Related papers: Feynman Checkers with Absorption
The kinetics of annihilating random walks in one dimension, with the half-line x>0 initially filled, is investigated. The survival probability of the nth particle from the interface exhibits power-law decay, S_n(t)~t^{-alpha_n}, with…
The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…
Quantum walks with long-range steps $R^{-\gamma}$ ($R$ being the distance between sites) on a discrete line behave in similar ways for all $\gamma\geq2$. This is in contrast to classical random walks, which for $\gamma >3$ belong to a…
This is the second in a series of articles devoted to showing that a typical covering map of large degree to a fixed, regular graph has its new adjacency eigenvalues within the bound conjectured by Alon for random regular graphs. The first…
Spatially homogeneous random walks in $(\mathbb{Z}_{+})^{2}$ with non-zero jump probabilities at distance at most 1, with non-zero drift in the interior of the quadrant and absorbed when reaching the axes are studied. Absorption…
We give a new expression for the expected number of inversions in the product of n random adjacent transpositions in the symmetric group S_{m+1}. We then derive from this expression the asymptotic behaviour of this number when n scales with…
The Feynman path integral formalism has inspired the development of memory-efficient and parallelizable classical algorithms for simulating quantum computers. We adapt this approach for the calculation of probability amplitudes of…
We investigate state estimation in discrete-time quantum walks with a single absorbing boundary. Using a spectral approach, we obtain closed expressions for the escape probability as a function of the initial coin state and the boundary…
In this paper we investigate one dimensional quantum walks with two-step memory, which can be viewed as an extension of quantum walks with one-step memory. We develop a general formula for the amplitudes of the two-step-memory walk with…
In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step towards this objective, the following question is being…
We introduce the $q,t$-Catalan measures, a sequence of piece-wise polynomial measures on $\mathbb{R}^2$. These measures are defined in terms of suitable area, dinv, and bounce statistics on continuous families of paths in the plane, and…
This article provides a new theory for the analysis of forward and backward particle approximations of Feynman-Kac models. Such formulae are found in a wide variety of applications and their numerical (particle) approximation are required…
We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail…
Richard Feynman's method of path integrals is based on the fundamental assumption that a system starting at a point A and arriving at a point B takes all possible paths from A to B, with each path contributing its own (complex) probability…
Optical transitions in a semiconductor quantum dot are theoretically investigated, with emphasis on the coupling to longitudinal optical phonons, and including excitonic effects. When limiting to a finite number of $m$ electron and $n$ hole…
A discrete time quantum walk is considered in which the step lengths are chosen to be either $1$ or $2$ with the additional feature that the walker is persistent with a probability $p$. This implies that with probability $p$, the walker…
We present a new method which uses Feynman-like diagrams to calculate the statistical quantities of embedded many-body random matrix problems. The method provides a promising alternative to existing techniques and offers many important…
We investigate the quantum versions of a one-dimensional random walk, whose corresponding Markov Chain is of order 2. This corresponds to the walk having a memory of up to two previous steps. We derive the amplitudes and probabilities for…
Hardy's paradox is analysed within Feynman's formulation of quantum mechanics. A transition amplitude is represented as a sum over virtual paths which different intermediate measurements convert into different sets of real pathways.…
We present the first robust implementation of a coined quantum walk over five steps using only passive optical elements. By employing a fiber network loop we keep the amount of required resources constant as the walker's position Hilbert…