Background: A path-integral algorithm, PATHINT used previously for several systems, has been generalized from 1 dimension to N dimensions, and from classical to quantum systems into qPATHINT. Previous publications applied qPATHINT to two systems developed by the author, in neocortical interactions and financial options. Also, previous publications using classical PATHINT have developed a Statistical Mechanics of Neocortical Interactions (SMNI) that has been fitted to EEG data under attentional experimental paradigms. Classical PATHINT also has been published demonstrating development of Eurodollar options in industrial applications.Background: A path-integral algorithm, PATHINT used previously for several systems, has been generalized from 1 dimension to N dimensions, and from classical to quantum systems into qPATHINT. Previous publications applied qPATHINT to two systems developed by the author, in neocortical interactions and financial options. Also, previous publications using classical PATHINT have developed a Statistical Mechanics of Neocortical Interactions (SMNI) that has been fitted to EEG data under attentional experimental paradigms. Classical PATHINT also has been published demonstrating development of Eurodollar options in industrial applications.

The Open Cybernetics & Systemics JournalDec 29, 201728 citations

Chiral Potts model and the discrete Sine-Gordon model at roots of unity

Vladimir V. Bazhanov

The discrete quantum Sine-Gordon model at roots of unity remarkably combines a classical integrable system with an integrable quantum spin system, whose parameters obey classical equations of motion. We show that the fundamental $R$ -matrix of the model (which satisfies a difference property Yang–Baxter equation) naturally splits into a product of a singular "classical" part and a finite dimensional quantum part. The classical part of the $R$ -matrix itself satisfies the quantum Yang–Baxter equation, and therefore can be factored out producing, however, a certain "twist" of the quantum part. We show that the resulting equation exactly coincides with the star-triangle relation of the $N$ -state chiral Potts model. The associated spin model on the whole lattice is, in fact, more general than the chiral Potts and reduces to the latter only for the simplest (constant) classical background. In a general case the model is inhomogeneous: its Boltzmann weights are determined by non-trivial background solutions of the equations of motion of the classical discrete sine-Gordon model. The discrete quantum Sine-Gordon model at roots of unity remarkably combines a classical integrable system with an integrable quantum spin system, whose parameters obey classical equations of motion. We show that the fundamental $R$-matrix of the model (which satisfies a difference property Yang–Baxter equation) naturally splits into a product of a singular "classical" part and a finite dimensional quantum part. The classical part of the $R$-matrix itself satisfies the quantum Yang–Baxter equation, and therefore can be factored out producing, however, a certain "twist" of the quantum part. We show that the resulting equation exactly coincides with the star-triangle relation of the $N$-state chiral Potts model. The associated spin model on the whole lattice is, in fact, more general than the chiral Potts and reduces to the latter only for the simplest (constant) classical background. In a general case the model is inhomogeneous: its Boltzmann weights are determined by non-trivial background solutions of the equations of motion of the classical discrete sine-Gordon model.

arXiv:0809.2351Advanced studies in pure mathematicsMar 7, 20199 citations

Non-equilibrium Aspects of Quantum Integrable Systems

Natan Andrei

APSJan 1, 20160 citations

Perspectives and limitations of QKD integration in metropolitan area networks

Slaviša Aleksić, Florian Hipp, Dominic Winkler +3 more

Quantum key distribution (QKD) systems have already reached a reasonable level of maturity. However, a smooth integration and a wide adoption of commercial QKD systems in metropolitan area networks has still remained challenging because of technical and economical obstacles. Mainly the need for dedicated fibers and the strong dependence of the secret key rate on both loss budget and background noise in the quantum channel hinder a practical, flexible and robust implementation of QKD in current and next-generation optical metro networks. In this paper, we discuss these obstacles and present approaches to share existing fiber infrastructures among quantum and classical channels. Particularly, a proposal for a smooth integration of QKD in optical metro networks, which implies removing spurious background photons caused by optical transmitters, amplifiers and nonlinear effects in fibers, is presented and discussed. We determine and characterize impairments on quantum channels caused by many classical telecom channels at practically used power levels coexisting within the same fiber. Extensive experimental results are presented and indicate that a practical integration of QKD in conventional optical metro networks is possible.Quantum key distribution (QKD) systems have already reached a reasonable level of maturity. However, a smooth integration and a wide adoption of commercial QKD systems in metropolitan area networks has still remained challenging because of technical and economical obstacles. Mainly the need for dedicated fibers and the strong dependence of the secret key rate on both loss budget and background noise in the quantum channel hinder a practical, flexible and robust implementation of QKD in current and next-generation optical metro networks. In this paper, we discuss these obstacles and present approaches to share existing fiber infrastructures among quantum and classical channels. Particularly, a proposal for a smooth integration of QKD in optical metro networks, which implies removing spurious background photons caused by optical transmitters, amplifiers and nonlinear effects in fibers, is presented and discussed. We determine and characterize impairments on quantum channels caused by many classical telecom channels at practically used power levels coexisting within the same fiber. Extensive experimental results are presented and indicate that a practical integration of QKD in conventional optical metro networks is possible.

Optics ExpressApr 14, 201563 citations

“Quantum Groups and Quantum Integrable Systems”

Ukrainian Journal of PhysicsNov 1, 201324 citations

R

-matrix of the model (which satisfies a difference property Yang–Baxter equation) naturally splits into a product of a singular "classical" part and a finite dimensional quantum part. The classical part of the

R

-matrix itself satisfies the quantum Yang–Baxter equation, and therefore can be factored out producing, however, a certain "twist" of the quantum part. We show that the resulting equation exactly coincides with the star-triangle relation of the

N

-state chiral Potts model. The associated spin model on the whole lattice is, in fact, more general than the chiral Potts and reduces to the latter only for the simplest (constant) classical background. In a general case the model is inhomogeneous: its Boltzmann weights are determined by non-trivial background solutions of the equations of motion of the classical discrete sine-Gordon model.