Related papers: Feynman Checkers with Absorption
A quantum walk places a traverser into a superposition of both graph location and traversal "spin." The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the…
We exhibit a way to associate a quantum walk (QW) on the non-negative integers to any probability measure on the unit circle. This forces us to consider one step transitions that are not traditionally allowed. We illustrate this in the case…
Even after decades of research the problem of first passage time statistics for quantum dynamics remains a challenging topic of fundamental and practical importance. Using a projective measurement approach, with a sampling time $\tau$, we…
We prove a probabilistic Fourier extension theorem that says Fourier extension holds when averaged over certain smooth Alpert multipliers. The proofs use smooth Alpert wavelets with the classical techniques of stationary phase and…
In learning quantum mechanics, an essential question has always been: How does one go about developing a "physical feel" for quantum phenomena? Naturally, one needs a basis or ground zero to start from, and that basis must be unlike…
We study search by quantum walk on a finite two dimensional grid. The algorithm of Ambainis, Kempe, Rivosh (quant-ph/0402107) takes O(\sqrt{N log N}) steps and finds a marked location with probability O(1/log N) for grid of size \sqrt{N} *…
Propagation and interference of quantum-mechanical particles comprise an important part of elementary processes in quantum physics, and their essence can be modeled using a quantum walk, a mathematical concept that describes the motion of a…
The Feynman path integral in p-adic quantum mechanics is considered. The probability amplitude ${\cal K}_p (x^{\prime\prime},t^{\prime\prime}; x^\prime,t^\prime)$ for one-dimensional systems with quadratic actions is calculated in an exact…
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…
We study the convergence rate of translation-invariant discrete-time quantum dynamics on a one-dimensional lattice. We prove that the cumulative distributions function of the ballistically scaled position $X(n)/{n}$ after $n$ steps…
Topological data analysis is a rapidly developing area of data science where one tries to discover topological patterns in data sets to generate insight and knowledge discovery. In this project we use quantum walk algorithms to discover…
Branching random walks are key to the description of several physical and biological systems, such as neutron multiplication, genetics and population dynamics. For a broad class of such processes, in this Letter we derive the discrete…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
Feynman's path integrals in ordinary, p-adic and adelic quantum mechanics are considered. The corresponding probability amplitudes $ K(x^{"},t^{"};x',t')$ for two-dimensional systems with quadratic Lagrangians are evaluated analytically 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…
An analysis is presented of a Brownian particle moving on the half-line, subject to a restoring force proportional to its displacement and an absorbing boundary at the origin. When the initial displacement is large, the central moments of…
We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle making the walk simply advances one unit at each time step, so that…
We investigate, by numerical simulation, the path probability of non dissipative mechanical systems undergoing stochastic motion. The aim is to search for the relationship between this probability and the usual mechanical action. The model…
We consider a discrete random walk on a diagonal lattice in two and three dimensions and obtain explicit solutions of absorption probabilities and probabilities of return in several domains. In three dimensions we consider both the cube and…
We study the one-dimensional motion of a Brownian particle inside a confinement described by two reactive boundaries which can partially reflect or absorb the particle. Understanding the effects of such boundaries is important in physics,…