scholarly journals Universal dynamical scaling laws in three-state quantum walks

2021 ◽  
Vol 104 (5) ◽  
Author(s):  
P. R. N. Falcão ◽  
A. R. C. Buarque ◽  
W. S. Dias ◽  
G. M. A. Almeida ◽  
M. L. Lyra
Keyword(s):  
Scaling Laws ◽  
Quantum Walks ◽  
Dynamical Scaling

Critical dynamics and renormalization group (RG)

2021 ◽  
pp. 875-898
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Renormalization Group ◽  
Time Evolution ◽  
Langevin Equation ◽  
Scaling Laws ◽  
Transport Coefficients ◽  
Time Dependent ◽  
Critical Systems ◽  
Static Properties ◽  
Critical Domain ◽  
Dynamical Scaling

Time evolution, near a phase transition in the critical domain of critical systems not far from equilibrium, using a Langevin-type evolution is studied. Typical quantities of interest are relaxation rates towards equilibrium, time-dependent correlation functions and transport coefficients. The main motivation for such a study is that, in systems in which the dynamics is local (on short time-scales, a modification of a dynamic variable has an influence only locally in space) when the correlation length becomes large, a large time-scale emerges, which characterizes the rate of time evolution. This phenomenon called critical slowing down leads to universal behaviour and scaling laws for time-dependent quantities. In contrast with the situation in static critical phenomena, there is no clean and systematic derivation of the dynamical equations governing the time evolution in the critical domain, because often the time evolution is influenced by conservation laws involving the order parameter, or other variables like energy, momentum, angular momentum, currents and so on. Indeed, the equilibrium distribution does not determine the driving force in the Langevin equation, but only the dissipative couplings are generated by the derivative of the equilibrium Hamiltonian, and directly related to the static properties. The purely dissipative Langevin equation specifically discussed, corresponding to static models like the f4 field theory and two-dimensional models. Renormalization group (RG) equations are derived, and dynamical scaling relations established.

Phase Separation Dynamics of Blends of Telechelic Epoxy Terminated Polybutadiene and Maltene

1995 ◽  
Vol 68 (1) ◽  
pp. 158-166 ◽  
Author(s):  
Tsunehiro Yamamoto ◽  
Thein Kyu
Keyword(s):  
Phase Separation ◽  
Scaling Laws ◽  
Phase Region ◽  
Solution Temperature ◽  
Two Phase ◽  
Time Resolved ◽  
Thermally Induced ◽  
Dynamical Scaling ◽  
Upper Critical Solution Temperature ◽  
Deep Temperature

Abstract Thermally induced phase separation in a mixture of telechelic epoxy terminated polybutadiene (ETPB) and maltene has been studied by means of time-resolved light scattering and optical microscopy. Maltene, consisting of various hydrocarbon derivatives, was extracted from asphalt with n-heptane and isolated by centrifugation. The cloud point studies of the ETPB/maltene mixture showed an upper critical solution temperature (UCST) which is thermally reversible. Several deep temperature quench experiments were conducted at an off-critical composition (27/73 ETPB/maltene) from a single phase (80°C) to a two-phase region (27, 29, 31 and 33 °C). The time-evolution of the structure factor for the late stage of spinodal decomposition (SD) was analyzed in the framework of nonlinear and dynamical scaling laws. The reverse quench experiments were also undertaken to elucidate the phase dissolution process.

scholarly journals Kibble–Zurek mechanism in the Ising Field Theory

2020 ◽  
Vol 9 (4) ◽  
Author(s):  
Kristóf Hódsági ◽  
Márton Kormos
Keyword(s):  
Field Theory ◽  
Scaling Laws ◽  
Time Window ◽  
Quantum Phase Transitions ◽  
Quantum Critical Point ◽  
Continuous Phase ◽  
Scaling Properties ◽  
Dynamical Scaling ◽  
Dynamical Aspect ◽  
Dimensional Coupling

