scholarly journals Anharmonic oscillators, the thermodynamic Bethe ansatz and nonlinear integral equations

1999 ◽  
Vol 32 (38) ◽  
pp. L419-L425 ◽  
Author(s):  
Patrick Dorey ◽  
Roberto Tateo
Keyword(s):  
Integral Equations ◽  
Bethe Ansatz ◽  
Anharmonic Oscillators ◽  
Nonlinear Integral Equations ◽  
Thermodynamic Bethe Ansatz

The Thermodynamic Bethe Ansatz and a Connection with Painlevé Equations

1997 ◽  
Vol 11 (01n02) ◽  
pp. 69-74
Author(s):  
Craig A. Tracy ◽  
Harold Widom
Keyword(s):  
Integral Equations ◽  
Bethe Ansatz ◽  
Painlevé Equations ◽  
Nonlinear Integral Equations ◽  
Thermodynamic Bethe Ansatz ◽  
Painleve Equations ◽  
Linear Integral ◽  
Linear Integral Equations

We summarize some recent connections between a class of nonlinear integral equations related to the thermodynamic Bethe Ansatz and a class of linear integral equations related to the Painlevé equations.

scholarly journals THERMODYNAMIC BETHE ANSATZ EQUATION FROM FUSION HIERARCHY OF osp(1|2) INTEGRABLE SPIN CHAIN

2000 ◽  
Vol 15 (15) ◽  
pp. 2329-2346 ◽  
Author(s):  
KAZUMITSU SAKAI ◽  
ZENGO TSUBOI
Keyword(s):  
Free Energy ◽  
Excited State ◽  
Bethe Ansatz ◽  
Spin Chain ◽  
Lie Superalgebra ◽  
Nonlinear Integral Equations ◽  
Thermodynamic Bethe Ansatz ◽  
Functional Relations ◽  
Integrable Spin ◽  
T System

The thermodynamic Bethe ansatz (TBA) and the excited state TBA equations for an integrable spin chain related to the Lie superalgebra osp (1|2) are proposed by the quantum transfer matrix (QTM) method. We introduce the fusion hierarchy of the QTM and derive the functional relations among them (T-system) and their certain combinations (Y-system). Their analytical property leads to the nonlinear integral equations which describe the free energy and the correlation length at any finite temperatures. With regard to the free energy, they coincide with the TBA equation based on the string hypothesis.

scholarly journals THERMODYNAMIC BETHE ANSATZ EQUATION FOR osp(1|2) INTEGRABLE SPIN CHAIN

1999 ◽  
Vol 14 (35) ◽  
pp. 2427-2435 ◽  
Author(s):  
KAZUMITSU SAKAI ◽  
ZENGO TSUBOI
Keyword(s):  
Free Energy ◽  
Low Temperature ◽  
Bethe Ansatz ◽  
Infinite Number ◽  
Spin Chain ◽  
Lie Superalgebra ◽  
Temperature Limit ◽  
Nonlinear Integral Equations ◽  
Thermodynamic Bethe Ansatz ◽  
Integrable Spin

The thermodynamic Bethe ansatz is applied to a quantum integrable spin chain associated with the Lie superalgebra osp (1|2). Using the string hypothesis, we derive a set of infinite number of nonlinear integral equations (thermodynamic Bethe ansatz equation), which characterize the free energy. The low temperature limit of the free energy is also discussed.

scholarly journals Solution of Baxter equation for the $q$-Toda and Toda$_2$ chains by NLIE

2018 ◽  
Vol 5 (4) ◽  
Author(s):  
Olivier Babelon ◽  
Karol Kozlowski ◽  
Vincent Pasquier
Keyword(s):  
Integral Equations ◽  
Bethe Ansatz ◽  
Baxter Equation ◽  
Thermodynamic Bethe Ansatz ◽  
Non Linear ◽  
Linear Integral ◽  
Linear Integral Equations

We construct a basis of solutions of the scalar t-Q equation describing the spectrum of the q-Toda and Toda_22 chains by using auxiliary non-linear integral equations. Our construction allows us to provide quantisation conditions for the spectra of these models in the form of thermodynamic Bethe Ansatz-like equations.

scholarly journals Quantum periods and TBA-like equations for a class of Calabi-Yau geometries

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bao-ning Du ◽  
Min-xin Huang
Keyword(s):  
Large Class ◽  
Bethe Ansatz ◽  
Difference Equations ◽  
The Other ◽  
Elementary Functions ◽  
Quantum Dilogarithm ◽  
Thermodynamic Bethe Ansatz ◽  
Dilogarithm Function ◽  
Quantum Operators

Abstract We continue the study of a novel relation between quantum periods and TBA(Thermodynamic Bethe Ansatz)-like difference equations, generalize previous works to a large class of Calabi-Yau geometries described by three-term quantum operators. We give two methods to derive the TBA-like equations. One method uses only elementary functions while the other method uses Faddeev’s quantum dilogarithm function. The two approaches provide different realizations of TBA-like equations which are nevertheless related to the same quantum period.

scholarly journals Fixed point results for rational contraction in function weighted dislocated quasi-metric spaces with an application

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdullah Shoaib ◽  
Qasim Mahmood ◽  
Aqeel Shahzad ◽  
Mohd Salmi Md Noorani ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Multivalued Mapping ◽  
Metric Spaces ◽  
Nonlinear Integral Equations ◽  
Rational Contraction ◽  
Rational Type

AbstractThe objective of this article is to introduce function weighted L-R-complete dislocated quasi-metric spaces and to present fixed point results fulfilling generalized rational type F-contraction for a multivalued mapping in these spaces. A suitable example confirms our results. We also present an application for a generalized class of nonlinear integral equations. Our results generalize and extend the results of Karapınar et al. (IEEE Access 7:89026–89032, 2019).

scholarly journals An extension of Darbo’s fixed point theorem for a class of system of nonlinear integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Amar Deep ◽  
Deepmala ◽  
Jamal Rezaei Roshan ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Nonlinear Integral Equations ◽  
Existence Of A Solution ◽  
Darbo’S Fixed Point Theorem ◽  
Novi Sad

Abstract We introduce an extension of Darbo’s fixed point theorem via a measure of noncompactness in a Banach space. By using our extension we study the existence of a solution for a system of nonlinear integral equations, which is an extended result of (Aghajani and Haghighi in Novi Sad J. Math. 44(1):59–73, 2014). We give an example to show the specified existence results.

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