Quantum integrability of the generalized elliptic Ruijsenaars models

The important requirements are stated for the success of quantum computation. These requirements involve coherent preserving Hamiltonians as well as exact integrability of the corresponding Feynman path integrals. Also we explain the role of metric entropy in dynamical evolutionary system and outline some of the open problems in the design of quantum computational systems. Finally, we observe that unless we understand quantum nondemolition measurements, quantum integrability, quantum chaos and the direction of time arrow, the quantum control and computational paradigms will remain elusive and the design of systems based on quantum dynamical evolution may not be feasible.

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On String Integrability: A Journey through the Two-Dimensional Hidden Symmetries in the AdS/CFT Dualities

Advances in High Energy Physics ◽

10.1155/2010/471238 ◽

2010 ◽

Vol 2010 ◽

pp. 1-133 ◽

Cited By ~ 5

Author(s):

Valentina Giangreco Marotta Puletti

Keyword(s):

String Theory ◽

Two Dimensional ◽

Pure Spinor ◽

Hidden Symmetries ◽

Quantum Integrability ◽

Conserved Charges ◽

Phd Thesis

One of the main topics in the modern String Theory are the AdS/CFT dualities. Proving such conjectures is extremely difficult since the gauge and string theory perturbative regimes do not overlap. In this perspective, the discovery of infinitely many conserved charges, that is, the integrability, in the planar AdS/CFT has allowed us to reach immense progresses in understanding and confirming the duality. We review the fundamental concepts and properties of integrability in two-dimensionalσ-models and in the AdS/CFT context. The first part is focused on theAdS5/CFT4duality, especially the classical and quantum integrability of the type IIB superstring onAdS5×S5which is discussed in both pure spinor and Green-Schwarz formulations. The second part is dedicated to theAdS4/CFT3duality with particular attention to the type IIA superstring onAdS4×ℂP3and its integrability. This review is based on the author's PhD thesis discussed at Uppsala University the 21st September 2009.

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QUANTUM INTEGRABILITY OF COUPLED N=1 SUPER SINE/SINH–GORDON THEORIES AND THE LIE SUPERALGEBRA D(2,1;α)

International Journal of Modern Physics A ◽

10.1142/s0217751x99001275 ◽

1999 ◽

Vol 14 (16) ◽

pp. 2551-2580 ◽

Cited By ~ 3

Author(s):

JONATHAN M. EVANS ◽

JENS OLE MADSEN

Keyword(s):

Quantum Theory ◽

Lie Superalgebra ◽

Field Theories ◽

Continuous Family ◽

Quantum Field Theories ◽

Quantum Field ◽

Classical Level ◽

Quantum Integrability ◽

Integrable Quantum ◽

Conserved Currents

We discuss certain integrable quantum field theories in 1+1 dimensions consisting of coupled sine/sinh–Gordon theories with N=1 supersymmetry, positive kinetic energy, and bosonic potentials which are bounded from below. We show that theories of this type can be constructed as Toda models based on the exceptional affine Lie superalgebra D(2,1;α)(1) (or on related algebras which can be obtained as various limits) provided one adopts appropriate reality conditions for the fields. In particular, there is a continuous family of such models in which the couplings and mass ratios all depend on the parameter α. The structure of these models is analyzed in some detail at the classical level, including the construction of conserved currents with spins up to 4. We then show that these currents generalize to the quantum theory, thus demonstrating quantum-integrability of the models.

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POISSON STRUCTURE AND INTEGRABILITY OF THE NEUMANN-MOSER-UHLENBECK MODEL

International Journal of Modern Physics A ◽

10.1142/s0217751x90001884 ◽

1990 ◽

Vol 05 (23) ◽

pp. 4477-4488 ◽

Cited By ~ 20

Author(s):

J. AVAN ◽

M. TALON

Keyword(s):

Poisson Structure ◽

Point Of View ◽

Conserved Quantities ◽

Poisson Brackets ◽

Quantum Level ◽

Quantum Integrability ◽

Commuting Operators ◽

Lax Operator

Neumann’s model, describing the motion of a particle on an N-sphere under harmonic forces, is studied from the point of view of classical and quantum integrability. Classical integrability is derived from a generalized structure, “R-S couple” or “D-matrix” for the Poisson brackets of the Lax operator. The already-known set of conserved quantities for this model turns out to follow straightforwardly from this structure. It gives rise to a set of commuting operators at the quantum level, and the algebra of Lax operators directly follows from the classical one.

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Quantum Integrability of 1D Ionic Hubbard Model

Annalen der Physik ◽

10.1002/andp.201900601 ◽

2020 ◽

Vol 532 (3) ◽

pp. 1900601

Author(s):

Abolfath Hosseinzadeh ◽

Seyed Akbar Jafari

Keyword(s):

Hubbard Model ◽

Quantum Integrability ◽

Ionic Hubbard Model

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Quantum integrability in the lab

Journal of Statistical Mechanics Theory and Experiment ◽

10.1088/1742-5468/2008/11/n11001 ◽

2008 ◽

Vol 2008 (11) ◽

pp. N11001 ◽

Cited By ~ 1

Author(s):

Robert Weston

Keyword(s):

Quantum Integrability

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STOKES PHENOMENA AND QUANTUM INTEGRABILITY IN NON-CRITICAL STRING/M THEORY

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194513009549 ◽

2013 ◽

Vol 21 ◽

pp. 147-148

Author(s):

CHUAN-TSUNG CHAN ◽

HIROTAKA IRIE ◽

CHI-HSIEN YEH

Keyword(s):

String Theory ◽

Matrix Models ◽

Recent Progress ◽

Solvable Model ◽

First Principle ◽

Stokes Phenomenon ◽

Quantum Integrability ◽

Key Concepts ◽

M Theory ◽

Stokes Phenomena

Non-critical string/M theory is a solvable model which has been studied to reveal various non-perturbative aspects of string theory with providing new key concepts to the next developments of string theory. Here we show some recent progress in study of Stokes phenomenon in non-critical string theory of the multi-cut two-matrix models. In particular, we argue that it is Stokes phenomenon which allows us to know concepts of non-perturbative completion with analytic study of string-theory landscape from the first principle.

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