The Kibble--Zurek mechanism captures universality when a system is driven through a continuous phase transition. Here we study the dynamical aspect of quantum phase transitions in the Ising Field Theory where the quantum critical point can be crossed in different directions in the two-dimensional coupling space leading to different scaling laws. Using the Truncated Conformal Space Approach, we investigate the microscopic details of the Kibble--Zurek mechanism in terms of instantaneous eigenstates in a genuinely interacting field theory. For different protocols, we demonstrate dynamical scaling in the non-adiabatic time window and provide analytic and numerical evidence for specific scaling properties of various quantities. In particular, we argue that the higher cumulants of the excess heat exhibit universal scaling in generic interacting models for a slow enough ramp.

scholarly journals Dynamical scaling laws of out-of-time-ordered correlators

2019 ◽  
Vol 100 (19) ◽  
Author(s):  
Bo-Bo Wei ◽  
Gaoyong Sun ◽  
Myung-Joong Hwang
Keyword(s):  
Scaling Laws ◽  
Dynamical Scaling

scholarly journals Understanding nonequilibrium scaling laws governing collapse of a polymer

2020 ◽  
Vol 93 (8) ◽  
Author(s):  
Suman Majumder ◽  
Henrik Christiansen ◽  
Wolfhard Janke
Keyword(s):  
Computer Simulations ◽  
Preliminary Data ◽  
Scaling Laws ◽  
Space Dimension ◽  
Spin Systems ◽  
Polymer Dynamics ◽  
Dynamical Scaling ◽  
Evolution Dynamics ◽  
Coarsening Dynamics ◽  
Primary Focus

Abstract Recent emerging interest in experiments of single-polymer dynamics urge computational physicists to revive their understandings, particularly in the nonequilibrium context. Here we briefly discuss the currently evolving approaches of investigating the evolution dynamics of homopolymer collapse using computer simulations. Primary focus of these approaches is to understand various dynamical scaling laws related to coarsening and aging during the collapse in space dimension d = 3, using tools popular in nonequilibrium coarsening dynamics of particle or spin systems. In addition to providing an overview of those results, we also present new preliminary data for d = 2. Graphical abstract

Dynamical scaling laws and time dependent Landau-Ginzburg equation

1969 ◽  
Vol 29 (8) ◽  
pp. 458-459 ◽  
Author(s):  
C. Di Castro ◽  
F. Ferro-Luzzi ◽  
J.A. Tayson
Keyword(s):  
Scaling Laws ◽  
Time Dependent ◽  
Dynamical Scaling

scholarly journals Scale-invariant topology and bursty branching of evolutionary trees emerge from niche construction

2020 ◽  
Vol 117 (14) ◽  
pp. 7879-7887 ◽  
Author(s):  
Chi Xue ◽  
Zhiru Liu ◽  
Nigel Goldenfeld
Keyword(s):  
Phylogenetic Trees ◽  
Scaling Laws ◽  
Niche Construction ◽  
Finite Size ◽  
Evolutionary Process ◽  
Community Diversity ◽  
Coarse Grained ◽  
Scaling Analysis ◽  
Scale Invariant ◽  
Dynamical Scaling

Phylogenetic trees describe both the evolutionary process and community diversity. Recent work has established that they exhibit scale-invariant topology, which quantifies the fact that their branching lies in between the two extreme cases of balanced binary trees and maximally unbalanced ones. In addition, the backbones of phylogenetic trees exhibit bursts of diversification on all timescales. Here, we present a simple, coarse-grained statistical model of niche construction coupled to speciation. Finite-size scaling analysis of the dynamics shows that the resultant phylogenetic tree topology is scale-invariant due to a singularity arising from large niche construction fluctuations that follow extinction events. The same model recapitulates the bursty pattern of diversification in time. These results show how dynamical scaling laws of phylogenetic trees on long timescales can reflect the indelible imprint of the interplay between ecological and evolutionary processes.

Siphon Flows in Stratified Coronal Loops

1994 ◽  
Vol 144 ◽  
pp. 185-187
Author(s):  
S. Orlando ◽  
G. Peres ◽  
S. Serio
Keyword(s):  
Heat Flux ◽  
Scaling Laws ◽  
Flow Model ◽  
Supersonic Flows ◽  
Coronal Loops ◽  
Characteristic Parameters

AbstractWe have developed a detailed siphon flow model for coronal loops. We find scaling laws relating the characteristic parameters of the loop, explore systematically the space of solutions and show that supersonic flows are impossible for realistic values of heat flux at the base of the upflowing leg.

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