Related papers: Steering random walks with kicked ultracold atoms
The periodically $\delta$-kicked quantum linear rotor is known to experience non-classical bounded energy growth due to quantum dynamical localization in angular momentum space. We study the effect of random deviations of the kick period in…
In this paper we develop a random walk model on lattice for coordinate dependent diffusion at constant temperature in contact with a heat bath. We employ here a coordinate dependent waiting time of the random walker to make the diffusivity…
In this paper we create a model of particle motion on a three-dimensional lattice using discrete random walk with small steps. We rigorously construct a probability space of the particle trajectories. Unlike deterministic approach in…
We experimentally investigate a scheme for studying lattice transport phenomena, based on the controlled momentum-space dynamics of ultracold atomic matter waves. In the effective tight-binding models that can be simulated, we demonstrate…
The random walk of photons in a tight-binding lattice is known to exhibit diffusive motion similar to classical random walks under decoherence, clearly illustrating the quantum-to-classical transition. In this study, we reveal that the…
In this Chapter, we present some interesting properties of quantum walks on the line. We concentrate our attention in the emergence of invariance and provide some insights into the ultimate origin of the observed behavior. In the first part…
Quantum kicked rotor was recently realized in experiments with cold atomic gases and standing optical waves. As predicted, it exhibits dynamical localization in the momentum space. Here we consider the weak localization regime concentrating…
Quantum random walk finds application in efficient quantum algorithms as well as in quantum network theory. Here we study the mixing time of a discrete quantum walk over a square lattice in presence percolation and decoherence. We consider…
We investigate continuous-time quantum walks of two indistinguishable particles (bosons, fermions or hard-core bosons) in one-dimensional lattices with nearest-neighbour interactions. The two interacting particles can undergo independent-…
We report the experimental observation of rectified momentum transport for a Bose-Einstein Condensate kicked at the Talbot time (quantum resonance) by an optical standing wave. Atoms are initially prepared in a superposition of the 0 and…
We study the resonances of the quantum kicked rotor subjected to an excitation that follows a deterministic time-dependent prescription. For the primary resonances we find an analytical relation between the long-time behavior of the…
Controlling the translational motion of cold atoms using optical lattice potentials is of both theoretical and experimental interest. By designing two on-resonance time sequences of kicking optical lattice potentials, a novel connection…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…
We investigate a connection between a property of the distribution and a conserved quantity for the reversible cellular automaton derived from a discrete-time quantum walk in one dimension. As a corollary, we give a detailed information of…
Random walks of particles on a lattice are a classical paradigm for the microscopic mechanism underlying diffusive processes. In deterministic walks, the role of space and time can be reversed, and the microscopic dynamics can produce quite…
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…
Properties of random and fluctuating systems are often studied through the use of Gaussian distributions. However, in a number of situations, rare events have drastic consequences, which can not be explained by Gaussian statistics.…
Quantum walks are known to propagate quadratically faster than their classical counterparts and are used to model dynamics in various quantum systems. The spread of the quantum walk in position space shows anomalous diffusion behavior. By…
We elaborate on a model of quantum random walk proposed by Hillery et. al., and Jeong et. al., which uses the multiports for quantum "coin tossing". The dynamics of this model is analyzed for the case when the multiports are arranged on the…
Quantization and asymptotic behaviour of a variant of discrete random walk on integers are investigated. This variant, the $\epsilon_{V^{k}}$ walk, has the novel feature that it uses many identical quantum coins keeping at the same time…