Levy Flight

This report summarizes our research process on the behaviour of quantum random walks within the specific
model of the Creutz ladder. We begin by introducing fundamental concepts related to classical random walks,
quantum random walks and some key differences between them. We then focus on our specific case study,
examining the property of localization. By utilizing combinatorial methods and providing some visualization,
we obtained interesting results regarding the confinement of the particle on the quantum lattice

A diffuse interface or “front” at the top of the suspension is investigated experimentally and numerically. The width of the front is found to grow linearly in time, mainly due to a polydispersity of particle size in the very dilute experiments, and due only to fluctuations in particle density in the simulations. Away from the front, the fluctuations in the particle velocities are found not to decay.

This paper presents the study conducted on the optimization algorithm called KGCS (Knowledge Gradient Cuckoo Search) using benchmark functions. The algorithm is highly effective due to the combination of the specific characteristics of the Cuckoo Search algorithm and the ones of the Knowledge Gradient policy. The paper also presents the benchmark mathematical functions usually used to test optimization algorithms such as Rosenbrock, Griewank or Ackley’s function. The results of the conducted tests are compared to the results obtained using the unenhanced evolutionary algorithms in order to prove efficiency of the KGCS algorithm.

The dimensionality of the internal coin space of discrete-time quantum walks has a strong impact on the complexity and richness of the dynamics of quantum walkers. While two-dimensional coin operators have successfully been used for defining dynamics on complex graphs, higher dimensional coins are necessary to unleash the full potential of discrete-time quantum walks. In this work we present an experimental realisation of a discrete-time quantum walk on a line graph, that instead of a two-dimensional exhibits a four-dimensional coin space. Making use of the extra degree of freedom, we are able to generate quantum walks on cyclic graphs of various sizes and topologies, with mixing and non-mixing coins and different input positions and polarisations. By exploiting the full dimensionality of the coin we additionally demonstrate walk evolutions on figure eight graphs consisting of two cycles connected by a central node of rank four. We implemented the quantum walks via time-multiplexing scheme in a Michelson interferometer loop architecture, employing polarisation and travelling direction of the pulses in the loop as the coin degrees of freedom. The experimental results are supplemented by theoretical analysis of accessible coin operations, plus a scheme to produce arbitrary $4\times 4$ unitary coin operations.

We report our studies of emission from a dye-scatterer system, commonly known as random amplifying medium (RAM). It is found to exhibit non-Gaussian statistics of emission intensity over the ensemble of random realizations. The amplification is dominated by certain improbable events that are "larger than rare", which give the intensity statistics a Lévy-like fat tail. This, to the best of our knowledge, provides the first experimental realization of the Lévy statistics in the optics of a random amplifying medium, and the analysis thereof. Notably, the Lévy exponent is continuously tunable parametrically.

In many real situations, randomness is considered to be uncertainty or even confusion which impedes human beings from making a correct decision. Here we study the combined role of randomness and determinism in particle dynamics for complex network community detection. In the proposed model, particles walk in the network and compete with each other in such a way that each of them tries to possess as many nodes as possible. Moreover, we introduce a rule to adjust the level of randomness of particle walking in the network, and we have found that a portion of randomness can largely improve the community detection rate. Computer simulations show that the model has good community detection performance and at the same time presents low computational complexity.

Context. The Pluto-Charon (PC) pair is usually thought of as a binary in a dual synchronous state, which is the endpoint of its tidal evolution. The discovery of the small circumbinary moons, Styx, Nix, Kerberos, and Hydra, placed close to the mean motion resonances (MMRs) 3/1, 4/1, 5/1, and 6/1 with Charon, respectively, reveals a complex dynamical system architecture. Several formation mechanisms for the PC system have been proposed. Aims. Assuming the hypothesis of an in situ formation of the moons, our goal is to analyse the past and current orbital dynamics of the satellite system. We plan to elucidate on in which scenario the small moons can survive a rapid tidal expansion of the PC binary. Methods. We study the past and current dynamics of the PC system through a large set of numerical integrations of the exact equations of motion, accounting for the gravitational interactions of the PC binary with the small moons and the tidal evolution, modelled by the constant time lag app...