Related papers: Quantum dynamics and relaxation in comb turbulent …
A quantum particle subjected to a constant force undergoes an accelerated motion following a parabolic path, which differs from the classical motion just because of wave packet spreading (quantum diffusion). However, when a periodic…
Quantum walks obey unitary dynamics: they form closed quantum systems. The system becomes open if the walk suffers from imperfections represented as missing links on the underlying basic graph structure, described by dynamical percolation.…
We numerically investigate momentum diffusion rates for the pulse kicked rotor across the quantum to classical transition as the dynamics are made more macroscopic by increasing the total system action. For initial and late time rates we…
We derive the continuous spacetime limit of the one dimensional lazy discrete time quantum walk, obtaining explicit macroscopic evolution equations for a three state model in the presence of decoherence. While continuum limits of two state…
We introduce a minimal set of physically motivated postulates that the Hamiltonian H of a continuous-time quantum walk should satisfy in order to properly represent the quantum counterpart of the classical random walk on a given graph. We…
Quantum walks are versatile simulators of topological phases and phase transitions as observed in condensed matter physics. Here, we utilize a step dependent coin in quantum walks and investigate what topological phases we can simulate with…
Quantum walks are powerful tools for quantum applications and for designing topological systems. Although they are simulated in a variety of platforms, genuine two-dimensional realizations are still challenging. Here we present an…
We develop a quantum landscape approach to characterize the long-time behavior of wave packet spreading in linear open quantum systems. Instead of treating diffusion, localization, and collapse of the wave packet as separate dynamical…
A vibrational model of transport properties of dense fluids assumes that solid-like oscillations of atoms around their temporary equilibrium positions dominate the dynamical picture. The temporary equilibrium positions of atoms do not form…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
Quantum versions of random walks on the line and the cycle show a quadratic improvement over classical random walks in their spreading rates and mixing times respectively. Non-unitary quantum walks can provide a useful optimisation of these…
Quantum random walk in a two-dimensional lattice with randomly distributed traps is investigated. Distributions of quantum walkers are evaluated dynamically for the cases of Hadamard, Fourier, and Grover coins, and quantum to classical…
We discuss the model of a one-dimensional, discrete-time walk on a line with spatial heterogeneity in the form of a variable set of ultrametric barriers. Inspired by the homogeneous quantum walk on a line, we develop a formalism by which…
We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly…
We investigate the global chirality distribution of the quantum walk on the line when decoherence is introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. The first…
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…
The presence of static off-diagonal disorder promotes coherent exciton transport while diffusive motion can be recovered in the presence of fluctuations in the diagonal and off-diagonal elements of the Hamiltonian. Here we study the…
Based on the Dirac representation of Maxwell equations we present an explicit, discrete space-time, quantum walk-inspired algorithm suitable for simulating the electromagnetic wave propagation and scattering from inhomogeneities within…
Combinatorial quantum gravity is governed by a discrete Einstein-Hilbert action formulated on an ensemble of random graphs. There is strong evidence for a second-order quantum phase transition separating a random phase at strong coupling…
We introduce a new type of discrete quantum walks, called vertex-face walks, based on orientable embeddings. We first establish a spectral correspondence between the transition matrix $U$ and the vertex-face incidence structure. Using the…