emission and lower temperature regimes. Such findings reveal the lucrativeness in the field of engineering applications.

Evidence for temperature chaos in spin glasses

We study the field cooled magnetization of a CuMn spin glass (SG) under temperature perturbations. The $T$-cycling curves are compared with the reference curve without temperature cycling. There is a crossover from the cumulative aging region to noncumulative aging region as the temperature change is increased. The cumulative aging range scales with the chaos length, ${\ensuremath{\ell}}_{\mathrm{c}}$, becoming comparable to the correlation length, $\ensuremath{\xi}$, at the crossover boundary. The extracted chaos exponent, $\ensuremath{\zeta}=1.1$, is in agreement with theoretical predictions. Our results strongly suggest temperature chaos exists in real SG systems.

Topological approach to electron correlations at fractional quantum Hall effect

The classification of homotopy invariants in interacting multi-electron 2D systems at quantizing magnetic fields is presented, explaining the topologically protected correlations occurring at integer and fractional quantum Hall effects. The long-range quantum entanglement is essential for homotopy correlated phases in contrast to the binary entanglement for conventional phases with local order parameters. The classification of homotopy long-range correlated phases induced by the Coulomb interaction of electrons has been derived in terms of homotopy invariants, which are universal and robust against local disorder and single-particle crystal field, as illustrated by experimental observations in various materials with different microscopic structure, like GaAs 2DES, graphene monolayer and bilayer and in Chern topological insulators. The homotopy phases are demonstrated to be topologically protected and immune to single-particle perturbations, temperature chaos and variation of the electron interaction strength. The nonzero repulsive interaction between electrons is shown, however, to be essential for the definition of the homotopy invariants, which disappear in gaseous systems.

Two-temperatures overlap distribution for the 2D discrete Gaussian free field

In this paper, we prove absence of temperature chaos for the two-dimensional discrete Gaussian free field using the convergence of the full extremal process, which has been obtained recently by Biskup and Louidor. This means that the overlap of two points chosen under Gibbs measures at different temperatures has a nontrivial distribution. Whereas this distribution is the same as for the random energy model when the two points are sampled at the same temperature, we point out here that they are different when temperatures are distinct: more precisely, we prove that the mean overlap of two points chosen under Gibbs measures at different temperatures for the DGFF is strictly smaller than the REM’s one. Therefore, although neither of these models exhibits temperature chaos, one could say that the DGFF is more chaotic in temperature than the REM.

Temperature chaos is present in off-equilibrium spin-glass dynamics

Experiments featuring non-equilibrium glassy dynamics under temperature changes still await interpretation. There is a widespread feeling that temperature chaos (an extreme sensitivity of the glass to temperature changes) should play a major role but, up to now, this phenomenon has been investigated solely under equilibrium conditions. In fact, the very existence of a chaotic effect in the non-equilibrium dynamics is yet to be established. In this article, we tackle this problem through a large simulation of the 3D Edwards-Anderson model, carried out on the Janus II supercomputer. We find a dynamic effect that closely parallels equilibrium temperature chaos. This dynamic temperature-chaos effect is spatially heterogeneous to a large degree and turns out to be controlled by the spin-glass coherence length ξ. Indeed, an emerging length-scale ξ* rules the crossover from weak (at ξ ≪ ξ*) to strong chaos (ξ ≫ ξ*). Extrapolations of ξ* to relevant experimental conditions are provided.

Numerical analysis of inclined jet impingement heat transfer in microchannel

Abstract The current study focuses on investigating of the performance of inclined microjet array to reduce the temperature of electronic devices. The capacity of the inclined jet arrays has been investigated through a computational fluid dynamics analysis for incompressible laminar flow to find out surface temperature, pressure drop, and flow chaos for the change in jet spacing and diameter, which is related to the number of jets under the constrained heat sink volume. Five different jet arrays consisting of 4, 5, 9, 13, and 16 jets were investigated for different jet diameters. The jet inclination kept constant at 45° to the impingement surface. The results show that the average exit liquid temperature increases with increasing the number of jets. The effects also manifest as the number of jets increases the pressure drop reduces monotonously for all jet diameters under constant mass flow rate in the module. Inclined microjet impingement heat sink having 13 jets showed better potential than the other microjet array configurations.

A constrained TAP approach for disordered spin models: application to the mixed spherical case

We revisit the metastability properties of the mixed p-spin spherical disordered models. Firstly, using known methods, we show that there is temperature chaos in a broad range of temperatures. Secondly, we modify the definition of the Thouless–Anderson–Palmer free energy density by including constraints that enforce a chosen overlap between the searched metastable states and another reference state, that could be a characteristic one of a different temperature. We argue that this refined analysis provides clues to understand the weird behaviour of the low temperature relaxation dynamics of these models, and suggests ways to improve the treatment of the initial conditions to overcome the difficulties encountered so far.

