v - in t / 9 50 60 06 v 1 7 J ul 1 99 5 Fredholm Determinants and the mKdV / Sinh - Gordon Hierarchies
نویسندگان
چکیده
For a particular class of integral operators K we show that the quantity φ := log det (I +K)− log det (I −K) satisfies both the integrated mKdV hierarchy and the sinh-Gordon hierarchy. This proves a conjecture of Zamolodchikov.
منابع مشابه
Fredholm Determinants and the mKdV / Sinh - Gordon Hierarchies
For a particular class of integral operators K we show that the quantity φ := log det (I + K)log det (/ K) satisfies both the integrated mKdV hierarchy and the Sinh-Gordon hierarchy. This proves a conjecture of Zamolodchikov.
متن کامل1 J ul 1 99 9 Exact Results for Thermodynamics of the Classical Field
Using the recently obtained exact results for the expectation values of operators in the sineand sinh-Gordon models [A. B. Zamolodchikov and S. Lukyanov, Nucl. Phys. B493, 571 (1997), V. Fateev, S. Lukyanov, A. B. Zamolodchikov and Al. B. Zamolodchikov, Phys. Lett. B406, 83 (1997)] we calculate the specific heat of the corresponding two dimensional Euclidean (classical) models. We show that the...
متن کاملA Combined Sine-gordon and Modified Korteweg{de Vries Hierarchy and Its Algebro-geometric Solutions
We derive a zero-curvature formalism for a combined sine-Gordon (sG) and modi-ed Korteweg{de Vries (mKdV) equation which yields a local sGmKdV hierarchy. In complete analogy to other completely integrable hierarchies of soliton equations, such as the KdV, AKNS, and Toda hierarchies, the sGmKdV hierarchy is recursively constructed by means of a fundamental polynomial formalism involving a spectr...
متن کاملar X iv : h ep - t h / 97 07 06 0 v 1 5 J ul 1 99 7 Zamalodchikov ’ s C - Theorem and The Logarithmic Conformal Field Theory
We consider perturbation of a conformal field theory by a pair of relevant logarithmic operators and calculate Zamalodchikov's C function up to two loops. We observe that the renormalization group trajectories are not always along decreasing values of C. However there exists a domain of structure constants in which the c-theorem still holds.
متن کاملar X iv : c on d - m at / 9 30 70 06 v 1 5 J ul 1 99 3 Flux flow dissipation in superconductors with short coherence length
In superconductors where the coherence length is comparable to the Fermi wavelength , the electronic levels within a vortex core are quantized, and separated by energies of the order of the superconducting gap. The absence of a continuum modifies significantly the energy dissipation due to the motion of vortices. At zero temperature , dissipation is suppressed, and the system shows non ohmic be...
متن کامل