scholarly journals Novel mechanism for discrete scale invariance in sandpile models

2000 ◽  
Vol 15 (1) ◽  
pp. 193-197 ◽  
Author(s):  
M.W. Lee ◽  
D. Sornette
Keyword(s):  
Scale Invariance ◽  
Discrete Scale Invariance ◽  
Sandpile Models ◽  
Discrete Scale

scholarly journals Log-periodic quantum magneto-oscillations and discrete-scale invariance in topological material HfTe5

2019 ◽  
Vol 6 (5) ◽  
pp. 914-920 ◽  
Author(s):  
Huichao Wang ◽  
Yanzhao Liu ◽  
Yongjie Liu ◽  
Chuanying Xi ◽  
Junfeng Wang ◽  
...  
Keyword(s):  
Scale Invariance ◽  
Quantum Effect ◽  
Transport Coefficients ◽  
Resonant Scattering ◽  
Hall Resistance ◽  
Quantum Oscillations ◽  
Discrete Scale Invariance ◽  
Dirac Materials ◽  
Theoretical Simulations ◽  
Discrete Scale

Abstract Discrete-scale invariance (DSI) is a phenomenon featuring intriguing log-periodicity that can be rarely observed in quantum systems. Here, we report the log-periodic quantum oscillations in the longitudinal magnetoresistivity (ρxx) and the Hall traces (ρyx) of HfTe5 crystals, which reveal the DSI in the transport-coefficients matrix. The oscillations in ρxx and ρyx show the consistent logB-periodicity with a phase shift. The finding of the logB oscillations in the Hall resistance supports the physical mechanism as a general quantum effect originating from the resonant scattering. Combined with theoretical simulations, we further clarify the origin of the log-periodic oscillations and the DSI in the topological materials. This work evidences the universality of the DSI in the Dirac materials and provides indispensable information for a full understanding of this novel phenomenon.

scholarly journals Evidence of Discrete Scale Invariance in DLA and Time-to-Failure by Canonical Averaging

1998 ◽  
Vol 09 (03) ◽  
pp. 433-447 ◽  
Author(s):  
A. Johansen ◽  
D. Sornette
Keyword(s):  
Scale Invariance ◽  
Time To Failure ◽  
Laplacian Growth ◽  
Ensemble Averaging ◽  
Diffusion Limited Aggregation ◽  
Discrete Scale Invariance ◽  
Diffusion Limited ◽  
Market Crashes ◽  
Discrete Scale

Discrete scale invariance, which corresponds to a partial breaking of the scaling symmetry, is reflected in the existence of a hierarchy of characteristic scales l0,l0λ,l0λ2,…, where λ is a preferred scaling ratio and l0 a microscopic cut-off. Signatures of discrete scale invariance have recently been found in a variety of systems ranging from rupture, earthquakes, Laplacian growth phenomena, "animals" in percolation to financial market crashes. We believe it to be a quite general, albeit subtle phenomenon. Indeed, the practical problem in uncovering an underlying discrete scale invariance is that standard ensemble averaging procedures destroy it as if it was pure noise. This is due to the fact, that while λ only depends on the underlying physics, l0 on the contrary is realization-dependent. Here, we adapt and implement a novel so-called "canonical" averaging scheme which re-sets the l0 of different realizations to approximately the same value. The method is based on the determination of a realization-dependent effective critical point obtained from, e.g., a maximum susceptibility criterion. We demonstrate the method on diffusion limited aggregation and a model of rupture.

scholarly journals N-boson spectrum from a discrete scale invariance

2014 ◽  
Vol 90 (3) ◽  
Author(s):  
A. Kievsky ◽  
N. K. Timofeyuk ◽  
M. Gattobigio
Keyword(s):  
Scale Invariance ◽  
Discrete Scale Invariance ◽  
Discrete Scale

scholarly journals Tunable discrete scale invariance in transition-metal pentatelluride flakes

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Yanzhao Liu ◽  
Huichao Wang ◽  
Haipeng Zhu ◽  
Yanan Li ◽  
Jun Ge ◽  
...  
Keyword(s):  
Transition Metal ◽  
Scale Invariance ◽  
Bound States ◽  
Scale Factor ◽  
Coulomb Interactions ◽  
Many Body ◽  
Body Effect ◽  
Discrete Scale Invariance ◽  
The Many ◽  
Discrete Scale

AbstractLog-periodic quantum oscillations discovered in transition-metal pentatelluride give a clear demonstration of discrete scale invariance (DSI) in solid-state materials. The peculiar phenomenon is convincingly interpreted as the presence of two-body quasi-bound states in a Coulomb potential. However, the modifications of the Coulomb interactions in many-body systems having a Dirac-like spectrum are not fully understood. Here, we report the observation of tunable log-periodic oscillations and DSI in ZrTe5 and HfTe5 flakes. By reducing the flakes thickness, the characteristic scale factor is tuned to a much smaller value due to the reduction of the vacuum polarization effect. The decreasing of the scale factor demonstrates the many-body effect on the DSI, which has rarely been discussed hitherto. Furthermore, the cut-offs of oscillations are quantitatively explained by considering the Thomas-Fermi screening effect. Our work clarifies the many-body effect on DSI and paves a way to tune the DSI in quantum materials.

scholarly journals Signatures of discrete scale invariance inDsttime series

2011 ◽  
Vol 38 (13) ◽  
pp. n/a-n/a ◽  
Author(s):  
Georgios Balasis ◽  
Constantinos Papadimitriou ◽  
Ioannis A. Daglis ◽  
Anastasios Anastasiadis ◽  
Labrini Athanasopoulou ◽  
...  
Keyword(s):  
Scale Invariance ◽  
Discrete Scale Invariance ◽  
Discrete Scale

Discrete scale-invariance in cross-correlations between time series

2015 ◽  
Vol 421 ◽  
pp. 161-170 ◽  
Author(s):  
Qin Xiao ◽  
Xue Pan ◽  
Mutua Stephen ◽  
Yue Yang ◽  
Xinli Li ◽  
...  
Keyword(s):  
Time Series ◽  
Scale Invariance ◽  
Discrete Scale Invariance ◽  
Cross Correlations ◽  
Discrete Scale
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