# On the quantum inverse problem for the closed Toda chain

@article{Babelon2003OnTQ, title={On the quantum inverse problem for the closed Toda chain}, author={Olivier Babelon}, journal={Journal of Physics A}, year={2003}, volume={37}, pages={303-316} }

We reconstruct the canonical operators pi, qi of the quantum closed Toda chain in terms of Sklyanin's separated variables.

## 15 Citations

### Bispectrality for the quantum open Toda chain

- Physics
- 2013

An alternative to Babelon (2003 Lett. Math. Phys. 65 229) construction of dual variables for the quantum open Toda chain is proposed that is based on the 2 × 2 Lax matrix and the corresponding…

### Asymptotic analysis and quantum integrable models

- Physics
- 2015

This habilitation thesis reviews the progress made by the author respectively to studying various asymptotic regimes of correlation functions in quantum integrable models.

### Aspects of the inverse problem for the Toda chain

- Mathematics
- 2013

We generalize Babelon's approach to equations in dual variables so as to be able to treat new types of operators which we build out of the sub-constituents of the model's monodromy matrix. Further,…

### Equations in Dual Variables for Whittaker Functions

- Mathematics
- 2003

It is known that the Whittaker functions w(qλ) associated with the group GL(N) are eigenfunctions of the Hamiltonians of the open Toda chain, hence satisfy a set of differential equations in the Toda…

### Quantum chaos for point scatterers on flat tori

- Mathematics, PhysicsPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2014

The main conjectures regarding the spectral and wave function statistics of the delta potential on flat two- and three-dimensional tori in the so-called weak and strong coupling regimes are introduced.

### Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables

- Mathematics
- 2013

The antiperiodic transfer matrices associated to higher spin representations of the rational 6-vertex Yang-Baxter algebra are analyzed by generalizing the approach introduced recently in the…

### On the Form Factors of Local Operators in the Bazhanov–Stroganov and Chiral Potts Models

- MathematicsAnnales Henri Poincaré
- 2014

We consider general cyclic representations of the six-vertex Yang–Baxter algebra and analyze the associated quantum integrable systems, the Bazhanov–Stroganov model and the corresponding chiral Potts…

### On the Form Factors of Local Operators in the Bazhanov–Stroganov and Chiral Potts Models

- Mathematics
- 2015

We consider general cyclic representations of the six-vertex Yang–Baxter algebra and analyze the associated quantum integrable systems, the Bazhanov–Stroganov model and the corresponding chiral Potts…

### Quantum discrete Dubrovin equations

- Physics, Mathematics
- 2004

The discrete equations of motion for the quantum mappings of KdV type are given in terms of the Sklyanin variables (which are also known as quantum separated variables). Both temporal (discrete-time)…

### On the form factors of local operators in the lattice sine–Gordon model

- Mathematics
- 2012

We develop a method for computing form factors of local operators in the framework of Sklyanin’s separation of variables (SOV) approach to quantum integrable systems. For that purpose, we consider…

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