Exponential spatial decay of spin-spin correlations in translation invariant quasifree states

2007 ◽  
Vol 48 (11) ◽  
pp. 113302 ◽  
Author(s):  
Walter H. Aschbacher ◽  
Jean-Marie Barbaroux
Keyword(s):  
Spatial Decay ◽  
Translation Invariant ◽  
Spin Correlations

The Calder´on-Zygmund Theory I: Ellipticity

2017 ◽  
Author(s):  
Brian Street
Keyword(s):  
Classical Theory ◽  
Singular Integral ◽  
Singular Integrals ◽  
Differential Operators ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Single Parameter ◽  
Partial Differential ◽  
Translation Invariant ◽  
Partial Differential Operators

This chapter discusses a case for single-parameter singular integral operators, where ρ‎ is the usual distance on ℝn. There, we obtain the most classical theory of singular integrals, which is useful for studying elliptic partial differential operators. The chapter defines singular integral operators in three equivalent ways. This trichotomy can be seen three times, in increasing generality: Theorems 1.1.23, 1.1.26, and 1.2.10. This trichotomy is developed even when the operators are not translation invariant (many authors discuss such ideas only for translation invariant, or nearly translation invariant operators). It also presents these ideas in a slightly different way than is usual, which helps to motivate later results and definitions.

Enhancement of spin correlations in ZnTe/MnTe superlattices by Cl doping

2000 ◽  
Vol 87 (9) ◽  
pp. 6460-6462 ◽  
Author(s):  
L. E. Stumpe ◽  
J. J. Rhyne ◽  
H. Kaiser ◽  
S. Lee ◽  
U. Bindley ◽  
...  
Keyword(s):  
Spin Correlations

High-Performance Image Filters via Sparse Approximations

2020 ◽  
Vol 3 (2) ◽  
pp. 1-19
Author(s):  
Kersten Schuster ◽  
Philip Trettner ◽  
Leif Kobbelt
Keyword(s):  
High Performance ◽  
Hardware Acceleration ◽  
Optimization Method ◽  
Translation Invariant ◽  
Approximation Quality ◽  
Trade Offs ◽  
Sparse Approximations ◽  
Image Filters ◽  
Good Trade ◽  
And Performance

We present a numerical optimization method to find highly efficient (sparse) approximations for convolutional image filters. Using a modified parallel tempering approach, we solve a constrained optimization that maximizes approximation quality while strictly staying within a user-prescribed performance budget. The results are multi-pass filters where each pass computes a weighted sum of bilinearly interpolated sparse image samples, exploiting hardware acceleration on the GPU. We systematically decompose the target filter into a series of sparse convolutions, trying to find good trade-offs between approximation quality and performance. Since our sparse filters are linear and translation-invariant, they do not exhibit the aliasing and temporal coherence issues that often appear in filters working on image pyramids. We show several applications, ranging from simple Gaussian or box blurs to the emulation of sophisticated Bokeh effects with user-provided masks. Our filters achieve high performance as well as high quality, often providing significant speed-up at acceptable quality even for separable filters. The optimized filters can be baked into shaders and used as a drop-in replacement for filtering tasks in image processing or rendering pipelines.

scholarly journals Isomorphisms between determinantal point processes with translation-invariant kernels and Poisson point processes

2020 ◽  
pp. 1-14
Author(s):  
SHOTA OSADA
Keyword(s):  
Point Processes ◽  
Duke Math ◽  
Random Point ◽  
Determinantal Point Processes ◽  
Fredholm Determinants ◽  
Poisson Point Processes ◽  
Translation Invariant ◽  
Ergodic Properties ◽  
Tree Representations ◽  
Invariant Kernels

Abstract We prove the Bernoulli property for determinantal point processes on $ \mathbb{R}^d $ with translation-invariant kernels. For the determinantal point processes on $ \mathbb{Z}^d $ with translation-invariant kernels, the Bernoulli property was proved by Lyons and Steif [Stationary determinantal processes: phase multiplicity, bernoullicity, and domination. Duke Math. J.120 (2003), 515–575] and Shirai and Takahashi [Random point fields associated with certain Fredholm determinants II: fermion shifts and their ergodic properties. Ann. Probab.31 (2003), 1533–1564]. We prove its continuum version. For this purpose, we also prove the Bernoulli property for the tree representations of the determinantal point processes.

scholarly journals Dynamical spin correlations of the kagome antiferromagnet

2021 ◽  
Vol 103 (1) ◽  
Author(s):  
P. Prelovšek ◽  
M. Gomilšek ◽  
T. Arh ◽  
A. Zorko
Keyword(s):  
Spin Correlations ◽  
Dynamical Spin

scholarly journals Probing the interplay between lattice dynamics and short-range magnetic correlations in CuGeO3 with femtosecond RIXS

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
E. Paris ◽  
C. W. Nicholson ◽  
S. Johnston ◽  
Y. Tseng ◽  
M. Rumo ◽  
...  
Keyword(s):  
Short Range ◽  
Degrees Of Freedom ◽  
Time Resolved ◽  
Model Calculations ◽  
Spin Correlations ◽  
Singlet Exciton ◽  
Magnetic Correlations ◽  
Local Lattice ◽  
Frustrated Systems ◽  
A Charge

AbstractInvestigations of magnetically ordered phases on the femtosecond timescale have provided significant insights into the influence of charge and lattice degrees of freedom on the magnetic sub-system. However, short-range magnetic correlations occurring in the absence of long-range order, for example in spin-frustrated systems, are inaccessible to many ultrafast techniques. Here, we show how time-resolved resonant inelastic X-ray scattering (trRIXS) is capable of probing such short-ranged magnetic dynamics in a charge-transfer insulator through the detection of a Zhang–Rice singlet exciton. Utilizing trRIXS measurements at the O K-edge, and in combination with model calculations, we probe the short-range spin correlations in the frustrated spin chain material CuGeO3 following photo-excitation, revealing a strong coupling between the local lattice and spin sub-systems.

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