The KdV and modified KdV integrable hierarchies are shown to be different descriptions of the same 2D gravitational system – open-closed string theory. Nonperturbative solutions of the multi-critical unitary matrix models map to nonsingular solutions of the ‘renormalisation group’ equation for the string susceptibility, [P̃ , Q] =Q . We also demonstrate that the large N solutions of unitary matr...

Power line channel is the time-frequency variant channel with impulsive noise. Therefore, power line communication makes performance degradation due to time-frequency variant and impulsive noise. To overcome performance degradation, we consider the unitary signal constellation scheme and investigate the performance improvement of unitary matrix frequency modulated orthogonal frequencydivision m...

We find the conditions under which the spectrum of the unitary time evolution operator for a periodically rank-N kicked system remains pure point. This stability result allows one to analyse the onset of, or lack of chaos in this class of quantum mechanical systems, extending the results for rank-1 systems produced by Combescure and others. This work includes a number of unitary theorems equiva...

We find the conditions under which the spectrum of the unitary timeevolution operator for a periodically rank-N kicked system remains pure point. This stability result allows one to analyse the onset of, or lack of chaos in this class of quantum mechanical systems, extending the results for rank-1 systems produced by Combescure and others. This work includes a number of unitary theorems equival...

Among the discrete evolution equations describing a quantum system HS undergoing repeated quantum interactions with a chain of exterior systems, we study and characterize those which are directed by classical random variables in RN . The characterization we obtain is entirely algebraical in terms of the unitary operator driving the elementary interaction. We show that the solutions of these equ...

In recent years, a lively debate in neuroeconomics has focused on what appears to be a fundamental question: Is the brain a unitary or a dual system? We are still far from a consensus view. The accumulating evidence supports both sides of the debate. A reason for the difficulty in reaching a convincing solution is that we do not yet have a clear theoretical model for either position. Here I rev...

To implement any quantum operation (a.k.a. “superoperator” or “CP map”) on a d-dimensional quantum system, it is enough to apply a suitable overall unitary transformation to the system and a d-dimensional environment which is initialized in a fixed pure state. It has been suggested that a d-dimensional environment might be enough if we could initialize the environment in a mixed state of our ch...

We show that any unitary transformation performed on the quantum state of a closed quantum system describes an inner, reversible, generalized quantum measurement. We also show that under some specific conditions it is possible to perform a unitary transformation on the state of the closed quantum system by means of a collection of generalized measurement operators. In particular, given a comple...

Abstract A 9×9 unitary R̆−matrix, solution of the Yang-Baxter Equation, is obtained in this paper. The entanglement properties of R̆−matrix is investigated, and the arbitrary degree of entanglement for two-qutrit entangled states can be generated via R̆-matrix acting on the standard basis. A Yang-Baxter Hamiltonian can be constructed from unitary R̆−matrix. Then the geometric properties of this sys...