Spatiotemporal spread of perturbations in power-law models at low temperatures: Exact results for classical out-of-time-order correlators

2021 ◽  
Vol 104 (4) ◽  
Author(s):  
Bhanu Kiran S. ◽  
David A. Huse ◽  
Manas Kulkarni
Keyword(s):  
Power Law ◽  
Low Temperatures ◽  
Exact Results ◽  
Time Order

scholarly journals RANDOM WALKS ON DIRECTED NETWORKS: THE CASE OF PAGERANK

2007 ◽  
Vol 17 (07) ◽  
pp. 2343-2353 ◽  
Author(s):  
SANTO FORTUNATO ◽  
ALESSANDRO FLAMMINI
Keyword(s):  
Random Walk ◽  
Power Law ◽  
Degree Distribution ◽  
Directed Graphs ◽  
Damping Factor ◽  
Web Pages ◽  
Stationary Probability ◽  
Exact Results ◽  
Limit Values ◽  
Underlying Graph

PageRank, the prestige measure for Web pages used by Google, is the stationary probability of a peculiar random walk on directed graphs, which interpolates between a pure random walk and a process where all nodes have the same probability of being visited. We give some exact results on the distribution of PageRank in the cases in which the damping factor q approaches the two limit values 0 and 1. When q → 0 and for several classes of graphs the distribution is a power law with exponent 2, regardless of the in-degree distribution. When q → 1 it can always be derived from the in-degree distribution of the underlying graph, if the out-degree is the same for all nodes.

Magnetic Penetration Depth Measurements and Inhomogeneity in YBa2Cu3O7−δ Superconducting Thin Films

1990 ◽  
Vol 195 ◽  
Author(s):  
Steven M. Anlage ◽  
Brian W. Langley ◽  
Jurgen Halbritter ◽  
Chang-Beom Eom ◽  
Neil Switz ◽  
...  
Keyword(s):  
Thin Films ◽  
Temperature Dependence ◽  
Penetration Depth ◽  
Exponential Decay ◽  
Power Law ◽  
Low Temperatures ◽  
Bcs Theory ◽  
Magnetic Penetration Depth ◽  
Microstrip Resonator ◽  
Magnetic Penetration

ABSTRACTThe microstrip resonator technique has been applied to study the temperature dependence of the magnetic penetration depth in high quality YBa2Cu3O7−δ thin films. The temperature dependence at low temperatures comes out directly from measured data, with no assumptions about transmission line geometry, dielectric properties, or a model for the temperature dependence of the penetration depth. One can interpret the data in terms of either an exponential decay of λ(T) at low temperatures or as a power law decay. The energy gaps obtained from the exponential decay at low temperature are found to be significantly smaller than weak coupled BCS theory and power-law exponents are in the range of 1.3 to 3.2. These results will be discussed in terms of microscopic theories and the possibility that materials properties dominate the measurement.

scholarly journals Power-law out of time order correlation functions in the SYK model

2017 ◽  
Vol 921 ◽  
pp. 727-752 ◽  
Author(s):  
Dmitry Bagrets ◽  
Alexander Altland ◽  
Alex Kamenev
Keyword(s):  
Power Law ◽  
Correlation Functions ◽  
Time Order

Dimensionality dependence of dynamical correlations: exact results from a quantum many body system

1993 ◽  
Vol 441 (1911) ◽  
pp. 169-179 ◽  
Keyword(s):  
Low Temperatures ◽  
Relaxation Function ◽  
Mean Field ◽  
Exact Results ◽  
Body System ◽  
Many Body ◽  
Many Body Systems

Using one of the simplest model interacting quantum many body systems it is shown that the relaxation function behaves remarkably differently at low temperatures depending upon whether the lattice dimensionality of the system, D < ∞ or → ∞. The results illustrate the possible limitations of mean-field descriptions of dynamics at T < T c in quantum many body systems.

scholarly journals Fractional Power-Law Intraband Optical Conductivity in the Low-Dimensional Dirac Material CaMnBi2

Crystals ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 428
Author(s):  
M. B. Schilling ◽  
C. X. Wang ◽  
Y. G. Shi ◽  
R. K. Kremer ◽  
M. Dressel ◽  
...  
Keyword(s):  
Power Law ◽  
Optical Conductivity ◽  
Low Temperatures ◽  
Fractional Power ◽  
Electronic System ◽  
Quantum Criticality ◽  
Free Carriers ◽  
Universal Power Law ◽  
Low Dimensional ◽  
Open Question

