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In this paper we present a model exhibiting a new type of continuous-time quantum walk (as a quantum mechanical transport process) on networks, which is described by a non-Hermitian Hamiltonian possessing a real spectrum. We call it pseudo-Hermitian continuous-time quantum walk. We introduce a method to obtain the probability distribution of walk on any vertex and then study a specific system. We observe that the probability distribution on certain vertices increases compared to that of the Hermitian case. This formalism makes the transport process faster and can be useful for search algorithms.
In this note, we consider a physical system given by a two-dimensional quantum walk in an external magnetic field. In this setup, we show that both the topological structure as well as its type depend sensitively on the value of the magnetic flux $Ph
We have briefly analyzed the existence of the pseudofermionic structure of multilevel pseudo-Hermitian systems with odd time-reversal and higher order involutive symmetries. We have shown that 2N-level Hamiltonians with N-order eigenvalue degeneracy
We investigate the effects of markovian resseting events on continuous time random walks where the waiting times and the jump lengths are random variables distributed according to power law probability density functions. We prove the existence of a n
Given its importance to many other areas of physics, from condensed matter physics to thermodynamics, time-reversal symmetry has had relatively little influence on quantum information science. Here we develop a network-based picture of time-reversal
We analyse here the pseudo-Hermitian Dynamical Casimir effect, proposing a non-Hermitian version of the effective Laws Hamiltonian used to describe the phenomenon. We verify that the average number of created photons can be substantially increased, a