Related papers: QKZ-Ruijsenaars correspondence revisited
We describe the correspondence of the Matsuo-Cherednik type between the quantum $n$-body Ruijsenaars-Schneider model and the quantum Knizhnik-Zamolodchikov equations related to supergroup $GL(N|M)$. The spectrum of the Ruijsenaars-Schneider…
We discuss the correspondence between the Knizhnik-Zamolodchikov equations associated with $GL(N)$ and the $n$-particle quantum Calogero model in the case when $n$ is not necessarily equal to $N$. This can be viewed as a natural…
The quantum-to-classical correspondence (QCC) in spin models is a puzzling phenomenon where the static susceptibility of a quantum system agrees with its classical-system counterpart, at a different corresponding temperature, within the…
This note is a review of the recently revealed intriguing connection between integrable quantum spin chains and integrable many-body systems of classical mechanics. The essence of this connection lies in the fact that the spectral problem…
This paper tackles the long-standing problem of quantizing the rational spin Ruijsenaars--Schneider model originating in the work of Krichever and Zabrodin. We make use of the technique of quantum Hamiltonian reduction to construct a…
A special case of the geometric Langlands correspondence is given by the relationship between solutions of the Bethe ansatz equations for the Gaudin model and opers - connections on the projective line with extra structure. In this paper,…
We construct special solutions to the rational quantum Knizhnik-Zamolodchikov equation associated with the Lie algebra $gl_N$. The main ingredient is a special class of the shifted non-symmetric Jack polynomials. It may be regarded as a…
In this note we propose a compatible set of equations which commutes with the Knizhnik-Zamolodchikov equations based on the $\mathfrak{{gl}}(n\vert m)$ symmetry algebra and establish the Matsuo-Cherednik correspondence in this context.
The principle of correspondence (or classical limit) is essential in quantum mechanics. Yet, how and why quantum phenomena vanish at the macroscopic scale are issues still open to debate. Here, quantum mechanical predictions for…
An exact correspondence is established between a $N$-body classical interacting system and a $N-1$-body quantum system with respect to the partition function. The resulting quantum-potential is a $N-1$-body one. Inversely the Kelbg…
This is an extension of quantum spinor construction in \cite{DF2}. We define quantum affine Clifford algebras based on the tensor category and the solutions of q-KZ equations, construct quantum spinor representations of $U_q(\hat{\frak…
The problem of consistent formulation of the correspondence principle in quantum gravity is considered. The usual approach based on the use of the two-particle scattering amplitudes is shown to be in disagreement with the classical result…
The investigation of quantum-classical correspondence may lead to gain a deeper understanding of the classical limit of quantum theory. We develop a quantum formalism on the basis of a linear-invariant theorem, which gives an exact…
We study the quantum-classical correspondence for systems with interacting spin-particles that are strongly chaotic in the classical limit. This is done in the presence of constants of motion associated with the fixed angular momenta of…
The semiclassical interaction of the gravitational with a quantum scalar field is considered, in view of the renormalizability of the associated energy-momentum tensor in a n-dimensional curved spacetime resulting from a quadratic…
We extend duality between the quantum integrable Gaudin models with boundary and the classical Calogero-Moser systems associated with root systems of classical Lie algebras $B_N$, $C_N$, $D_N$ to the case of supersymmetric ${\rm gl}(m|n)$…
Presented is an integral formula for solutions to the quantum Knizhnik--Zamolodchikov equation of level $0$ associated with the vector representation of $U_q (\widehat{ sl_n})$. This formula gives a generalization of both our previous work…
Von Neumann entropy production rates of the quantised kicked rotor interacting with an environment are calculated. A significant correspondence is found between the entropy contours of the classical and quantised systems. This is a…
Two types of Poisson pencils connected to classical R-matrices and their quantum counterparts are considered. A representation theory of the quantum algebras related to some symmetric orbits in $sl(n)^*$ is constructed. A twisted version of…
It is shown that the Foldy-Wouthuysen transformation for relativistic particles in strong external fields provides the possibility of obtaining a meaningful classical limit of the relativistic quantum mechanics. The full agreement between…