We studied the broadband optical conductivity of CaMnBi2, a material with two-dimensional Dirac electronic bands, and found that both components of the intraband conductivity follow a universal power law as a function of frequency at low temperatures. This conductivity scaling differs from the Drude(-like) behavior, generally expected for free carriers, but matches the predictions for the intraband response of an electronic system in a quantum critical region. Since no other indications of quantum criticality are reported for CaMnBi2 so far, the cause of the observed unusual scaling remains an open question.

scholarly journals SEMIRELATIVISTIC HAMILTONIANS AND THE AUXILIARY FIELD METHOD

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4695-4726 ◽  
Author(s):  
BERNARD SILVESTRE-BRAC ◽  
CLAUDE SEMAY ◽  
FABIEN BUISSERET
Keyword(s):  
Schrödinger Equation ◽  
Power Law ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Field Method ◽  
Auxiliary Field ◽  
Square Root ◽  
Exact Results ◽  
Approximate Analytical Solutions ◽  
Envelope Theory

Approximate analytical closed energy formulas for semirelativistic Hamiltonians of the form [Formula: see text] are obtained within the framework of the auxiliary field method. This method, which is equivalent to the envelope theory, has been recently proposed as a powerful tool to get approximate analytical solutions of the Schrödinger equation. Various shapes for the potential V(r) are investigated: power-law, funnel, square root, and Yukawa. A comparison with the exact results is discussed in detail.

THE SURFACE IMPEDANCE OF HIGH Tc SUPERCONDUCTORS

1989 ◽  
Vol 03 (01) ◽  
pp. 5-13 ◽  
Author(s):  
J. CARINI ◽  
L. DRABECK ◽  
G. GRÜNER
Keyword(s):  
High Temperature ◽  
Temperature Dependence ◽  
Power Law ◽  
Surface Impedance ◽  
Low Temperatures ◽  
Qualitative Agreement ◽  
Surface Resistance ◽  
High Temperature Superconductors ◽  
High Tc Superconductors ◽  
High Tc

Recent experiments on the surface impedance of the high temperature superconductors are summarized. The overall temperature dependence of the penetration depth is in broad qualitative agreement with conventional pairing, but with an anomolous power law behavior observed at low temperatures. The surface resistance is orders of magnitude larger than estimates based on the Mattis-Bardeen theory. One possibility is unconventional pairing, but structural inhomogenities are the most likely explanation for the experimental results.

MAGNETIZATION PLATEAUS ON THE ZIGZAG LADDER WITH TWO-, AND THREE-SITE EXCHANGES

2007 ◽  
Vol 21 (20) ◽  
pp. 3567-3579 ◽  
Author(s):  
V. V. HOVHANNISYAN ◽  
L. N. ANANIKYAN ◽  
N. S. ANANIKIAN
Keyword(s):  
Magnetic Field ◽  
Partition Function ◽  
Strong Magnetic Field ◽  
Low Temperatures ◽  
Heisenberg Model ◽  
Spin Exchange ◽  
Exchange Interactions ◽  
Exact Results ◽  
Recursion Method ◽  
Exchange Parameters

We consider the Heisenberg model with two-, and three-spin exchange interactions on a zigzag ladder in a strong magnetic field. Using the recursion method for the partition function in Ising approximation we have found exact results for the magnetization. We have shown the existence of magnetization plateaus in the case of mutual two-, and three-spin exchanges at low temperatures and different exchange parameters. The system exhibits different magnetic behaviors, depending on the values of the exchange parameters.

TWO-DIMENSIONAL HOLES IN GaAs HIGFETs: FABRICATION METHODS AND TRANSPORT MEASUREMENTS

2007 ◽  
Vol 21 (08n09) ◽  
pp. 1219-1227 ◽  
Author(s):  
JIAN HUANG ◽  
D. S. NOVIKOV ◽  
D. C. TSUI ◽  
L. N. PFEIFFER ◽  
K. W. WEST
Keyword(s):  
Power Law ◽  
Low Temperatures ◽  
Field Effect ◽  
Field Effect Transistors ◽  
Fabrication Process ◽  
Hole Density ◽  
Two Dimensional ◽  
Transport Mechanisms ◽  
Transport Measurements ◽  
Dilute System

We present a fabrication process and results of transport measurements of a number of p-channel heterojunction-insulated-gate field-effect transistors (HIGFETs). Without intentional doping in HIGFETs, the disorder is likely to be less than that in the modulation-doped samples. We established a process that eliminates the well-known gate leakage problem. The hole density in our devices can be continuously tuned down to a record low value of 7 × 108 cm -2. Remarkably, such a dilute system (with Fermi wavelength approaching 1 μm) exhibits a non-activated conductivity that grows with temperature approximately as a power law at sufficiently low temperatures. We contrast it with the activated transport found in more disordered samples and discuss possible transport mechanisms in this strongly-interacting regime.

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