Imaginary-time approach and equilibrium dynamics

2021 ◽  
pp. 73-120
Keyword(s):  
Imaginary Time ◽  
Equilibrium Dynamics

Thermodynamic Green’s Functions and Spectral Structure

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Spectral Weight ◽  
Statistical Thermodynamic ◽  
Spectral Structure ◽  
Imaginary Time ◽  
Translational Invariance ◽  
The One

Multiparticle thermodynamic Green’s functions, defined in terms of grand canonical ensemble averages of time-ordered products of creation and annihilation operators, are interpreted as tracing the amplitude for time-developing correlated interacting particle motions taking place in the background of a thermal ensemble. Under equilibrium conditions, time-translational invariance permits the one-particle thermal Green’s function to be represented in terms of a single frequency, leading to a Lehmann spectral representation whose frequency poles describe the energy spectrum. This Green’s function has finite values for both t>t′ and t<t′ (unlike retarded Green’s functions), and the two parts G1> and G1< (respectively) obey a simple proportionality relation that facilitates the introduction of a spectral weight function: It is also interpreted in terms of a periodicity/antiperiodicity property of a modified Green’s function in imaginary time capable of a Fourier series representation with imaginary (Matsubara) frequencies. The analytic continuation from imaginary time to real time is discussed, as are related commutator/anticommutator functions, also retarded/advanced Green’s functions, and the spectral weight sum rule is derived. Statistical thermodynamic information is shown to be embedded in physical features of the one- and two-particle thermodynamic Green’s functions.

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

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Marco Baity-Jesi ◽  
Enrico Calore ◽  
Andrés Cruz ◽  
Luis Antonio Fernandez ◽  
José Miguel Gil-Narvion ◽  
...  
Keyword(s):  
Spin Glass ◽  
Dynamic Effect ◽  
Large Degree ◽  
Equilibrium Temperature ◽  
Experimental Conditions ◽  
Temperature Changes ◽  
Equilibrium Dynamics ◽  
Glass Dynamics ◽  
Extreme Sensitivity ◽  
Non Equilibrium

AbstractExperiments 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.

ANTICIPATED FUTURE CONSUMPTION IN AN ENDOGENOUS GROWTH MODEL

2020 ◽  
pp. 1-37
Author(s):  
Manuel A. Gómez ◽  
Goncalo Monteiro
Keyword(s):  
Theoretical Analysis ◽  
Endogenous Growth ◽  
Growth Model ◽  
Reference Point ◽  
Time Varying ◽  
Standard Specification ◽  
Equilibrium Dynamics ◽  
Current Consumption ◽  
Endogenous Growth Model ◽  
Future Consumption

We devise an endogenous growth model in which agents’ utility depends not only on current consumption but also on the pleasure of anticipated future consumption. We consider the case in which agents derive satisfaction from their own anticipatory feelings—inward-looking or internal anticipation—and the case in which agents derive utility from anticipation of other people’s future consumption—outward-looking or external anticipation. We characterize the effects of introducing a forward-looking consumption reference on the dynamics of the economy. Whereas the inward-looking economy features transitional dynamics, the outward-looking economy does not. The distortions caused by the externality in the economy with external habits can be corrected by subsidizing income at a time-varying rate or by means of a tax on consumption at a decreasing rate. We contrast the equilibrium dynamics of our specification to the more standard specification of the habit formation consumption reference point. Numerical simulations supplement the theoretical analysis.

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.

Temporal Dynamics of the Blueberry Maggot Fly (Diptera: Tephritidae) and its Primary Parasitoid, Biosteres melleus (Hymenoptera: Braconidae), in the Maine Wild Blueberry System

2019 ◽  
Vol 113 (2) ◽  
pp. 720-730 ◽  
Author(s):  
Francis A Drummond ◽  
Judith A Collins
Keyword(s):  
Predictive Model ◽  
Stable Equilibrium ◽  
Temporal Dynamics ◽  
Equilibrium Dynamics ◽  
Rhagoletis Mendax ◽  
Parasitism Rates ◽  
Blueberry Maggot Fly ◽  
Rates Of Growth ◽  
Wild Blueberry ◽  
Insecticide Sprays

Abstract Between 1998 and 2017, we conducted studies in wild blueberry, Vaccinium angustifolium Aiton (Ericales: Ericaceae), to elucidate the temporal dynamics of the blueberry maggot fly, Rhagoletis mendax Curran, and its parasitoid, Biosteres melleus (Gahan). A predictive model for the emergence of R. mendax was validated at two sites over 3 yr. A second predictive model for the major parasitoid, B. melleus, of R. mendax was constructed and suggests that the delay in emergence of the parasitoid relative to its host provides a period or ‘biological window’ of 9 d where insecticide sprays can be applied to manage R. mendax with a limited impact on the parasitoid. A 20-yr study on the parasitoid/host dynamics showed parasitism rates ranging from 0.5 to 28.2%. It appears that R. mendax populations in Maine wild blueberry are characterized by stable equilibrium dynamics, significantly affected by stochastic processes. There was a weak, but significant relationship between B. melleus density and R. mendax intrinsic rates of growth. Our data suggest that R. mendax population dynamics in wild blueberry is characterized by an unstable equilibrium tipping point of 7.9 maggots per liter of blueberries or an average of 10 flies per trap.

scholarly journals On the Complexities of Complex Economic Dynamics

1999 ◽  
Vol 13 (4) ◽  
pp. 169-192 ◽  
Author(s):  
J. Barkley Rosser
Keyword(s):  
Adaptive Learning ◽  
Rational Expectations ◽  
Interacting Particle Systems ◽  
Complexity Analysis ◽  
Evolutionary Game ◽  
Equilibrium Dynamics ◽  
Self Organized ◽  
Policy Debates ◽  
Interacting Particle ◽  
Self Organized Criticality

Complex economic nonlinear dynamics endogenously do not converge to a point, a limit cycle, or an explosion. Their study developed out of earlier studies of cybernetic, catastrophic, and chaotic systems. Complexity analysis stresses interactions among dispersed agents without a global controller, tangled hierarchies, adaptive learning, evolution, and novelty, and out-of-equilibrium dynamics. Complexity methods include interacting particle systems, self-organized criticality, and evolutionary game theory, to simulate artificial stock markets and other phenomena. Theoretically, bounded rationality replaces rational expectations. Complexity theory influences empirical methods and restructures policy debates.

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