Related papers: Quantum Lattice Wave Guides with Randomness -- Loc…
We prove that localization near band edges of multi-dimensional ergodic random Schr\"odinger operators with periodic background potential in $L^2(\mathbb{R}^d)$ is universal. By this we mean that localization in its strongest dynamical form…
Disorder is a key factor influencing the behavior of condensed states of matter, however the true extent of its impact is generally difficult to determine due to the prominent roles played by quantum interference, entanglement between spin…
In this paper, we investigate the bound states of $2+1$ fermionic trimers on a three-dimensional lattice at strong coupling. Specifically, we analyze the discrete spectrum of the associated three-body discrete Schr\"odinger operator…
Let $H=-\Delta+V$ be a Schr\"odinger operator on $L^2(\mathbb R^2)$ with real-valued potential $V$, and let $H_0=-\Delta$. If $V$ has sufficient pointwise decay, the wave operators $W_{\pm}=s-\lim_{t\to \pm\infty} e^{itH}e^{-itH_0}$ are…
For any positive real number $s$, we study the scattering theory in a unified way for the fractional Schr\"{o}dinger operator $H=H_0+V$, where $H_0=(-\Delta)^\frac s2$ and the real-valued potential $V$ satisfies short range condition. We…
In the spectral theory of positive elliptic operators, an important role is played by certain smoothing kernels, related to the Fourier transform of the trace of a wave operator, which may be heuristically interpreted as smoothed spectral…
We consider a sequence of finite quantum graphs with few loops, so that they converge, in the sense of Benjamini-Schramm, to a random infinite quantum tree. We assume these quantum trees are spectrally delocalized in some interval $I$, in…
We investigate the spectral properties of Schr\"odinger operators in l^2(Z) with limit-periodic potentials. The perspective we take was recently proposed by Avila and is based on regarding such potentials as generated by continuous sampling…
We consider the Schroedinger operator L_{\alpha} on the half-line with a periodic background potential and the Wigner-von Neumann potential of Coulomb type: csin(2\omega x+d)/(x+1). It is known that the continuous spectrum of the operator…
Harper's equation (aka the "almost Mathieu" equation) famously describes the quantum dynamics of an electron on a one dimensional lattice in the presence of an incommensurate potential with magnitude $V$ and wave number $Q$. It has been…
In three-dimensional case, we consider two classical operators: Schrodinger operator and an operator in the divergence form. For slowly-decaying oscillating potentials, we establish spatial asymptotics of the Green's function. The main term…
Gapped periodic quantum systems exhibit an interesting Localization Dichotomy, which emerges when one looks at the localization of the optimally localized Wannier functions associated to the Bloch bands below the gap. As recently proved,…
We prove that the wave operators for $n \times n$ matrix Schr\"odinger equations on the half line, with general selfadjoint boundary condition, are bounded in the spaces $L^p(\mathbb R^+, \mathbb C^n), 1 < p < \infty, $ for slowly decaying…
A new class of lattice Dirac operators $D$ which satisfy the index theorem have been recently proposed on the basis of the algebraic relation $\gamma_{5}(\gamma_{5}D) + (\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$. Here $k$…
We study the energy minima of the fully-connected $m$-components vector spin glass model at zero temperature in an external magnetic field for $m\ge 3$. The model has a zero temperature transition from a paramagnetic phase at high field to…
The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schr{\"o}dinger operator with magnetic field and a random potential which may be…
We present a comprehensive study of the dynamical properties of the quantum Heisenberg antiferromagnet on a triangular lattice within the framework of spin-wave theory. The distinct features of spin-wave excitations in the…
In this paper, we show that one-dimensional discrete multi-frequency quasiperiodic Schr\"odinger operators with smooth potentials demonstrate ballistic motion on the set of energies on which the corresponding Schr\"odinger cocycles are…
The behaviour of solutions to the partial differential equation $(D + \lambda W)f_\lambda = 0$ is discussed, where $D$ is a normal hyperbolic partial differential operator, or pre-normal hyperbolic operator, on $n$-dimensional Minkowski…
We consider the Hamiltonian of a system of three quantum mechanical particles (two identical fermions and boson)on the three-dimensional lattice $\Z^3$ and interacting by means of zero-range attractive potentials. We describe the location…