scholarly journals Epidemic growth and Griffiths effects on an emergent network of excited atoms

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
T. M. Wintermantel ◽  
M. Buchhold ◽  
S. Shevate ◽  
M. Morgado ◽  
Y. Wang ◽  
...  
Keyword(s):  
Complex Systems ◽  
Power Laws ◽  
Excitation Density ◽  
Griffiths Phase ◽  
Many Body ◽  
Excited Atoms ◽  
Equilibrium Dynamics ◽  
Many Body Systems ◽  
Excitation Number ◽  
Non Equilibrium

AbstractWhether it be physical, biological or social processes, complex systems exhibit dynamics that are exceedingly difficult to understand or predict from underlying principles. Here we report a striking correspondence between the excitation dynamics of a laser driven gas of Rydberg atoms and the spreading of diseases, which in turn opens up a controllable platform for studying non-equilibrium dynamics on complex networks. The competition between facilitated excitation and spontaneous decay results in sub-exponential growth of the excitation number, which is empirically observed in real epidemics. Based on this we develop a quantitative microscopic susceptible-infected-susceptible model which links the growth and final excitation density to the dynamics of an emergent heterogeneous network and rare active region effects associated to an extended Griffiths phase. This provides physical insights into the nature of non-equilibrium criticality in driven many-body systems and the mechanisms leading to non-universal power-laws in the dynamics of complex systems.

scholarly journals Non-equilibrium dynamics of an ultracold Bose gas under multi-pulsed interaction quenches

2016 ◽  
Vol 30 (30) ◽  
pp. 1650367 ◽  
Author(s):  
Lei Chen ◽  
Zhidong Zhang ◽  
Zhaoxin Liang
Keyword(s):  
Bose Gas ◽  
Quantum Gases ◽  
Zero Temperature ◽  
Many Body ◽  
Equilibrium Dynamics ◽  
Many Body Systems ◽  
Multiple Interaction ◽  
The One ◽  
Body Correlation ◽  
Non Equilibrium

We investigate the non-equilibrium properties of a weakly interacting Bose gas subjected to a multi-pulsed quench at zero temperature, where the interaction parameter in the Hamiltonian system switches between values [Formula: see text] and [Formula: see text] for multiple times. The one-body and two-body correlation functions as well as Tan’s contact are calculated. The quench induced excitations are shown to increase with the number of quenches for both [Formula: see text] and [Formula: see text]. This implies the possibility to use multi-pulsed quantum quench as a more powerful way as compared to the “one-off” quench in controllable explorations of non-equilibrium quantum many-body systems. In addition, we study the ultra-short-range property of the two-body correlation function after multiple interaction quenches, which can serve as a probe of the “Tan’s contact” in the experiments. Our findings allow for an experimental probe using state of the art techniques with ultracold quantum gases.

scholarly journals Scaling approach to quantum non-equilibrium dynamics of many-body systems

2010 ◽  
Vol 12 (11) ◽  
pp. 113005 ◽  
Author(s):  
Vladimir Gritsev ◽  
Peter Barmettler ◽  
Eugene Demler
Keyword(s):  
Many Body ◽  
Equilibrium Dynamics ◽  
Many Body Systems ◽  
Non Equilibrium

Coarse-Graining, Scaling, and Hierarchies

2004 ◽  
Author(s):  
Juan Pérez-Mercade
Keyword(s):  
Differential Equations ◽  
Fixed Points ◽  
Correlation Functions ◽  
Nonlinear Partial Differential Equations ◽  
Coarse Graining ◽  
Power Laws ◽  
Effective Parameters ◽  
Many Body ◽  
Anomalous Dimensions ◽  
Many Body Systems