Geometry and Temperature Chaos in Mixed Spherical Spin Glasses at Low Temperature: The Perturbative Regime

We study the Gibbs measure of mixed spherical p‐spin glass models at low temperature, in (part of) the 1‐RSB regime, including, in particular, models close to pure in an appropriate sense. We show that the Gibbs measure concentrates on spherical bands around deep critical points of the (extended) Hamiltonian restricted to the sphere of radius , where is the rightmost point in the support of the overlap distribution. We also show that the relevant critical points are pairwise orthogonal for two different low temperatures. This allows us to explain why temperature chaos occurs for those models, in contrast to the pure spherical models. © 2019 Wiley Periodicals, Inc.

Temperature Chaos, Memory Effect, and Domain Fluctuations in the Spiral Antiferromagnet Dy

The spiral antiferromagnetic phase of polycrystalline dysprosium between 140 K and the Néel temperature at 178 K and its domain wall (DW) dynamics were investigated using high-resolution ultrasonic spectroscopy. Two kinetic processes of quasi-static DW motion occur under non-isothermal and isothermal conditions. A “fast” process is proportional to the rate of the temperature change and results in a new category of anelastic phenomena: magnetic transient ultrasonic internal friction (IF). This IF, related to fast moving magnetic DWs, decays rapidly after interruptions of cooling/heating cycles. A second, “slow” kinetic process is seen as logarithmic IF relaxation under isothermal conditions. This second process is glass-like and results in memory and temperature chaos effects. Low-frequency thermal fluctuations of DWs, previously detected by X-ray photon correlation spectroscopy, are related to critical fluctuations with Brownian motion-like dynamics of DWs.

Application of Singular Spectrum Analysis for Investigating Chaos in Sea Surface Temperature

The goal of this study is to explore the chaotic behavior of sea surface temperature (SST) in the Indian Ocean and in the equatorial Pacific Ocean. The SST time series is analyzed for Bay of Bengal, Arabian Sea and South Indian Ocean as well as for two extreme phenomena: El Nino and Indian Ocean Dipole (IOD). The analysis is based on Singular spectrum analysis, and singular value decomposition (SVD). Our analysis reveals that the dynamics of SST is chaotic in varying degrees in all the studied cases, since Lyapunov exponent, an indicator of chaoticity, is positive in each case. To study the degree of predictability of these SST series, we search for embedded periodic component(s) using two different approaches: Orthogonal functions extracted from the Singular spectrum analysis and Periodicity spectrum analysis based on SVD. Both the methods reveal presence of a strong periodic component(s) for the SST signals in the Arabian Sea, Bay of Bengal and South Indian Ocean, whereas no periodicity is found for El Nino and IOD. Therefore, it can be concluded that the dynamics of SST is more complex in the El Nino and IOD region compared to Bay of Bengal, Arabian Sea and South Indian Ocean; hence it is much more difficult to predict El Nino and IOD.

Chaotic temperature and bond dependence of four-dimensional Gaussian spin glasses with partial thermal boundary conditions

Spin glasses have competing interactions and complex energy landscapes that are highly-susceptible to perturbations, such as the temperature or the bonds. The thermal boundary condition technique is an effective and visual approach for characterizing chaos, and has been successfully applied to three dimensions. In this paper, we tailor the technique to partial thermal boundary conditions, where thermal boundary condition is applied in a subset (3 out of 4 in this work) of the dimensions for better flexibility and efficiency for a broad range of disordered systems. We use this method to study both temperature chaos and bond chaos of the four-dimensional Edwards-Anderson model with Gaussian disorder to low temperatures. We compare the two forms of chaos, with chaos of three dimensions, and also the four-dimensional $\pm J$ model. We observe that the two forms of chaos are characterized by the same set of scaling exponents, bond chaos is much stronger than temperature chaos, and the exponents are also compatible with the $\pm J$ model. Finally, we discuss the effects of chaos on the number of pure states in the thermal boundary condition ensemble.

Dynamic variational study of chaos: spin glasses in three dimensions

We have introduced a variational method to improve the computation of integrated correlation times in parallel tempering dynamics, obtaining a better estimate (a lower bound, at least) of the exponential correlation time. Using this determination of the correlation times, we revisited the problem of the characterization of the chaos in temperature in finite dimensional spin glasses, by way of the study of correlations between various chaos indicators computed in the static and the correlation times of the parallel tempering dynamics. The sample-distribution of the characteristic time for the parallel tempering dynamics turns out to be fat-tailed, and to obey finite-size scaling.

