The ODE/IM correspondence

Dorey, Patrick; Dunning, Clare; Tateo, Roberto

doi:10.1088/1751-8113/40/32/r01

Cited by 281 publications

(391 citation statements)

References 227 publications

Supporting

Mentioning

375

Contrasting

Order By: Relevance

“…There are four independent solutions, whose asymptotic forms are respectively given by 20) where w = z P (z) 1/4 dz ∼ z n/4 and e i are constant vectors. One can determine which of the four solutions shows the fastest decay for |z| → ∞ in each sector One can determine the proportionality coefficient case by case whether n = 2k − 1,…”

Section: Auxiliary Linear Problem and Small Solutionsmentioning

confidence: 99%

Six-point gluon scattering amplitudes from $$ {\mathbb{Z}_4} $$ -symmetric integrable model

Hatsuda

Ito

Sakai

et al. 2010

J. High Energ. Phys.

View full text Add to dashboard Cite

We study six-point gluon scattering amplitudes in N = 4 super Yang-Mills theory at strong coupling by investigating the thermodynamic Bethe ansatz equations of the underlying Z 4 -symmetric integrable model both analytically and numerically.By the conformal field theory (CFT) perturbation, we compute the free energy part of the remainder function with generic chemical potential near the CFT/small mass limit. Combining this with the expansion of the Y-functions, we obtain the remainder function near the small mass limit up to a function of the chemical potential, which can be evaluated numerically. We also find the leading corrections to the remainder function near the large mass limit. We confirm that these results are in good agreement with numerical computations.

show abstract

Section: Auxiliary Linear Problem and Small Solutionsmentioning

confidence: 99%

Six-point gluon scattering amplitudes from $$ {\mathbb{Z}_4} $$ -symmetric integrable model

Hatsuda

Ito

Sakai

et al. 2010

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…Here we will not deal with these issues. The interested reader may consult the review article [80]. Another related line of research is the mathematical theory of linear spaces with an indefinite metric and its applications [53,18].…”

mentioning

confidence: 99%

Pseudo-Hermitian Representation of Quantum Mechanics

Mostafazadeh

2010

Int. J. Geom. Methods Mod. Phys.

834

1,210

View full text Add to dashboard Cite

A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review of the basic ideas and techniques responsible for the recent developments in this subject. We provide a critical assessment of the role of the geometry of the Hilbert space in conventional quantum mechanics to reveal the basic physical principle motivating our study. We then offer a survey of the necessary mathematical tools, present their utility in establishing a lucid and precise formulation of a unitary quantum theory based on a non-Hermitian Hamiltonian, and elaborate on a number of relevant issues of fundamental importance. In particular, we discuss the role of the antilinear symmetries such as PT , the true meaning and significance of the so-called charge operators C and the CPT -inner products, the nature of the physical observables, the equivalent description of such models using ordinary Hermitian quantum mechanics, the pertaining duality between localnon-Hermitian versus nonlocal-Hermitian descriptions of their dynamics, the corresponding classical systems, the pseudo-Hermitian canonical quantization scheme, various methods of calculating the (pseudo-) metric operators, subtleties of dealing with time-dependent quasi-Hermitian Hamiltonians and the path-integral formulation of the theory, and the structure of the state space and its ramifications for the quantum Brachistochrone problem. We also explore some concrete physical applications and manifestations of the abstract concepts and tools that have been developed in the course of this investigation. These include applications in nuclear physics, condensed matter physics, relativistic quantum mechanics and quantum field theory, quantum cosmology, electromagnetic wave propagation, open quantum systems, magnetohydrodynamics, quantum chaos, and biophysics.

show abstract

“…A deeper explanation of such an apparent paradox may be found in Refs. [1,2,14]. Its resolution is easy, in principle at least.…”

Section: The Modelmentioning

confidence: 99%

The Large −g Observability of the Low-Lying Energies in the Strongly Singular Potentials V (x) = x 2 + g 2/x 6 after their PT −symmetric Regularization

Znojil

2014

Int J Theor Phys

View full text Add to dashboard Cite

The large−g observability of the low-lying energies in the strongly singular potentials V (x) = x 2 + g 2 /x 6 after their PT −symmetric regularization Miloslav ZnojilNuclear Physics Institute ASCR, 250 68Řež, Czech Republic e-mail: znojil@ujf.cas.cz AbstractThe elementary quadratic plus inverse sextic interaction V (x) = x 2 +g 2 /x 6 containing a strongly singular repulsive core in the origin is made regular by a complex shift of coordinate x = s − iε. The shift ε > 0 is fixed while the value of s is kept real and potentially observable, s ∈ (−∞, ∞). The low-lying energies of bound states are found in closed form for the large couplings g ≫ 1. Within the asymptotically vanishing O(g −1/4 ) error bars these energies are real so that the time-evolution of the system may be expected unitary in an ad hoc physical Hilbert space.

show abstract

The ODE/IM correspondence

Cited by 281 publications

References 227 publications

Six-point gluon scattering amplitudes from $$ {\mathbb{Z}_4} $$ -symmetric integrable model

Six-point gluon scattering amplitudes from $$ {\mathbb{Z}_4} $$ -symmetric integrable model

Pseudo-Hermitian Representation of Quantum Mechanics

The Large −g Observability of the Low-Lying Energies in the Strongly Singular Potentials V (x) = x 2 + g 2/x 6 after their PT −symmetric Regularization

Contact Info

Product

Resources

About