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We study twisted products $H=alpha^rH_r$ of natural autonomous Hamiltonians $H_r$, each one depending on a separate set, called here separate $r$-block, of variables. We show that, when the twist functions $alpha^r$ are a row of the inverse of a block-Stackel matrix, the dynamics of $H$ reduces to the dynamics of the $H_r$, modified by a scalar potential depending only on variables of the corresponding $r$-block. It is a kind of partial separation of variables. We characterize this block-separation in an invariant way by writing in block-form classical results of Stackel separation of variables. We classify the block-separable coordinates of $mathbb E^3$.
We pursue our study of the antiperiodic dynamical 6-vertex model using Sklyanins separation of variables approach, allowing in the model new possible global shifts of the dynamical parameter. We show in particular that the spectrum and eigenstates of
We explain how to compute correlation functions at zero temperature within the framework of the quantum version of the Separation of Variables (SoV) in the case of a simple model: the XXX Heisenberg chain of spin 1/2 with twisted (quasi-periodic) bou
We present a microscopic approach in the framework of Sklyanins quantum separation of variables (SOV) for the exact solution of 1+1-dimensional quantum field theories by integrable lattice regularizations. Sklyanins SOV is the natural quantum analogu
The quantum SL(3,C) invariant spin magnet with infinite-dimensional principal series representation in local spaces is considered. We construct eigenfunctions of Sklyanin B-operator which define the representation of separated variables of the model.
The Maxwell operator in a 3D cylinder is considered. The coefficients are assumed to be scalar functions depending on the longitudinal variable only. Such operator is represented as a sum of countable set of matrix differential operators of first ord