"Lieb-Liniger delta Bose gas"의 두 판 사이의 차이

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-==introduction==
-* N bosons interacting on the line $[0,L]$ of length L via the delta function potential
-* one-dimensional Bose gas
-* 1963 Lieb and Liniger solved by [[Bethe ansatz]]
-* In 1963, Lieb and Liniger solved exactly a one dimensional model of bosons interacting by a repulsive \delta-potential and calculated the ground state in the thermodynamic limit
-==Hamiltonian==
-*  quantum mechanical Hamiltonian
-:<math>H=-\sum_{j=1}^{N}\frac{\partial^2}{\partial x_j^2}+2c\sum_{1\leq i<j\leq N}^{N}\delta(x_i-x_j)</math><br>
-==wave function==
-* $\psi(x_1, x_2, \dots, x_j, \dots,x_N)$
-* $\psi(x_1, \dots, x_N) =  \sum_P a(P)\exp \left( i \sum_{j=1}^N k_{Pj} x_j\right)$
-$$
-a(P) = \prod\nolimits_{1\leq i<j \leq N}\left(1+\frac{ic}{k_{Pi}  -k_{Pj}}\right) \ .
-$$
-==two-body scattering term==
-* <math>s_{ab}=k_a-k_b+ic</math><br>
-==Bethe-ansatz equation==
-:<math>\exp(ik_jL)=\prod_{l=1}^{N}\frac{k_j-k_l+ic}{k_j-k_l-ic}</math>
-==energy spectrum==
-* energy of a Bethe state
-:<math>E=\sum_{j=1}^{N}k_j^2</math>
-==related items==
-==computational resource==
-* [http://msstp.org/?q=node/275 Day 5 - Yang-Baxter, Delta Bosons, Contact Terms]
-** [http://msstp.org/sites/default/files/Problems4.pdf Bose-Einstein Condensation and BAE exercise .pdf]
-** [http://msstp.org/sites/default/files/problem4.nb Bose-Einstein Condensation and BAE solution .nb]
-==encyclopedia==
-* http://en.wikipedia.org/wiki/Lieb-Liniger_model
-==articles==
-* Tracy, Craig A., and Harold Widom. “On the Ground State Energy of the Delta-Function Bose Gas.” arXiv:1601.04677 [math-Ph], January 18, 2016. http://arxiv.org/abs/1601.04677.
-* Zill, J. C., T. M. Wright, K. V. Kheruntsyan, T. Gasenzer, and M. J. Davis. “A Coordinate Bethe Ansatz Approach to the Calculation of Equilibrium and Nonequilibrium Correlations of the One-Dimensional Bose Gas.” arXiv:1601.00434 [cond-Mat, Physics:hep-Th], January 4, 2016. http://arxiv.org/abs/1601.00434.
-* Veksler, Hagar, and Shmuel Fishman. “A Generalized Lieb-Liniger Model.” arXiv:1508.02011 [cond-Mat, Physics:math-Ph], August 9, 2015. http://arxiv.org/abs/1508.02011.
-* Flassig, Daniel, Andre Franca, and Alexander Pritzel. “Large-N Ground State of the Lieb-Liniger Model and Yang-Mills Theory on a Two-Sphere.” arXiv:1508.01515 [cond-Mat, Physics:hep-Th], August 6, 2015. http://arxiv.org/abs/1508.01515.
-* Dorlas, T. C. “Orthogonality and Completeness of the Bethe Ansatz Eigenstates of the Nonlinear Schroedinger Model.” Communications in Mathematical Physics 154, no. 2 (June 1, 1993): 347–76. doi:10.1007/BF02097001.
-* Yang, C. N., and C. P. Yang. “Thermodynamics of a One‐Dimensional System of Bosons with Repulsive Delta‐Function Interaction.” Journal of Mathematical Physics 10, no. 7 (July 1, 1969): 1115–22. doi:[10.1063/1.1664947 http://dx.doi.org/10.1063/1.1664947].
-* C.N. Yang [http://dx.doi.org/10.1103/PhysRevLett.19.1312 Some exact results for the many-body problem in one dimension with repulsive delta-function interaction], Phys. Rev. Lett. 19 (1967), 1312-1315
-* Elliott H. Lieb and Werner Liniger [http://link.aps.org/doi/10.1103/PhysRev.130.1605 Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State], 1963
-[[분류:integrable systems]]
-[[분류:math and physics]]
-[[분류:migrate]]

"Lieb-Liniger delta Bose gas"의 두 판 사이의 차이

2020년 11월 12일 (목) 05:54 판

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