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The probability distributions of discrete-time quantum walks have been often investigated, and many interesting properties of them have been discovered. The probability that the walker can be find at a position is defined by diagonal…

When random walks on a square lattice are biased horizontally to move solely to the right, the probability distribution of their algebraic area can be exactly obtained. We explicitly map this biased classical random system on a non…

The quantum walk is the quantum analogue of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to…

We investigate the two-component quantum walk in one-dimensional lattice. We show that the inter-component interaction strength together with the hopping imbalance between the components exhibit distinct features in the quantum walk for…

We study Markov chains on a lattice in a codimension-one stratified independent random environment, exploiting results established in [2]. First of all the random walk is transient in dimension at least three. Focusing on dimension two,…

Quantum walks exhibit many unique characteristics compared to classical random walks. In the classical setting, self-avoiding random walks have been studied as a variation on the usual classical random walk. Classical self-avoiding random…

In this work, we study the effect of a moving detector on a discrete time one dimensional Quantum Random Walk where the movement is realized in the form of hopping/shifts. The occupation probability $f(x,t;n,s)$ is estimated as the number…

In this paper, we study the properties of lackadaisical quantum walks on a line. This model is first proposed in~\cite{wong2015grover} as a quantum analogue of lazy random walks where each vertex is attached $\tau$ self-loops. We derive an…

We consider a discrete time simple symmetric random walk on Z^d, d>=1, where the path of the walk is perturbed by inserting deterministic jumps. We show that for any time n and any deterministic jumps that we insert, the expected number of…

Coined quantum walks may be interpreted as the motion in position space of a quantum particle with a spin degree of freedom; the dynamics are determined by iterating a unitary transformation which is the product of a spin transformation and…

In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the nowadays widespread discrete-time quantum walk on a line. Here the walker at each time step can either remain in…

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…

Due to the unitary evolution, quantum walks display different dynamical features from that of classical random walks. In contrast to this expectation, in this work, we show that extreme events can arise in unitary dynamics and its…

Quantum walk research has mainly focused on evolutions due to repeated applications of time-independent unitary coin operators. However, the idea of controlling the single particle evolution using time-dependent unitary coins has still been…

We give a lower bound for the non-collision probability up to a long time T in a system of n independent random walks with fixed obstacles on the two-dimensional lattice. By `collision' we mean collision between the random walks as well as…

Temporal fluctuations in the Hadamard walk on circles are studied. A temporal standard deviation of probability that a quantum random walker is positive at a given site is introduced to manifest striking differences between quantum and…

Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with…

The first general analytic solutions for the one-dimensional walk in position and momentum space are derived. These solutions reveal, among other things, new symmetry features of quantum walk probability densities and further insight into…

We propose a novel implementation of discrete time quantum walks for a neutral atom in an array of optical microtraps or an optical lattice. We analyze a one-dimensional walk in position space, with the coin, the additional qubit degree of…

Random walks are powerful tools to analyze spatial-temporal patterns produced by living organisms ranging from cells to humans. At the same time, it is evident that these patterns are not completely random but are results of a convolution…