We present a scenario that is useful for describing hierarchies within classes of many-component systems. Although this scenario may be quite general, it will be illustrated in the case of many-body systems whose space-time evolution can be described by a class of stochastic parabolic nonlinear partial differential equations. The stochastic component we will consider is in the form of additive noise, but other forms of noise such as multiplicative noise may also be incorporated. It will turn out that hierarchical behavior is only one of a class of asymptotic behaviors that can emerge when an out-of-equilibrium system is coarse grained. This phenomenology can be analyzed and described using the renormalization group (RG) [6, 15]. It corresponds to the existence of complex fixed points for the parameters characterizing the system. As is well known (see, for example, Hochberg and Perez-Mercader [8] and Onuki [12] and the references cited there), parameters such as viscosities, noise couplings, and masses evolve with scale. In other words, their values depend on the scale of resolution at which the system is observed (examined). These scaledependent parameters are called effective parameters. The evolutionary changes due to coarse graining or, equivalently, changes in system size, are analyzed using the RG and translate into differential equations for the probability distribution function [8] of the many-body system, or the n-point correlation functions and the effective parameters. Under certain conditions and for systems away from equilibrium, some of the fixed points of the equations describing the scale dependence of the effective parameters can be complex; this translates into complex anomalous dimensions for the stochastic fields and, therefore, the correlation functions of the field develop a complex piece. We will see that basic requirements such as reality of probabilities and maximal correlation lead, in the case of complex fixed points, to hierarchical behavior. This is a first step for the generalization of extensive behavior as described by real power laws to the case of complex exponents and the study of hierarchical behavior.

scholarly journals Learning the non-equilibrium dynamics of Brownian movies

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Federico S. Gnesotto ◽  
Grzegorz Gradziuk ◽  
Pierre Ronceray ◽  
Chase P. Broedersz
Keyword(s):  
Degrees Of Freedom ◽  
Time Lapse ◽  
Direct Access ◽  
Dynamical Analysis ◽  
Entropy Production Rate ◽  
Microscopy Imaging ◽  
Time Resolved ◽  
Equilibrium Dynamics ◽  
Many Body Systems ◽  
Non Equilibrium

Abstract Time-lapse microscopy imaging provides direct access to the dynamics of soft and living systems. At mesoscopic scales, such microscopy experiments reveal intrinsic thermal and non-equilibrium fluctuations. These fluctuations, together with measurement noise, pose a challenge for the dynamical analysis of these Brownian movies. Traditionally, methods to analyze such experimental data rely on tracking embedded or endogenous probes. However, it is in general unclear, especially in complex many-body systems, which degrees of freedom are the most informative about their non-equilibrium nature. Here, we introduce an alternative, tracking-free approach that overcomes these difficulties via an unsupervised analysis of the Brownian movie. We develop a dimensional reduction scheme selecting a basis of modes based on dissipation. Subsequently, we learn the non-equilibrium dynamics, thereby estimating the entropy production rate and time-resolved force maps. After benchmarking our method against a minimal model, we illustrate its broader applicability with an example inspired by active biopolymer gels.

scholarly journals Transient dynamics in non-equilibrium complex systems

2018 ◽  
Author(s):  
Diamantis Sellis
Keyword(s):  
Complex Systems ◽  
Equilibrium Dynamics ◽  
Box Counting ◽  
Box Counting Dimension ◽  
Model Complex ◽  
The World ◽  
And Control ◽  
Practical Implications ◽  
Control Complex ◽  
Non Equilibrium

The dynamics of complex systems far from their equilibrium state are currently not fully understood. Besides the theoretical interest for better understanding the world around us this limitation has important practical implications to our ability to model, understand and therefore manage and control complex systems. In a first step to better understand the non- equilibrium dynamics and improve our ability to model complex systems I implement a cellular automaton model of gas mixing. I simulate the evolution towards equilibrium starting from a state of macroscopic order and as the system evolves I calculate the Kolmogorov complexity, the information entropy and the box-counting dimension of the system. I observe a transient peak in complexity, entropy and fractality of the system. To test the genericity of this pattern I implement a very different model, the game of life, where I find the same statistical patterns.

scholarly journals On the General Properties of Non-linear Optical Conductivities

2020 ◽  
Vol 181 (6) ◽  
pp. 2050-2070
Author(s):  
Haruki Watanabe ◽  
Yankang Liu ◽  
Masaki Oshikawa
Keyword(s):  
Electric Fields ◽  
Optical Conductivity ◽  
Current Response ◽  
Many Body ◽  
Third Order ◽  
Sum Rule ◽  
The Third ◽  
General Properties ◽  
Many Body Systems ◽  
Non Equilibrium

AbstractThe optical conductivity is the basic defining property of materials characterizing the current response toward time-dependent electric fields. In this work, following the approach of Kubo’s response theory, we study the general properties of the nonlinear optical conductivities of quantum many-body systems both in equilibrium and non-equilibrium. We obtain an expression of the second- and the third-order optical conductivity in terms of correlation functions and present a perturbative proof of the generalized Kohn formula proposed recently. We also discuss a generalization of the f-sum rule to a non-equilibrium setting by focusing on the instantaneous response.

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