Related papers: Much Ado About Something: Why Lieb-Robinson bounds…
A lengthy bibliography of books referring to special and/or general relativity is provided to give a background for discussions on the historical use of the concept of relativistic mass.
We review recent progress on state-dependent Lieb-Robinson bounds for Bose-Hubbard Hamiltonians. In particular, Kuwahara, Vu, and Saito established that, for general bounded-density initial states, the Lieb-Robinson velocity is bounded by…
Courses in mathematical methods for physics students are not known for including too much in the way of mathematical rigour and, in some ways, understandably so. However, the conditions under which some quite commonly used mathematical…
This work advances knowledge of the threshold of prox-boundedness of a function; an important concern in the use of proximal point optimization algorithms and in determining the existence of the Moreau envelope of the function. In finite…
In this work, we prove a new family of Lieb-Robinson bounds for lattice spin systems with long-range interactions. Our results apply for arbitrary $k$-body interactions, so long as they decay with a power-law greater than $kd$, where $d$ is…
This short note aims to give an insight to Arveson's boundary theorem by means of non-commutative Poisson boundaries and its applications.
This is an introductory text reviewing Lieb-Robinson bounds for open and closed quantum many-body systems. We introduce the Heisenberg picture for time-dependent local Liouvillians and state a Lieb-Robinson bound that gives rise to a…
The complete set of bounds for the technical constants of an elastic layer, plate or laminate is given. The bounds are valid in general, also for completely anisotropic bodies. They are obtained transforming the polar bounds previously…
The goal of this Section is to formulate some of the basic results on the theory of integral equations and mention some of its applications. The literature of this subject is very large. Proofs are not given due to the space restriction.…
We present here the Robin boundary condition and its significance in mathematics and physics.
This paper has been withdrawn by the author in favor of a stronger result proven by the author with R. Frank and T. Weidl in arXiv:0707.0998
In this article I will review some basic results on elliptic boundary value problems with applications to General Relativity.
We attempt to survey recent results and open problems connected to Lieb-Thirring inequalities.
We consider the possibility of developing a Lieb-Robinson bound for the double bracket flow. This is a differential equation $$\partial_B H(B)=[[V,H(B)],H(B)]$$ which may be used to diagonalize Hamiltonians. Here, $V$ is fixed and $H(0)=H$.…
The Lieb-Robinson bound (LRB) states that the range and strength of interactions between the constituents of a complex many-body system impose upper limits to how fast the signal can propagate. It manifests in a light cone-like growth of…
The s-wave Klein-Gordon equation for the bound states is separated in two parts to see clearly the relativistic contributions to the solution in the non-relativistic limit. The reliability of the model is discussed with the specifically…
The relativistic 2-body problem, much like the non-relativistic one, is reduced to describing the motion of an effective particle in an external field. The concept of a relativistic reduced mass and effective particle energy introduced some…
The Lieb-Robinson bound shows that the speed of propagating information in a nonrelativistic quantum lattice system is bounded by a finite velocity, which entails the clustering of correlations. In this paper, we extend the Lieb-Robinson…
We obtain various versions of classical Lieb--Thirring bounds for one- and multi-dimensional complex Jacobi matrices. Our method is based on Fan-Mirski Lemma and seems to be fairly general.
This paper gives an overview of some basic properties of Leibniz algebras. Some of the results were known earlier, but in the article they are accompanied by new simple proofs. Some of the results are new. The article can be viewed as a…