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From Quantum Tori to Quantum Homogeneous Spaces
We construct dual objects for quantum complex projective spaces as quantum homogeneous spaces of quantum unitary groups, in which the deformation...
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Convergence of Spectral Triples on Fuzzy Tori to Spectral Triples on Quantum Tori
Fuzzy tori are finite dimensional C*-algebras endowed with an appropriate notion of noncommutative geometry inherited from an ergodic action of a...
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Quantum traces and embeddings of stated skein algebras into quantum tori
The stated skein algebra of a punctured bordered surface (or equivalently, a marked surface) is a generalization of the well-known Kauffman bracket...
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Logarithmic Sobolev Inequalities of Fractional Order on Noncommutative Tori
In this paper, we prove a version of the logarithmic Sobolev inequality of fractional order on noncommutative n-tori for any dimension...
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Maximal Tori in Infinite-Dimensional Hamiltonian Systems: a Renormalisation Group Approach
We study the existence of infinite-dimensional invariant tori in a mechanical system of infinitely many rotators weakly interacting with each...
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Hayward Quasilocal Energy of Tori
In this paper, the authors show that one cannot dream of the positivity of the Hayward energy in the general situation. They consider a scenario of a...
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Almost Global Existence for Some Hamiltonian PDEs with Small Cauchy Data on General Tori
In this paper we prove a result of almost global existence for some abstract nonlinear PDEs on flat tori and apply it to some concrete equations,...
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The soaring kite: a tale of two punctured tori
We consider the 5-mass kite family of self-energy Feynman integrals and present a systematic approach for constructing an ε -form basis, along with...
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Parrondo’s game of quantum search based on quantum walk
The Parrondo game is a game where a combination of losing strategies becomes a winning strategy. This phenomenon is called the Parrondo paradox. The...
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KAM Tori for the System of Coupled Quantum Harmonic Oscillators with Reversible Perturbations
In the present paper, we establish an infinite dimensional Kolmogorov–Arnold–Moser (KAM) theorem for reversible systems with double normal...
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On quantum Poisson-Lie T-duality of WZNW models
We study Poisson-Lie T-duality of the Wess-Zumino-Novikov-Witten (WZNW) models which are obtained from a class of Drinfel’d doubles and its...
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Quantum Chaos
In classical mechanics, chaos originates from nonlinearity and is extremely sensitive to initial conditions. For different but exceedingly close...
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Quantum Groups
In this chapter we introduce the compact quantum groups. Let us start with the finite case, which is elementary, and easy to explain. The idea will...
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Topological Quantum Field Theories and Operator Algebras
We have seen much fruitful interactions between 3-dimensional topology and operator algebras since the stunning discovery of the Jones polynomial for...
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Metaplectic flavor symmetries from magnetized tori
We revisit the flavor symmetries arising from compactifications on tori with magnetic background fluxes. Using Euler’s Theorem, we derive closed form...
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A Brief Introduction to Quantum Chaos of Generic Systems
This article is an updated revised version of a recent review paper on quantum chaos in mixed-type systems, between regularity and chaos (Robnik...
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Quantum Spaces
In order to introduce the quantum groups,we need some sort of algebraic geometry correspondence, between “quantum spaces” and noncommutative...
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Quantum Cinema and Quantum Computing
The author discusses philosophical, ontological and phenomenological questions of quantum phenomena and their possible visualization by means of...
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Aspects of GRMHD in high-energy astrophysics: geometrically thick disks and tori agglomerates around spinning black holes
This work focuses on some key aspects of the general relativistic (GR)—magneto-hydrodynamic (MHD) applications in high-energy astrophysics. We...
