Related papers: Separation of Variables. New Trends.
The $n$ integrals in involution for the motion on the $n$-dimensional ellipsoid under the influence of a harmonic force are explicitly found. The classical separation of variables is given by the inverse momentum map. In the quantum case…
In several articles, this author has advocated an alternative approach towards quantum foundation based upon a set of postulates, and based upon the notions of theoretical variables and of accessible theoretical variables. It is shown in…
This survey examines separation of variables for algebraically integrable Hamiltonian systems whose tori are Jacobians of Riemann surfaces. For these cases there is a natural class of systems which admit separations in a nice geometric…
The connections between standard theoretical tools used to study open quantum systems can sometimes seem opaque. Whether it is a Lindblad master equation, the equation of motion for the Wigner function or a dissipative Keldysh action,…
In this contribution I summarize the achievements of separation of variables in integrable quantum systems from the point of view of path integrals. This includes the free motion on homogeneous spaces, and motion subject to a potential…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
We derive quasi-collinear factorization formulas in generic spontaneously broken gauge theories with scalars, fermions, and vector bosons. Specifically, we obtain polarized leading-order splitting functions for all possible final-state and…
The Trotter-Suzuki decomposition is one of the main approaches for realization of quantum simulations on digital quantum computers. Variance-based global sensitivity analysis (the Sobol method) is a wide used method which allows to…
This paper explores the Petrov type D, stationary axisymmetric vacuum (SAV) spacetimes that were found by Carter to have separable Hamilton-Jacobi equations, and thus admit a second-order Killing tensor. The derivation of the spacetimes…
The Baxter-Bazhanov-Stroganov model (also known as the \tau^(2) model) has attracted much interest because it provides a tool for solving the integrable chiral Z_N-Potts model. It can be formulated as a face spin model or via cyclic…
Recently, [{arXiv:0810.3134}] is accepted and published. We present ultimate version of no-hidden-variables theorem. We derive a proposition concerning the quantum theory under the existence of the Bloch sphere in a single spin-1/2 system.…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
We study the relation between the partition function of refined SU(N) and SO(2N) Chern-Simons on the 3-sphere and the universal Chern-Simons partition function in the sense of Mkrtchyan and Veselov. We find a four-parameter generalization…
The article contains a review and new results of some mathematical models relevant to the interpretation of quantum mechanics and emulating well-known quantum gauge theories, such as scalar electrodynamics (Klein-Gordon-Maxwell…
We consider a particular class of equations of motion, generalizing to n degrees of freedom the "dissipative spin--orbit problem", commonly studied in Celestial Mechanics. Those equations are formulated in a pseudo-Hamiltonian framework…
This study presents fast and accurate analytical methods for transient thermal modeling in multi-layer composites with an arbitrary number of layers. The proposed approach accounts for internal heat generation and non-homogeneities in the…
Wide classes of nonlinear mathematical physics equations are described that admit order reduction through the use of the von Mises transformation, with the unknown function taken as the new independent variable and an appropriate partial…
In a specific class of open quantum systems with finite and fixed numbers of collapsed quantum states, the semi-Markov process method is used to calculate the large deviations of the first passage time statistics. The core formula is an…
We tackle the dynamical description of the quantum measurement process, by explicitly addressing the interaction between the system under investigation with the measurement apparatus, the latter ultimately considered as macroscopic quantum…
The article provides a framework to solve linear differential equations based on partial commutativity which is introduced by means of the Fedorov theorem. The framework is applied to specific types of three-level and four-level quantum…