Fractal Noise in Quantum Ballistic and Diffusive Lattice Systems

We demonstrate fractal noise in the quantum evolution of wave packets moving either ballistically or diffusively in periodic and quasiperiodic tight-binding lattices, respectively. For the ballistic case with various initial superpositions we obtain a space-time self-affine fractal $\Psi(x,t)$ which verify the predictions by Berry for "a particle in a box", in addition to quantum revivals. For the diffusive case self-similar fractal evolution is also obtained. These universal fractal features of quantum theory might be useful in the field of quantum information, for creating efficient quantum algorithms, and can possibly be detectable in scattering from nanostructures.Comment: 9 pages, 8 postscript figure

Exactly solvable model of quantum diffusion

We study the transport property of diffusion in a finite translationally invariant quantum subsystem described by a tight-binding Hamiltonian with a single energy band and interacting with its environment by a coupling in terms of correlation functions which are delta-correlated in space and time. For weak coupling, the time evolution of the subsystem density matrix is ruled by a quantum master equation of Lindblad type. Thanks to the invariance under spatial translations, we can apply the Bloch theorem to the subsystem density matrix and exactly diagonalize the time evolution superoperator to obtain the complete spectrum of its eigenvalues, which fully describe the relaxation to equilibrium. Above a critical coupling which is inversely proportional to the size of the subsystem, the spectrum at given wavenumber contains an isolated eigenvalue describing diffusion. The other eigenvalues rule the decay of the populations and quantum coherences with decay rates which are proportional to the intensity of the environmental noise. On the other hand, an analytical expression is obtained for the dispersion relation of diffusion. The diffusion coefficient is proportional to the square of the width of the energy band and inversely proportional to the intensity of the environmental noise because diffusion results from the perturbation of quantum tunneling by the environmental fluctuations in this model. Diffusion disappears below the critical coupling.Comment: Submitted to J. Stat. Phy

Strategies discovery in the active allothetic place avoidance task

The Active Allothetic Place Avoidance task is an alternative setup to Morris Water Maze that allows studying spatial memory in a dynamic world in the presence of conflicting information. In this task, a rat, freely moving on a rotating circular arena, has to avoid a sector defined within the room frame where shocks are presented. While for Morris Water Maze several studies have identified animal strategies which specifically affect performance, there were no such studies for the Active Allothetic Place Avoidance task. Using standard machine learning methods, we were able to reveal for the first time, to the best of our knowledge, explainable strategies that the animals employ in this task and demonstrate that they can provide a high-level interpretation for performance differences between an animal group treated with silver nanoparticles (AgNPs) and the control group