Built on

P. Plamondon, Cluster algebras via cluster categories with infinite-dimensional morphism spaces , Compos. Math. 147
Original
1954
Earlier work this paper cites.
B. Keller, Cluster algebras, quiver representations and triangulated categories , Triangulated categories (T. Holm, P. Jørgensen, and R. Rouquier, eds.), Lecture Note Series, vol. 375, London Mathematical Society, Cambridge University Press, 2010, pp. 76–160; arXiv:0807.1960 [math.RT]
Original
1960
Earlier work this paper cites.
A. Voros, The return of the quartic oscillator. the complex WKB method , Ann. Inst. Henri Poincaré 39
1983
Earlier work this paper cites.
J. Ecallé, Cinq applications des fonctions résurgentes , 1984, Preprint, Prepub. Math. d’Orsay, 84T62, 110 pp
1984
Earlier work this paper cites.
K. Strebel, Quadratic differentials , Springer-Verlag, 1984
1984
Earlier work this paper cites.
T. Aoki, T. Kawai, and Y. Takei, The Bender-Wu analysis and the Voros theory , ICM-90 Satellite Conf. Proc. “Special Functions”, Springer-Verlag, 1991, pp. 1–29
1991
Earlier work this paper cites.
A. Hatcher, On triangulations of surfaces , Topololy Appl. 40
1991
Earlier work this paper cites.
E. Delabaere, H. Dillinger, and F. Pham, Résurgence de Voros et périodes des courbes hyperelliptiques , Ann. Inst. Fourier (Grenoble) 43
1993
Earlier work this paper cites.
M. V. Fedoryuk, Asymptotic analysis: linear ordinary differential equations , Springer-Verlag, 1993
1993
Earlier work this paper cites.
E. Delabaere and F. Pham, Resurgent methods in semi-classical asymptotics , Ann. Inst. Henri Poincaré 71
1999
Earlier work this paper cites.
T. Koike, On the exact WKB anlysis of second order linear ordinary differential equations with simple poles , Publ. RIMS (2000), 297–319
2000
Earlier work this paper cites.
S. Fomin and A. Zelevinsky, Cluster algebras I. Foundations , J. Amer. Math. Soc. 15
2002
Earlier work this paper cites.
A. Berenstein, S. Fomin, and A. Zelevinsky, Cluster algebras III: upper bounds and double Bruhat cells , Duke Math. J. 126
2005
Earlier work this paper cites.
M. Gekhtman, M. Shapiro, and A. Vainshtein, Cluster algebras and Weil-Petersson forms , Duke Math. J. 127
2005
Earlier work this paper cites.

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T. Kawai and Y. Takei, Algebraic analysis of sigular perturbation theory , Translations of mathematical monographs, no. 227, American Mathematical Society, 2005
2005
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O. Costin, Asymptotics and Borel Summability , Monographs and surveys in pure and applied mathematics, vol. 141, Chapmann and Hall/CRC, 2008
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S. Fomin, M. Shapiro, and D. Thurston, Cluster algebras and triangulated surfaces. Part I: Cluster complexes , Acta Math. 201
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M. Kontsevich and Y. Soibelman, Stability structures, Donaldson-Thomas invariants and cluster transformations , 2008, arXiv:0811.2435 [math.AG]
Original
2008

Then

K. Nagao, Quantumd dilogarithm identities , RIMS Kôkyûroku Bessatsu B28
2011
Later among the works it cites.
S. Fomin and D. Thurston, Cluster algebras and triangulated surfaces. Part II: Lambda lengths , 2012, arXiv:1210.5569
Original
2012
Later among the works it cites.
D. Labardini-Fragoso, Quivers with potentials associated to triangulated surfaces, Part IV: Removing boundary assumptions , 2012, arXiv:1206.1798 [math.CO]
Original
2012
Later among the works it cites.
T. Nakanishi, Tropicalization method in cluster algebras , Contemp. Math. 580
Original
2012
Later among the works it cites.
T. Nakanishi and S. Stella, Wonder of sine-Gordon Y Y -systems , 2012, preprint version in arXiv:1212.6853
Original
2012

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2014

Exact WKB analysis and cluster algebras

Iwaki, Kohei, Nakanishi, Tomoki

Understand

We develop the mutation theory in the exact WKB analysis using the framework of cluster algebras.

Under a continuous deformation of the potential of the Schr\"odinger equation on a compact Riemann surface, the Stokes graph may change the topology.
We call this phenomenon the mutation of Stokes graphs.
Along the mutation of Stokes graphs, the Voros symbols, which are monodromy data of the equation, also mutate due to the Stokes phenomenon.

