Related papers: Explicit Form of Evolution Operator of Three Atoms…
The symlectic quantum tomography for the general linear quantization is introduced. Using the approach based upon the Wigner function techniques the evolution equation of quantum tomograms is derived for a parametric driven oscillator.
We present three explicit formulas for the number of electronic configurations in an atom, i.e. the number of ways to distribute $Q$ electrons in $N$ subshells of respective degeneracies $g_1$, $g_2$, ..., $g_N$. The new expressions are…
A novel theoretical reformulation of the conventional three-step photoemission model is presented by integrating the conceptual frameworks of constructor theory and quantum information theory. Each step of the photoemission process photon…
We construct quantum evolution operators on the space of states, that is represented by the vertices of the n-dimensional unit hypercube. They realize the metaplectic representation of the modular group SL(2,Z(2^n)). By construction this…
We give explicit expressions for the three-quark exchange operators, crossing matrices and Fierz transforms for the SU(2) and SU(3) groups. We identify the invariant terms in these operators and express them in terms of Casimir operators.
A distributed computing approach to solve the curse of dimensionality, caused by the complex quantum system modeling, is discussed. With the help of Cannon's algorithm, the distributed computing transformation of numerical method for…
In this paper, building on a previous analysis [1] of exact diagonalization of the space-discretized evolution operator for the study of properties of non-relativistic quantum systems, we present a substantial improvement to this method. We…
It is shown how formulas of the author for general operator transmutation can be adapted to a quantum group context
We give an explicit prescription for experimentally determining the evolution operators which completely describe the dynamics of a quantum mechanical black box -- an arbitrary open quantum system. We show necessary and sufficient…
One possible way to fix partly a ``canonical definition'' of $\tau$-functions beyond the conventional KP/Toda framework could be to postulate that evolution operators are {\it always} group elements. We discuss implications of this…
We consider evolution equations generated by quadratic operators admitting a decomposition in creation-annihilation operators without usual ellipticity-type hypotheses; this class includes hypocoercive model operators. We identify the…
There is a classical geometric construction which uses a binary quadratic form to define an involution on the space of binary d-ics. We give a complete characterization of a general class of such involutions which are definable using…
The recent progress in solution of the evolution equations of three particle hadron distribution amplitudes is reviewed.
In the paper we review some recent results of the theory of hierarchies of quantum evolution equations.
We show a right unitary transformation approach based on Susskind-Glogower operators that diagonalizes a generalized Dicke Hamiltonian in the field basis and delivers a tridiagonal Hamiltonian in the Dicke basis. This tridiagonal…
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the…
A new theoretical method is proposed to describe the ground and excited cluster states of atomic nuclei. The method utilizes the equation-of-motion of the Gaussian wave packets to generate the basis wave functions having various cluster…
A novel expansion -- which generalizes Magnus expansion -- of the evolution operator associated with a (in general, time-dependent) perturbed Hamiltonian is introduced. It is shown that it has a wide range of possible solutions that can be…
We study generalized solutions of an evolutionary equation related to some densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and suggest…
We present a fast, memory-efficient, unitarity-preserving numerical method beyond the rotating-wave approximation for the closed Tavis-Cummings model in which a multilevel spin system interacts with a cavity mode. This model can describe…