Derives weakest quantization conditions in terms of monodromy data for higher-order DEs tied to quantum Toda chain and proves duality predictions for deformed Schrödinger operators.
TBA for the Toda chain
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abstract
We give a direct derivation of a proposal of Nekrasov-Shatashvili concerning the quantization conditions of the Toda chain. The quantization conditions are formulated in terms of solutions to a nonlinear integral equation similar to the ones coming from the thermodynamic Bethe ansatz. This is equivalent to extremizing a certain function called Yang's potential. It is shown that the Nekrasov-Shatashvili formulation of the quantization conditions follows from the solution theory of the Baxter equation, suggesting that this way of formulating the quantization conditions should indeed be applicable to large classes of quantized algebraically integrable models.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Deformed quantum mechanics from Seiberg-Witten curves shows phases with real or complex instantons, leading to tunneling suppression at Toda points and anomalous scaling at critical monopole points.
citing papers explorer
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Higher-Rank Connections and Deformed Schr\"odinger Operators
Derives weakest quantization conditions in terms of monodromy data for higher-order DEs tied to quantum Toda chain and proves duality predictions for deformed Schrödinger operators.
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Thou shalt not tunnel: Complex instantons and tunneling suppression in deformed quantum mechanics
Deformed quantum mechanics from Seiberg-Witten curves shows phases with real or complex instantons, leading to tunneling suppression at Toda points and anomalous scaling at critical monopole points.