相关论文: Schr\"odinger maximal function estimates via the p…
We propose a method to solve the electronic Schr\"odinger equation for strongly correlated systems by applying a unitary transformation to reduce the complexity of the physical Hamiltonian. In particular, we seek a transformation that maps…
We apply the Frobenius method to the Schr\"{o}dinger equation with a truncated Coulomb potential. By means of the tree-term recurrence relation for the expansion coefficients we truncate the series and obtain exact eigenfunctions and…
The method of self-similar factor approximants is completed by defining the approximants of odd orders, constructed from the power series with the largest term of an odd power. It is shown that the method provides good approximations for…
A modified perturbation theory in the strength of the nonlinear term is used to solve the Nonlinear Schroedinger Equation with a random potential. It is demonstrated that in some cases it is more efficient than other methods. Moreover we…
The phenomenon "hypo-coercivity," i.e., the increased rate of contraction for a semi-group upon adding a large skew-adjoint part to the generator, is considered for 1D semigroups generated by the Schr\"odinger operators $-\partial^2_x + x^2…
Local scale invariance for lattice models is studied using new realizations of the Schr\"odinger algebra. The two-point function is calculated and it turns out that the result can be reproduced from exact two-point correlation functions…
The aim of the present paper is to obtain a Sj\"{o}lin-type maximal estimate for pseudo-differential operators with homogeneous symbols. The crux of the proof is to obtain a phase decomposition formula which does not involve the time…
We prove spectral properties for random Landau Schr\"odinger operators on $L^2(\mathbb{R}^2)$ with bounded, random potentials supported in a square $\Lambda_L \subset \mathbb{R}^2$ of side length $L>0$, using semiclassical…
In this work we prove a Strichartz estimate for the Schr\"odinger equation in the quasiperiodic setting. We also show a lower bound on the number of resonant frequency interactions in this situation.
A systematic treatment of O(a)-improvement in lattice theories with static quarks is presented. The Schr\"odinger functional is discussed and a renormalization condition for the static axial current in the SF-scheme is introduced. Its…
This article is devoted to the construction of new numerical methods for the semiclassical Schr\"odinger equation. A phase-amplitude reformulation of the equation is described where the Planck constant epsilon is not a singular parameter.…
A new fractional version of the Dunkl transform for real order $\alpha$ is obtained. An integral representation, a Bochner type identity and a Master formula for this transform are derived.
We study the semi-classical trace formula at a critical energy level for a Schr\"odinger operator on $\mathbb{R}^{n}$. We assume here that the potential has a totally degenerate critical point associated to a local maximum. The main result,…
In this paper we develop an abstract method to handle the problem of unique continuation for the Schr\"odinger equation $(i\partial_t+\Delta)u=V(x)u$. In general the problem is to find a class of potentials $V$ which allows the unique…
We derive H\"older regularity estimates for operators associated with a time independent Schr\"odinger operator of the form $-\Delta+V$. The results are obtained by checking a certain condition on the function $T1$. Our general method…
The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…
Recently maximum pseudo-likelihood (MPL) inference method has been successfully applied to statistical physics models with intractable likelihoods. We use information theory to derive a relation between the pseudo-likelihood and likelihood…
The matching between Schrodinger Functional renormalization schemes and conventional perturbative schemes is usually done using an intermediate lattice scheme. We propose to do the matching directly. This requires the perturbative…
When attempting to recover functions from observational data, one naturally seeks to do so in an optimal manner with respect to some modeling assumption. With a focus put on the worst-case setting, this is the standard goal of Optimal…
We test the scaling behaviour of Wilson, hypercube, maximally twisted mass and overlap fermion actions in dynamical simulations of the 2-dimensional massive Schwinger model. We also present possibilities to simulate overlap fermions…