Related papers: The Evolution Operator of The Three Atoms Tavis-Cu…
At present the theory of skew-symmetric exterior differential forms has been developed. The closed exterior forms possess the invariant properties that are of great importance. The operators of the exterior form theory lie at the basis of…
Using the theory of evolutionary equations, we consider abstract differential equations including non-local integral operators. After providing a condition for the well-posedness of the addressed equation we consider a numerical method of…
The exploration of potential energy operators in quantum systems holds paramount significance, offering profound insights into atomic behaviour, defining interactions, and enabling precise prediction of molecular dynamics. By embracing the…
Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators $T$…
Evolutional entanglement production is defined as the amount of entanglement produced by the evolution operator. This quantity is analyzed for systems whose Hamiltonians are characterized by spin operators. The evolutional entanglement…
Interaction among harmonic oscillators described by a trilinear Hamiltonian $\hbar \xi (a^{\dagger} b c + a b^{\dagger} c^{\dagger}$) is one of the most fundamental models in quantum optics. By employing the anharmonicity of the Coublomb…
The purpose of this paper is to further exemplify an approach to evolutionary problems originally developed in earlier works for a special case and later extended to more general evolutionary problems. We are here concerned with the $(1+1)$…
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…
The evolution equations of quantum observables are derived from the classical Hamiltonian equations of motion with the only additional assumption that the phase space is non-commutative. The demonstration of the quantum evolution laws is…
It is shown that the N-th power of the light-cone evolution operator of 2N-periodic quantum discrete Liouville model can be identified with the Dehn twist operator in quantum Teichmuller theory.
We provide a short proof for the twisted multiplicativity property of the operator-valued S-transform. This is my contribution to the topical collection ''Multivariable Operator Theory. The J\"org Eschmeier Memorial'' of Complex Analysis…
We consider a large number of two-level atoms interacting with the mode of a cavity in the rotating-wave approximation (Tavis-Cummings model). We apply the Holstein-Primakoff transformation to study the model in the limit of the number of…
The evolution equation for high twist operators is solved in the Double Logarithmic Approximation for cylinder-type diagrams which dominate in the limit of large number of colors. The asymptotic behaviour of the parton correlation function…
A double Tavis-Cummings model (DTCM) is developed to simulate the entanglement dynamics of realistic quantum information processing where two entangled atom-pairs $AB$ and $CD$ are distributed in such a way that atoms $AC$ are embedded in a…
It is shown how any Lindbladian evolution with selfadjoint Lindblad operators, either Markovian or nonMarkovian, can be understood as an averaged random unitary evolution. Both mathematical and physical consequences are analyzed. First a…
The model-QED-operator approach [Phys. Rev. A 88, 012513 (2013)] to calculations of the radiative corrections to binding and transition energies in atomic systems is extended to the range of nuclear charges $110 \leqslant Z \leqslant 170$.…
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…
A method based off of operator consideration for solving the time evolution of a wave function is developed. The method is applied to free space, constant force and harmonic oscillator potentials where general solutions are derived for the…
Evolutionary algorithms are good general problem solver but suffer from a lack of domain specific knowledge. However, the problem specific knowledge can be added to evolutionary algorithms by hybridizing. Interestingly, all the elements of…
A simple version for the extension of the Taylor theorem to the operator functions was found. The expansion was done with respect to a value given by a diagonal matrix for the non-commutative case, and the coefficients are given both by…