Related papers: Nonlinear three-state quantum walks
Topological matter exhibits exotic properties yet phases characterized by large topological invariants are difficult to implement, despite rapid experimental progress. A promising route toward higher topological invariants is via engineered…
A discrete time quantum walk is considered in which the step lengths are chosen to be either $1$ or $2$ with the additional feature that the walker is persistent with a probability $p$. This implies that with probability $p$, the walker…
We investigate the ballistic spreading behavior of the one-dimensional discrete time quantum walks whose time evolution is driven by any balanced quantum coin. We obtain closed-form expressions for the long-time variance of position of…
We study the spatio-temporal evolution of wave packets in one-dimensional quasiperiodic lattices which localize linear waves. Nonlinearity (related to two-body interactions) has destructive effect on localization, as recently observed for…
Here we present neutrino oscillation in the frame-work of quantum walks. Starting from a one spatial dimensional discrete-time quantum walk we present a scheme of evolutions that will simulate neutrino oscillation. The set of quantum walk…
It is demonstrated that in contrast to the well-known case with a quantum particle moving freely in a real line, the wave packets corresponding to the coherent states for a free quantum particle on a circle do not spread but develop…
We consider an special dynamics of a quantum walk (QW) on a line. Initially, the walker localized at the origin of the line with arbitrary chirality, evolves to an asymptotic stationary state. In this stationary state a measurement is…
Phase transitions induced by short optical pulses is a new mainstream in studies of cooperative electronic states. Its special realization in systems with neutral-ionic transformations stands out in a way that the optical pumping goes to…
A general theoretical framework for investigating nonlinear dynamics of phase space zonal structures is presented in this work. It is then, more specifically, applied to the limit where the nonlinear evolution time scale is smaller or…
We investigate optical nonlinear interactions in a dynamic environment by studying generation of photons in spontaneous parametric down conversion inside a nonlinear cavity where the optical path length is periodically modulated in time. We…
Using the Calogero model as an example, we show that the transport in interacting non-dissipative electronic systems is essentially non-linear. Non-linear effects are due to the curvature of the electronic spectrum near the Fermi energy. As…
A nonlinear dynamics of the thermal and electromagnetic instability of critical state in type II superconductors has been analysed taking into account effects of dissipation and dispersion. An existance of a nonlinear running waves…
We apply wave packet methods to study an ion-trap system in the strong excitation regime imposing neither the rotating wave nor the Lamb-Dicke approximations. By this approach we show the existence of states with restricted phase space…
A quantum walk in an ordered medium exhibits ballistic propagation. A related process is the driven quantum walk, in which the number of walkers varies along the propagation. In this work, we show that a driven quantum walk of biphoton…
In quantum interaction problems with explicitly time-dependent interaction Hamiltonians, the time ordering plays a crucial role for describing the quantum evolution of the system under consideration. In such complex scenarios, exact…
Quantum walks play an important role for developing quantum algorithms and quantum simulations. Here we present one dimensional three-state quantum walk(lazy quantum walk) and show its equivalence for circuit realization in ternary quantum…
I propose to study the complex physics of topological phases by an all optical implementation of a discrete-time quantum walk. The main novel ingredient is the use of parametric amplifiers in the random network which can in turn be used to…
Treating the ideal coherent state as a reference state, the effects due to departure from coherence of an initial wave packet propagating through a nonlinear medium, were examined, specifically in the context of non-classical effects such…
We analyse a nonlinear QW model which can be experimentally implemented using the components of the electric field on an optical nonlinear Kerr medium, which translates into a rotation in the coin operator, with an angle which depends (in a…
We introduce a family of quantum walks on cycles parametrized by their liveliness, defined by the ability to execute a long-range move. We investigate the behaviour of the probability distribution and time-averaged probability distribution.…