Zobrazeno 1 - 10
of 79
pro vyhledávání: '"Dunning, Clare"'
Autor:
Clarkson, Peter A., Dunning, Clare
Publikováno v:
Stud. Appl. Math, 152 (2024) 453-507
In this paper rational solutions of the fifth Painlev\'e equation are discussed. There are two classes of rational solutions of the fifth Painlev\'e equation, one expressed in terms of the generalised Laguerre polynomials, which are the main subject
Externí odkaz:
http://arxiv.org/abs/2304.01579
Publikováno v:
J. Phys. A: Math. Theor. (2020)
This review describes a link between Lax operators, embedded surfaces and Thermodynamic Bethe Ansatz equations for integrable quantum field theories. This surprising connection between classical and quantum models is undoubtedly one of the most strik
Externí odkaz:
http://arxiv.org/abs/1911.13290
Publikováno v:
Studies in Applied Mathematics 144 (2020), 245-288
We study Wronskians of Hermite polynomials labelled by partitions and use the combinatorial concepts of cores and quotients to derive explicit expressions for their coefficients. These coefficients can be expressed in terms of the characters of irred
Externí odkaz:
http://arxiv.org/abs/1909.03874
Publikováno v:
J. Phys. A: Math. Theor. 51 315204 (2018)
Starting with the Gaudin-like Bethe ansatz equations associated with the quasi-exactly solved (QES) exceptional points of the asymmetric quantum Rabi model (AQRM) a spectral equivalence is established with QES hyperbolic Schr\"odinger potentials on t
Externí odkaz:
http://arxiv.org/abs/1804.03878
Autor:
Adamopoulou, Panagiota, Dunning, Clare
We establish a correspondence between classical $A_n^{(1)}$ affine Toda field theories and $A_n$ Bethe Ansatz systems. We show that the connection coefficients relating specific solutions of the associated classical linear problem satisfy functional
Externí odkaz:
http://arxiv.org/abs/1401.1187
A correspondence between the sextic anharmonic oscillator and a pair of third-order ordinary differential equations is used to investigate the phenomenon of quasi-exact solvability for eigenvalue problems involving differential operators with order g
Externí odkaz:
http://arxiv.org/abs/1209.4736
Publikováno v:
Nucl. Phys. B 848 (2011) 372-397
We analyse a p+ip-wave pairing BCS Hamiltonian, coupled to a single bosonic degree of freedom representing a molecular condensate, and investigate the nature of the BEC-BCS crossover for this system. For a suitable restriction on the coupling paramet
Externí odkaz:
http://arxiv.org/abs/1102.2485
Publikováno v:
J. Stat. Mech. (2010) P08025
Using the well-known trigonometric six-vertex solution of the Yang-Baxter equation we derive an integrable pairing Hamiltonian with anyonic degrees of freedom. The exact algebraic Bethe ansatz solution is obtained using standard techniques. From this
Externí odkaz:
http://arxiv.org/abs/1001.1591
Publikováno v:
J.Phys.A42:465302,2009
We study a three-parameter family of PT-symmetric Hamiltonians, related via the ODE/IM correspondence to the Perk-Schultz models. We show that real eigenvalues merge and become complex at quadratic and cubic exceptional points, and explore the corres
Externí odkaz:
http://arxiv.org/abs/0907.3673
Publikováno v:
Pramana 73:217-239,2009
One of the simplest examples of a PT-symmetric quantum system is the scaling Yang-Lee model, a quantum field theory with cubic interaction and purely imaginary coupling. We give a historical review of some facts about this model in d <= 2 dimensions,
Externí odkaz:
http://arxiv.org/abs/0906.1130