Do you want to publish a course? Click here

Quantum solvable models with nonlocal one point interactions

67   0   0.0 ( 0 )
 Added by Sergii Kuzhel
 Publication date 2016
  fields Physics
and research's language is English




Ask ChatGPT about the research

Within the framework of quantum mechanics working with one-dimensional, manifestly non-Hermitian Hamiltonians $H=T+V$ the traditional class of the exactly solvable models with local point interactions $V=V(x)$ is generalized. The consequences of the use of the nonlocal point interactions such that $(V f)(x) = int K(x,s) f(s) ds$ are discussed using the suitably adapted formalism of boundary triplets.



rate research

Read More

In this note we consider non-equilibrium steady states of one-dimensional models of heat conduction (wealth exchange) which are coupled to some reservoirs creating currents. In particular we will give sufficient and necessary conditions which will depend only on the first two moments of the reservoir measures and the redistribution parameter under which the two-point functions are multilinear. This presents the first example of multilinear two-point functions in the absence of product stationary measures.
A $p$-adic Schr{o}dinger-type operator $D^{alpha}+V_Y$ is studied. $D^{alpha}$ ($alpha>0$) is the operator of fractional differentiation and $V_Y=sum_{i,j=1}^nb_{ij}<delta_{x_j}, cdot>delta_{x_i}$ $(b_{ij}inmathbb{C})$ is a singular potential containing the Dirac delta functions $delta_{x}$ concentrated on points ${x_1,...,x_n}$ of the field of $p$-adic numbers $mathbb{Q}_p$. It is shown that such a problem is well-posed for $alpha>1/2$ and the singular perturbation $V_Y$ is form-bounded for $alpha>1$. In the latter case, the spectral analysis of $eta$-self-adjoint operator realizations of $D^{alpha}+V_Y$ in $L_2(mathbb{Q}_p)$ is carried out.
76 - Chusei Kiumi , Kei Saito 2020
We study space-inhomogeneous quantum walks (QWs) on the integer lattice which we assign three different coin matrices to the positive part, the negative part, and the origin, respectively. We call them two-phase QWs with one defect. They cover one-defect and two-phase QWs, which have been intensively researched. Localization is one of the most characteristic properties of QWs, and various types of two-phase QWs with one defect exhibit localization. Moreover, the existence of eigenvalues is deeply related to localization. In this paper, we obtain a necessary and sufficient condition for the existence of eigenvalues. Our analytical methods are mainly based on the transfer matrix, a useful tool to generate the generalized eigenfunctions. Furthermore, we explicitly derive eigenvalues for some classes of two-phase QWs with one defect, and illustrate the range of eigenvalues on unit circles with figures. Our results include some results in previous studies, e.g. Endo et al. (2020).
263 - Jean Bertoin 2008
We consider two simple models for the formation of polymers where at the initial time, each monomer has a certain number of potential links (called arms in the text) that are consumed when aggregations occur. Loosely speaking, this imposes restrictions on the number of aggregations. The dynamics of concentrations are governed by modifications of Smoluchowskis coagulation equations. Applying classical techniques based on generating functions, resolution of quasi-linear PDEs, and Lagrange inversion formula, we obtain explicit solutions to these non-linear systems of ODEs. We also discuss the asymptotic behavior of the solutions and point at some connexions with certain known solutions to Smoluchowskis coagulation equations with additive or multiplicative kernels.
We prove that the local eigenvalue statistics at energy $E$ in the localization regime for Schrodinger operators with random point interactions on $mathbb{R}^d$, for $d=1,2,3$, is a Poisson point process with the intensity measure given by the density of states at $E$ times the Lebesgue measure. This is one of the first examples of Poisson eigenvalue statistics for the localization regime of multi-dimensional random Schrodinger operators in the continuum. The special structure of resolvent of Schrodinger operators with point interactions facilitates the proof of the Minami estimate for these models.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا