A deep understanding of the mechanisms underlying many-body quantum chaos is one of the big challenges in contemporary theoretical physics. We tackle this problem in the context of a set of perturbed quadratic Sachdev...
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A deep understanding of the mechanisms underlying many-body quantum chaos is one of the big challenges in contemporary theoretical physics. We tackle this problem in the context of a set of perturbed quadratic Sachdev-Ye-Kitaev (SYK) Hamiltonians defined on graphs. This allows us to disentangle the geometrical properties of the underlying single-particle problem and the importance of the interaction terms, showing that the former is the dominant feature ensuring the single-particle to many-body chaotic transition. Our results are verified numerically with state-of-the-art numerical techniques, capable of extracting eigenvalues in a desired energy window of very large Hamiltonians. Our approach essentially provides a new way of viewing many-body chaos from a single-particle perspective.
In this paper,we study the Cauchy problem for the Benjamin-Ono-Burgers equation ∂_(t)u−ϵ∂^(2)/_(x)u+H∂^(2)_(x)u+uu_(x)=0,where H denotes the Hilbert transform *** obtain that it is uniformly locally well-posed for sma...
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In this paper,we study the Cauchy problem for the Benjamin-Ono-Burgers equation ∂_(t)u−ϵ∂^(2)/_(x)u+H∂^(2)_(x)u+uu_(x)=0,where H denotes the Hilbert transform *** obtain that it is uniformly locally well-posed for small data in the refined Sobolev space H~σ(R)(σ■0),which is a subspace of L2(ℝ).It is worth noting that the low-frequency part of H~σ(R)is scaling critical,and thus the small data is *** high-frequency part of H~σ(R)is equal to the Sobolev space Hσ(ℝ)(σ■0)and reduces to L2(ℝ).Furthermore,we also obtain its inviscid limit behavior in H~σ(R)(σ■0).
The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger(NLS) equations was established by using n-dimensional versions of the Conley-Moser conditions. As a result, the discretized ...
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The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger(NLS) equations was established by using n-dimensional versions of the Conley-Moser conditions. As a result, the discretized perturbed NLS system is shown to possess an invariant set Λ on which the dynamics is topologically conjugate to a shift on four symbols.
I refer to the comments of Cseke and Fazekas concerning the thresholding algorithms proposed by Otsu and Brink, respectively. Contrary to the claim made by Cseke and Fazekas it is shown that these algorithms are not g...
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I refer to the comments of Cseke and Fazekas concerning the thresholding algorithms proposed by Otsu and Brink, respectively. Contrary to the claim made by Cseke and Fazekas it is shown that these algorithms are not generally identical, this case arising only when the black/white levels used for the bilevel image are the below- and above-threshold means of the original image.
作者：
Shengxin ZhuDepartment of Mathematics
Xi'an Jiaotong-Liverpool University Laboratory of Computational PhysicsInstitute of Applied Physics and Computational Mathematics
Linear mixed models are often used for analysing unbalanced data with certain missing values in a broad range of *** restricted maximum likelihood method is often preferred to estimate co-variance parameters in such m...
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ISBN:
(纸本)9781509036202
Linear mixed models are often used for analysing unbalanced data with certain missing values in a broad range of *** restricted maximum likelihood method is often preferred to estimate co-variance parameters in such models due to its unbiased estimation of the underlying variance *** restricted log-likelihood function involves log determinants of a complicated co-variance matrix which are computational *** efficient statistical estimate of the underlying model parameters and quantifying the accuracy of the estimation requires the observed or the Fisher information *** approaches to compute the observed and Fisher information matrix are computationally *** algorithms are of highly demand to keep the restricted log-likelihood method scalable for increasing high-throughput unbalanced data *** this paper,we explore how to leverage an information splitting technique and dedicate matrix transform to significantly reduce *** with a fill-in reducing multi-frontal sparse direct solvers,this approach improves performance of the computation process.
A novel Eulerian Gaussian beam method was developed in[8]to compute the Schrödinger equation efficiently in the semiclassical *** this paper,we introduce an efficient semi-Eulerian implementation of this *** new ...
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A novel Eulerian Gaussian beam method was developed in[8]to compute the Schrödinger equation efficiently in the semiclassical *** this paper,we introduce an efficient semi-Eulerian implementation of this *** new algorithm inherits the essence of the Eulerian Gaussian beam method where the Hessian is computed through the derivatives of the complexified level set functions instead of solving the dynamic ray tracing *** difference lies in that,we solve the ray tracing equations to determine the centers of the beams and then compute quantities of interests only around these *** yields effectively a local level set implementation,and the beam summation can be carried out on the initial physical space instead of the phase *** a consequence,it reduces the computational cost and also avoids the delicate issue of beam summation around the caustics in the Eulerian Gaussian beam ***,the semi-Eulerian Gaussian beam method can be easily generalized to higher order Gaussian beam methods,which is the topic of the second part of this *** numerical examples are provided to verify the accuracy and efficiency of both the first order and higher order semi-Eulerian methods.
As an important model in quantum semiconductor devices, the SchrSdinger-Poisson equations have generated widespread interests in both analysis and numerical simulations in recent years. In this paper, we present Gauss...
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As an important model in quantum semiconductor devices, the SchrSdinger-Poisson equations have generated widespread interests in both analysis and numerical simulations in recent years. In this paper, we present Gaussian beam methods for the numerical simulation of the one-dimensional Schrodinger-Poisson equations. The Gaussian beam methods for high frequency waves outperform the geometrical optics method in that the former are accurate even around caustics. The purposes of the paper are first to develop the Gaussian beam methods, based on our previous methods for the linear SchrSdinger equation, for the Schrodinger-Poisson equations, and then check their validity for this weakly-nonlinear system.
Until now multiscale quantum problems have appeared to be out of reach at the many-body level relevant to strongly correlated materials and current quantum information devices. In fact, they can be modeled with q-th o...
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