On correlation functions of Wilson loops, local and non-local operators

In this paper, the bond-based peridynamic system is analysed as a non-local boundary-value problem with volume constraint. The study extends earlier works in the literature on non-local diffusion and non-local peridynamic models, to include non-positive definite kernels. We prove the well-posedness of both linear and nonlinear variational problems with volume constraints. The analysis is based on some non-local Poincaré-type inequalities and the compactness of the associated non-local operators. It also offers careful characterizations of the associated solution spaces, such as compact embedding, separability and completeness. In the limit of vanishing non-locality, the convergence of the peridynamic system to the classical Navier equations of elasticity with Poisson ratio ¼ is demonstrated.

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Decay properties for evolution-parabolic coupled systems related to thermoelastic plate equations

AIMS Mathematics ◽

10.3934/math.2022017 ◽

2021 ◽

Vol 7 (1) ◽

pp. 260-275

Author(s):

Zihan Cai ◽

◽

Yan Liu ◽

Baiping Ouyang ◽

Keyword(s):

Cauchy Problem ◽

Phase Space ◽

Coupled Systems ◽

Decay Properties ◽

Representation Of Solutions ◽

The Cauchy Problem ◽

Plate Equations ◽

Thermoelastic Plate ◽

Local Operators ◽

Non Local

<abstract><p>In this paper, we consider the Cauchy problem for a family of evolution-parabolic coupled systems, which are related to the classical thermoelastic plate equations containing non-local operators. By using diagonalization procedure and WKB analysis, we derive representation of solutions in the phase space. Then, sharp decay properties in a framework of $ L^p-L^q $ are investigated via these representations. Particularly, some thresholds for the regularity-loss type decay properties are found.</p></abstract>

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Asymmetric butterfly velocities in 2-local Hamiltonians

SciPost Physics ◽

10.21468/scipostphys.9.2.024 ◽

2020 ◽

Vol 9 (2) ◽

Author(s):

Yong-Liang Zhang ◽

Vedika Khemani

Keyword(s):

Correlation Functions ◽

Quantum Systems ◽

Information Propagation ◽

Local Interactions ◽

Dimensional Lattice ◽

One Dimensional ◽

Local Operators ◽

Left And Right ◽

Model Hamiltonians

The speed of information propagation is finite in quantum systems with local interactions. In many such systems, local operators spread ballistically in time and can be characterized by a ``butterfly velocity", which can be measured via out-of-time-ordered correlation functions. In general, the butterfly velocity can depend asymmetrically on the direction of information propagation. In this work, we construct a family of simple 2-local Hamiltonians for understanding the asymmetric hydrodynamics of operator spreading. Our models live on a one dimensional lattice and exhibit asymmetric butterfly velocities between the left and right spatial directions. This asymmetry is transparently understood in a free (non-interacting) limit of our model Hamiltonians, where the butterfly speed can be understood in terms of quasiparticle velocities.

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