Built on

P. Plamondon, Cluster algebras via cluster categories with infinite-dimensional morphism spaces , Compos. Math. 147
Original
1954
Earlier work this paper cites.
B. Keller, Cluster algebras, quiver representations and triangulated categories , Triangulated categories (T. Holm, P. Jørgensen, and R. Rouquier, eds.), Lecture Note Series, vol. 375, London Mathematical Society, Cambridge University Press, 2010, pp. 76–160; arXiv:0807.1960 [math.RT]
Original
1960
Earlier work this paper cites.
A. Voros, The return of the quartic oscillator. the complex WKB method , Ann. Inst. Henri Poincaré 39
1983
Earlier work this paper cites.
J. Ecallé, Cinq applications des fonctions résurgentes , 1984, Preprint, Prepub. Math. d’Orsay, 84T62, 110 pp
1984
Earlier work this paper cites.
K. Strebel, Quadratic differentials , Springer-Verlag, 1984
1984
Earlier work this paper cites.
T. Aoki, T. Kawai, and Y. Takei, The Bender-Wu analysis and the Voros theory , ICM-90 Satellite Conf. Proc. “Special Functions”, Springer-Verlag, 1991, pp. 1–29
1991
Earlier work this paper cites.
A. Hatcher, On triangulations of surfaces , Topololy Appl. 40
1991
Earlier work this paper cites.
E. Delabaere, H. Dillinger, and F. Pham, Résurgence de Voros et périodes des courbes hyperelliptiques , Ann. Inst. Fourier (Grenoble) 43
1993
Earlier work this paper cites.
M. V. Fedoryuk, Asymptotic analysis: linear ordinary differential equations , Springer-Verlag, 1993
1993
Earlier work this paper cites.
E. Delabaere and F. Pham, Resurgent methods in semi-classical asymptotics , Ann. Inst. Henri Poincaré 71
1999
Earlier work this paper cites.
T. Koike, On the exact WKB anlysis of second order linear ordinary differential equations with simple poles , Publ. RIMS (2000), 297–319
2000
Earlier work this paper cites.
S. Fomin and A. Zelevinsky, Cluster algebras I. Foundations , J. Amer. Math. Soc. 15
2002
Earlier work this paper cites.
A. Berenstein, S. Fomin, and A. Zelevinsky, Cluster algebras III: upper bounds and double Bruhat cells , Duke Math. J. 126
2005
Earlier work this paper cites.
M. Gekhtman, M. Shapiro, and A. Vainshtein, Cluster algebras and Weil-Petersson forms , Duke Math. J. 127
2005
Earlier work this paper cites.

Similar

T. Kawai and Y. Takei, Algebraic analysis of sigular perturbation theory , Translations of mathematical monographs, no. 227, American Mathematical Society, 2005
2005
Cited alongside, same era.
V. V. Fock and A. B. Goncharov, Moduli spaces of local systems and higher Teichmüller theory , Publ. Math. IHES 103
2006
Cited alongside, same era.
O. Costin, Asymptotics and Borel Summability , Monographs and surveys in pure and applied mathematics, vol. 141, Chapmann and Hall/CRC, 2008
2008
Cited alongside, same era.
S. Fomin, M. Shapiro, and D. Thurston, Cluster algebras and triangulated surfaces. Part I: Cluster complexes , Acta Math. 201
2008
Cited alongside, same era.
M. Kontsevich and Y. Soibelman, Stability structures, Donaldson-Thomas invariants and cluster transformations , 2008, arXiv:0811.2435 [math.AG]
Original
2008

Then

K. Nagao, Quantumd dilogarithm identities , RIMS Kôkyûroku Bessatsu B28
2011
Later among the works it cites.
S. Fomin and D. Thurston, Cluster algebras and triangulated surfaces. Part II: Lambda lengths , 2012, arXiv:1210.5569
Original
2012
Later among the works it cites.
D. Labardini-Fragoso, Quivers with potentials associated to triangulated surfaces, Part IV: Removing boundary assumptions , 2012, arXiv:1206.1798 [math.CO]
Original
2012
Later among the works it cites.
T. Nakanishi, Tropicalization method in cluster algebras , Contemp. Math. 580
Original
2012
Later among the works it cites.
T. Nakanishi and S. Stella, Wonder of sine-Gordon Y Y -systems , 2012, preprint version in arXiv:1212.6853
Original
2012

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Cited alongside, same era.

Y. Takei, Sato’s conjecture for the Weber equation and transformation theory for Schrödinger equations with a merging pair of turning points , RIMS Kôkyûroku Bessatsu B10

2008

Cited alongside, same era.

A. Getmanenko, Shatalov-Sternin’s construction of complex WKB solutions and the associated Riemann surface , 2009, arXiv:0907.2934 [math.CA]

Original

2009

Cited alongside, same era.

D. Speyer and B. Sturmfels, Tropical mathematics , Mathematics Magazine 82

2009

Cited alongside, same era.

H. Derksen, J. Weyman, and A. Zelevinsky, Quivers with potentials and their representations II: Applications to cluster algebras , J. Amer. Math. Soc. 23

Original

2010

Cited alongside, same era.

T. Koike and R. Schäfke, On the Borel summability of WKB solutions of Schrödinger equations with polynomial potentials and its application , in preparation; also Talk given by T. Koike in the RIMS workshop “Exact WKB analysis – Borel summability of WKB solutions”, September, 2010

2010

Cited alongside, same era.

A. Getmanenko and D. Tamarkin, Microlocal properties of sheaves and complex WKB , 2011, arXiv:1111.6325 [math-ph]

Original

2011

Cited alongside, same era.

B. Keller, On cluster theory and quantum dilogarithm identities , Representations of algebras and related topics (A. Skowroński and K. Yamagata, eds.), EMS Series of Congress Reports, European Mathematical Society, 2011, pp. 85–116; arXiv:1102.4148 [math.RT]

Original

2011

Cited alongside, same era.

Later among the works it cites.

D. Xie, BPS spectrum, wall crossing and quantum dilogarithm identity , 2012, arXiv:1211.707 [hep-th]