Variational representations for the Parisi functional and the two-dimensional Guerra–Talagrand bound

The validity of the Parisi formula in the Sherrington-Kirkpatrick model (SK) was initially proved by Talagrand [18]. The central argument therein relied on a very dedicated study of the coupled free energy via the two-dimensional Guerra-Talagrand (GT) replica symmetry breaking bound. It is believed that this bound and its higher dimensional generalization are highly related to the conjectures of temperature chaos and ultrametricity in the SK model, but a complete investigation remains elusive. Motivated by Bovier-Klimovsky [2] and Auffinger-Chen [3], the aim of this paper is to present a novel approach to analyzing the Parisi functional and the two-dimensional GT bound in the mixed $p$-spin models in terms of optimal stochastic control problems. We compute the directional derivative of the Parisi functional and derive equivalent criteria for the Parisi measure. We demonstrate how our approach provides a simple and efficient control for the GT bound that yields several new results on Talagrand's positivity of the overlap [20,Section 14.12] and disorder chaos in Chatterjee [5] and Chen [6]. In particular, we provide some examples of the models containing odd $p$-spin interactions.

Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models

The Sachdev-Ye-Kitaev model is a (0 + 1)-dimensional model describing Majorana fermions or complex fermions with random interactions. This model has various interesting properties such as approximate local criticality (power law correlation in time), zero temperature entropy, and quantum chaos. In this article, we propose a higher dimensional generalization of the Sachdev-Ye-Kitaev model, which is a lattice model with N Majorana fermions at each site and random interactions between them. Our model can be defined on arbitrary lattices in arbitrary spatial dimensions. In the large N limit, the higher dimensional model preserves many properties of the Sachdev-Ye-Kitaev model such as local criticality in two-point functions, zero temperature entropy and chaos measured by the out-of-time-ordered correlation functions. In addition, we obtain new properties unique to higher dimensions such as diffusive energy transport and a “butterfly velocity” describing the propagation of chaos in space. We mainly present results for a (1 + 1)-dimensional example, and discuss the general case near the end.

The geometry of the Gibbs measure of pure spherical spin glasses

We analyze the statics for pure $p$-spin spherical spin glass models with $p\geq3$, at low enough temperature. With $F_{N,\beta}$ denoting the free energy, we compute the second order (logarithmic) term of $NF_{N,\beta}$ and prove that, for an appropriate centering $c_{N,\beta}$, $NF_{N,\beta}-c_{N,\beta}$ is a tight sequence. We establish the absence of temperature chaos and analyze the transition rate to disorder chaos of the Gibbs measure and ground state. Those results follow from the following geometric picture we prove for the Gibbs measure, of interest by itself: asymptotically, the measure splits into infinitesimal spherical `bands' centered at deep minima, playing the role of so-called `pure states'. For the pure models, the latter makes precise the so-called picture of `many valleys separated by high mountains' and significant parts of the TAP analysis from the physics literature.

Temperature Chaos in Some Spherical Mixed p-Spin Models

We give two types of examples of the spherical mixed even-$p$-spin models for which chaos in temperature holds. These complement some known results for the spherical pure $p$-spin models and for models with Ising spins. For example, in contrast to a recent result of Subag who showed absence of chaos in temperature in the spherical pure $p$-spin models for $p\geq 3$, we show that even a smaller order perturbation induces temperature chaos.

Temperature chaos is a non-local effect

Temperature chaos plays a role in important effects, for example memory and rejuvenation, in spin glasses, colloids, polymers. We numerically investigate temperature chaos in spin glasses, exploiting its recent characterization as a rare-event driven phenomenon. The peculiarities of the transformation from periodic to anti-periodic boundary conditions in spin glasses allow us to conclude that temperature chaos is non-local: no bounded region of the system causes it. We precisely show the statistical relationship between temperature chaos and the free-energy changes upon varying boundary conditions.

Spatial variation of deterministic chaos in mean daily temperature and rainfall over Nigeria

Daily rainfall and temperature data from 47 locations across Nigeria for the 36-year period 1979–2014 were treated to time series analysis technique to investigate some nonlinear trends in rainfall and temperature data. Some quantifiers such as Lyapunov exponents, correlation dimension, and entropy were obtained for the various locations. Positive Lyapunov exponents were obtained for the time series of mean daily rainfall for all locations in the southern part of Nigeria while negative Lyapunov exponents were obtained for all locations in the Northern part of Nigeria. The mean daily temperature had positive Lyapunov exponent values (0.35–1.6) for all the locations. Attempts were made in reconstructing the phase space of time series of rainfall and temperature.

Bond chaos in spin glasses revealed through thermal boundary conditions

Spin glasses have competing interactions that lead to a rough energy landscape which is highly susceptible to small perturbations. These chaotic effects strongly affect numerical simulations and, as such, gaining a deeper understanding of chaos in spin glasses is of much importance. The use of thermal boundary conditions is an effective approach to study chaotic phenomena. Here, we generalize population annealing Monte Carlo, combined with thermal boundary conditions, to study bond chaos due to small perturbations in the spin-spin couplings of the three-dimensional Edwards-Anderson Ising spin glass. We show that bond and temperature-induced chaos share the same scaling exponents and that bond chaos is stronger than temperature chaos.