Related papers: Exponential decay property for eigenfunctions of q…

We define and analyze random quantum walks on homogeneous trees of degree $q\geq 3$. Such walks describe the discrete time evolution of a quantum particle with internal degree of freedom in $\C^q$ hopping on the neighboring sites of the…

We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which…

The purpose of this paper is to give a direct proof of an eigenfunction expansion formula for one-dimensional 2-state quantum walks, which is an analog of that for Sturm-Liouville operators due to Weyl, Stone, Titchmarsh and Kodaira. In the…

We investigate a connection between a property of the distribution and a conserved quantity for the reversible cellular automaton derived from a discrete-time quantum walk in one dimension. As a corollary, we give a detailed information of…

We consider the spectrum of a Schroedinger operator in a multi-dimensional cylinder perturbed by a shrinking potential. We study the phenomenon of a new eigenvalue emerging from the threshold of the essential spectrum and give the…

We prove that the characteristic function of the quicksort distribution is exponentially decreasing at infinity. As a consequence it follows that the density of the quicksort distribution can be analytically extended to the vicinity of the…

We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudo-Friedrichs extension. We also give several generalisations of the aforementioned extension. The spectral bounds for…

We present a study of the effects of decoherence in the operation of a discrete quantum walk on a line, cycle and hypercube. We find high sensitivity to decoherence, increasing with the number of steps in the walk, as the particle is…

We construct a complete set of eigenfunctions of the q-deformed harmonic oscillator on the quantum line. In particular the eigenfunctions corresponding to the non-Fock part of the spectrum will be constructed.

A formal fourth order differential operator with a singular coefficient that is a linear combination of the Dirac delta-function and its derivatives is considered. The asymptotic behavior of spectra and eigenfunctions of a family of…

Results of theoretical studies of the quantum unstable systems caused that there are rather widespread belief that a universal feature od the quantum decay process is the presence of three time regimes of the decay process: the early time…

We consider eigenvalues of the Pauli operator in $\mathbb R^3$ embedded in the continuous spectrum. In our main result we prove the absence of such eigenvalues above a threshold which depends on the asymptotic behavior of the magnetic and…

We establish exact scalings for the maximal group velocity of translation-invariant quantum walks in periodic electric fields. Our main result shows that the maximal group velocity decays exponentially with the period of the field in the…

This paper is a continuation of the paper \cite{W} by the third author, which studied quantum walks with special long-range perturbations of the coin operator. In this paper, we consider general long-range perturbations of the coin operator…

We apply a discrete quantum walk from a quantum particle on a discrete quantum spacetime from loop quantum gravity and show that the related Entanglement Entropy can drive a entropic force. We apply this concepts to propose a model of a…

We analyze the distribution of eigenvectors for mesoscopic, mean-field perturbations of diagonal matrices in the bulk of the spectrum. Our results apply to a generalized $N\times N$ Rosenzweig-Porter model. We prove that the eigenvectors…

We study a class of discrete-time quantum walks with inhomogeneous coins defined in [Y. Shikano and H. Katsura, Phys. Rev. E {\bf 82}, 031122 (2010)]. We establish symmetry properties of the spectrum of the evolution operator, which…

We investigate properties of differential and difference operators annihilating certain finite-dimensional subspaces of exponential functions in two variables that are connected to the representation of real-valued trigonometric and…

We study the relation between the spectral gap above the ground state and the decay of the correlations in the ground state in quantum spin and fermion systems with short-range interactions on a wide class of lattices. We prove that, if two…

We consider a twisted quantum wave guide, and are interested in the spectral analysis of the associated Dirichlet Laplacian H. We show that if the derivative of rotation angle decays slowly enough at infinity, then there is an infinite…