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We analyze a completely integrable two-dimensional quantum-mechanical model that emerged in the recent studies of the compound gluonic states in multi-color QCD at high energy. The model represents a generalization of the well-known…

High Energy Physics - Theory · Physics 2014-11-18 S. E. Derkachov , G. P. Korchemsky , A. N. Manashov

We describe a method for obtaining the scattering matrix for nuclear or chemical reactions on a finite lattice. Aside from the preparation of the initial and final states as wave packets, the only other operation required is unitary time…

Nuclear Theory · Physics 2026-03-31 Evan Rule , Ionel Stetcu

We propose that Baxter's Z-invariant six-vertex model at the rational gl(2) point on a planar but in general not rectangular lattice provides a way to study Yangian invariants. These are identified with eigenfunctions of certain monodromies…

Mathematical Physics · Physics 2014-04-15 Rouven Frassek , Nils Kanning , Yumi Ko , Matthias Staudacher

We revisit the so-called folded XXZ model, which was treated earlier by two independent research groups. We argue that this spin-1/2 chain is one of the simplest quantum integrable models, yet it has quite remarkable physical properties.…

Statistical Mechanics · Physics 2021-10-13 Balázs Pozsgay , Tamás Gombor , Arthur Hutsalyuk , Yunfeng Jiang , Levente Pristyák , Eric Vernier

For selected classes of quantum mechanical Hamiltonians a canonical association of a decay semigroup is presented. The spectrum of the generator of this semigroup is a pure eigenvalue spectrum and it coincides with the set of all…

Mathematical Physics · Physics 2010-04-28 Hellmut Baumgärtel

The subject of this thesis is the rigorous construction of QFT models with nontrivial interaction. Two different approaches in the framework of AQFT are discussed. On the one hand, an inverse scattering problem is considered. A given…

Mathematical Physics · Physics 2015-03-04 Sabina Alazzawi

A general formulation of the Boundary Quantum Inverse Scattering Method is given which is applicable in cases where $R$-matrix solutions of the Yang--Baxter equation do not have the property of crossing unitarity. Suitably modified forms of…

Mathematical Physics · Physics 2013-01-03 K. A. Dancer , P. E. Finch , P. S. Isaac , J. Links

An integrable Kondo problem in the one-dimensional supersymmetric extended Hubbard model is studied by means of the boundary graded quantum inverse scattering method. The boundary $K$ matrices depending on the local moments of the…

Statistical Mechanics · Physics 2009-10-31 H. -Q. Zhou , X. -Y. Ge , M. D. Gould

In this work, we discuss the scattering theory of local, relativistic quantum fields with indefinite metric. Since the results of Haag--Ruelle theory do not carry over to the case of indefinite metric, we propose an axiomatic framework for…

Mathematical Physics · Physics 2009-11-11 S. Albeverio , H. Gottschalk

The general rational solution of the Yang-Baxter equation with the symmetry algebra sl(2) can be represented as the product of the simpler building blocks denoted as R-operators. The R-operators are constructed explicitly and have simple…

Quantum Algebra · Mathematics 2009-01-08 S. E. Derkachov

Integrable quantum field models are known to exist mostly in one space-dimension. Exploiting the concept of multi-time in integrable systems and a Lax matrix of higher scaling order, we construct a novel quantum field model in quasi-two…

Exactly Solvable and Integrable Systems · Physics 2016-05-16 Anjan Kundu

This note is a review of the recently revealed intriguing connection between integrable quantum spin chains and integrable many-body systems of classical mechanics. The essence of this connection lies in the fact that the spectral problem…

Mathematical Physics · Physics 2017-11-22 A. Zabrodin

In this paper, we study the inverse scattering problem for energy-dependent Schr\"{o}dinger equations on the half-line with energy-dependent boundary conditions at the origin. Under certain positivity and very mild regularity assumptions,…

Spectral Theory · Mathematics 2020-07-13 Rostyslav Hryniv , Stepan Manko

In this paper we study the linearized inverse problem associated with imaging of reflection seismic data. We introduce an inverse scattering transform derived from reverse-time migration (RTM). In the process, the explicit evaluation of the…

Analysis of PDEs · Mathematics 2011-01-24 Tim J. P. M. Op 't Root , Christiaan C. Stolk , Maarten V. de Hoop

We consider the inverse scattering on the quantum graph associated with the hexagonal lattice. Assuming that the potentials on the edges are compactly supported, we show that the S-matrix for all energies in any open set in the continuous…

Mathematical Physics · Physics 2021-01-28 Kazunori Ando , Hiroshi Isozaki , Evgeny Korotyaev , Hisashi Morioka

The procedure for obtaining integrable vertex models via reflection matrices on the square lattice with open boundaries is reviewed and explicitly carried out for a number of two- and three-state vertex models. These models include the…

High Energy Physics - Theory · Physics 2010-04-08 C. M. Yung , M. T. Batchelor

We consider lambda and anisotropic deformations of the SU(2) principal chiral model and show how they can be quantized in the Hamiltonian formalism on a lattice as a suitable spin chain. The spin chain is related to the higher spin XXZ…

High Energy Physics - Theory · Physics 2018-09-26 Calan Appadu , Timothy J. Hollowood , Dafydd Price , Daniel C. Thompson

Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related…

High Energy Physics - Theory · Physics 2016-09-06 Anjan Kundu

In this work we relate the spectral problem of the toroidal six-vertex model's transfer matrix with the theory of integrable non-linear differential equations. More precisely, we establish an analogy between the Classical Inverse Scattering…

Mathematical Physics · Physics 2018-08-30 W. Galleas

This paper considers aspects of a Kagome lattice system with states classified by plane partitions. Using two sets of free fermions, we rewrite the lattice in terms of two families of spin chains. In this formalism, the quantum crystals…

Mathematical Physics · Physics 2020-12-24 Thiago Araujo