Open Special Issues
Special Issue 1
Challenges in Quantum Dynamics
Stephen Barnett University of Glasgow, UK
Tamás Kiss Wigner Research Centre for Physics, Hungary
Martin Stefanak Czech Technical University in Prague, Czech Republic
Wolfgang Schleich Universität Ulm, Germany
The dynamics of a closed quantum system is determined by the properties of the Hamiltonian in the continuous time case, or the unitary evolution operator in the iterated discrete time scenario. Despite the simplicity of the description, the solution of quantum dynamics is often challenging. Understanding quantum dynamics allows us to design it for a particular useful application, e.g. quantum walk can be adjusted to perform a spatial search on a graph, or spin couplings can be arranged to realize a perfect state transfer across a chain or a network.
Various iterated quantum evolutions were successfully implemented in linear quantum optics with the help of time-multiplexing, which greatly reduces the number of optical elements and improves the scalability of the set-up. When equipped with quantum states of light, either single photons or squeezed states, and single-photon detectors, a unitary optical network can be utilized to demonstrate quantum supremacy through Boson sampling or its Gaussian variant. Additional challenges arise when the quantum dynamics is enriched with measurements, randomness or environmental interactions.
Measurement and post-selection can turn a quantum evolution to a complex non-linear chaotic map. Random unitary operations allow us to describe and investigate quantum walks on dynamically percolated graphs or evolution of networks of randomly interacting qubits. Transient dynamics of open quantum systems represents a particularly difficult task, however, much more can be said about the asymptotic evolution from the knowledge of attractors. This allows us to describe processes such as thermalization or synchronization on a quantum level.
The special issue is inspired by the works and career of our colleague, Igor Jex, who has made a significant number of telling contributions to this field.
Deadline: 30th June 2022
Special Issue 2
Advanced fractional calculus, differential equations and neural networks: analysis, modelling and numerical computations
Dumitru Baleanu Cankaya University, Ankara, Turkey and Institute of Space Sciences, Magurele-Bucharest, Romania
Yeliz Karaca University of Massachusetts Medical School, Worcester, USA
Luis Vázquez Universidad Complutense de Madrid, Spain
JE Macías-Díaz Tallinn University, Estonia and Universidad Autonoma de Aguascalientes, Mexico
The focus of this special issue is geared towards advanced Fractional Calculus, differential equations as well as Neural Networks for the purposes of analysis, modelling and numerical computations regarding non-linear phenomena virtually in every physical, biological, neuronal or technical processes, amongst others. To this end, we hope to expand research areas in different fields for a better grasp of the processes and attributes of dynamic and non-linear phenomena on image and signal processing, recurrent neural networks, differential/integral equations, nonlinear partial differential equations, to name just a few, along with the various aspects of the theoretical, numerical and applied studies.
Deadline: 1st December 2022