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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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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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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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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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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...
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Holography on the quantum disk
Motivated by recent study of DSSYK and the non-commutative nature of its bulk dual, we review and analyze an example of a non-commutative spacetime...
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On the construction of new toric quantum codes and quantum burst-error-correcting codes
A toric quantum error-correcting code construction procedure is presented in this work. A new class of an infinite family of toric quantum codes is...
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Low-dimensional quantum gases in curved geometries
Atomic gases confined in curved geometries are characterized by distinctive features that are absent in their flat counterparts, such as periodic...
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Aspects of Quantum Chaos
This chapter discusses two important ways of defining quantum chaoticity. One access to characterize dynamical quantum systems is offered by the...
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Quantum error correction beyond the toric code: dynamical systems meet encoding
We construct surface codes corresponding to genus greater than one in the context of quantum error correction. The architecture is inspired by the...
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New three- and four-dimensional toric and burst error-correcting quantum codes
Ongoing research and experiments have enabled quantum memory to realize the storage of qubits. On the other hand, interleaving techniques are used to...
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Topological Quantum Gates in Homotopy Type Theory
Despite the plausible necessity of topological protection for realizing scalable quantum computers, the conceptual underpinnings of topological...
