Related papers: Feynman Checkers with Absorption
In the present paper we find necessary and sufficient conditions for recurrence of random walks on arbitrary subgroups of the group of rational numbers $\mathbb{Q}$.
This article explores an operational model for transition amplitudes between measurements proposed by Goyal et al. within the quantum reconstruction program. To classify suitable amplitude algebras, we distinguish mathematical axioms,…
A particle entering a scattering and absorbing medium executes a random walk through a sequence of scattering events. The particle ultimately achieves first-passage, leaving the medium or it is absorbed. The Kubelka-Munk model describes a…
The Feynman path integral representation of quantum theory is used in a non--parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the…
We study Feynman checkers, the most elementary model of electron motion introduced by R. Feynman. For the model, we prove that the probability to find an electron vanishes nowhere inside the light cone. We also prove several results on the…
We present a continuous time generalization of a random walk with complete memory of its history [Phys. Rev. E 70, 045101(R) (2004)] and derive exact expressions for the first four moments of the distribution of displacement when the number…
Weak measurements of photon position can be used to obtain direct experimental evidence of the wavefunction of a photon between generation and ultimate detection. Significantly, these measurement results can also be understood as complex…
In this paper, we provide an application to the random distance-$t$ walk in finite planes and derive asymptotic formulas (as $q \to \infty$) for the probability of return to start point after $\ell$ steps based on the "vertical"…
Let $S_n$ be a random walk with i.i.d. increments which have zero mean and finite variance. For every $x\ge0$ we define the stopping time $\tau_x:=\inf\{n\ge1:x+S_n\le0\}$ and consider the probabilities $\mathbb{P}(x+S_n\ge y,\tau_x>n)$. We…
We investigate a combinatorial sum that can be interpreted as the moments of a random variate, measuring the absolute distance to the origin in a symmetric Bernoulli random walk. These sums can be characterized by polynomials related to the…
The Feynman path integral for nonrelativistic quantum electrodynamics is studied mathematically of a standard model in physics, where the electromagnetic potential is assumed to be periodic with respect to a large box and quantized thorough…
We present precise moderate deviation probabilities, in both quenched and annealed settings, for a recurrent diffusion process with a Brownian potential. Our method relies on fine tools in stochastic calculus, including Kotani's lemma and…
Let $S_n$ be a centered random walk with a finite variance, and define the new sequence $A_n:=\sum_{i=1}^n S_i$, which we call an integrated random walk. We are interested in the asymptotics of $$p_N:=P(\min_{1 \le k \le N} A_k \ge 0)$$ as…
We have made the first phonon absorption measurements in the fractional quantum Hall r\'egime. Experiments have been conducted on two samples which have similar electron densities but greatly differing mobilities. The energy gaps as…
The conventional postulate for the probabilistic interpretation of quantum mechanics is asymmetric in preparation and measurement, making retrodiction reliant on inference by use of Bayes' theorem. Here, a more fundamental symmetric…
We derive a quenched invariance principle for random walks in random environments whose transition probabilities are defined in terms of weighted cycles of bounded length. To this end, we adapt the proof for random walks among random…
It is shown how to construct quantum random walks with particles in an arbitrary faithful normal state. A convergence theorem is obtained for such walks, which demonstrates a thermalisation effect: the limit cocycle obeys a quantum…
We study the absorption time and spreading rate of the discrete-time quantum walk propagating on a line in the presence or absence of an absorber. We analytically establish that in the presence of an absorber, the average absorption time of…
Sophisticated quantum measurements are fundamental to obtain a quantum advantage in many informational problems. Here, we consider the task of guessing a direction encoded in a two-qubit pure state. We experimentally demonstrate that…
We propose a natural, parameter-free, discrete-variable formulation of Feynman path integrals. We show that for discrete-variable quantum systems, Feynman path integrals take the form of walks on the graph whose weighted adjacency matrix is…