Dynamical Casimir–Polder force in a semi-infinite rectangle waveguide

In this paper, we study the dynamical Casimir–Polder force between an ensemble of identical two-level atoms and the wall of a rectangle waveguide with semi-infinite length. With the presence of both the rotating wave and counter rotating wave terms in the light–matter interaction Hamiltonian, we utilize the perturbation theory to solve the Heisenberg equation. Up to the seconder of coupling strength, we obtain the energy shift analytically and the Casimir–Polder force numerically. Our result shows that the dynamical behavior of the Casimir force is closely connected to the photon propagation in the waveguide. Therefore, we hope this work will stimulate the studies about the quantum effect in waveguide scenario.

The relativistic feature of Hydrogen-like atoms in Heisenberg picture

The relativistic behavior of Hydrogen-like atoms (HLAs) is investigated in Heisenberg picture for the first time. The relativistic vibrational Hamiltonian (RVH) is first defined as a power series of harmonic oscillator Hamiltonian by using the relativistic energy eigenvalue . By applying the first-order RVH (proportional to ) to Heisenberg equation, a pair of coupled equations is turned out for the motion of electron position and its relativistic linear momentum. A simple comparison of the first-order relativistic and nonrelativistic equations reveals this reality that the natural (fundamental) frequency of electron oscillation (like entropy) is slowly raised by increasing the atomic number. The second-order RVH (proportional to ) have then been implemented to determine an exact expression for the electron relativistic frequency in the different atomic energy levels. In general, the physical role of RVH is fundamental because it not only specifies the temporal relativistic variations of position, velocity, and linear momentum of oscillating electron, but also identifies the corresponding relativistic potential, kinetic, and mechanical energies. The results will finally be testified by demonstrating the energy conservation.

Relativity: photon

For the case of interaction of polarized light with an analyzer (a polarizing device), an experimental scheme based on the Feynman idea of path integrals is proposed. Real and virtual photons are considered in the context of the Lenz rule (in terms of constructive and destructive induction). The Planck formula for the photon energy in the format of a verbal description is considered. The complexity of identifying the wave description of the photon with the ideas of the Ancient Greeks about elementary particles is shown. From the point of view of chronogeometry, it is shown that the stationary observer does not exist at the point of intersection of the cone of the past and the future, but in the time interval separating these regions. It is proposed to consider the fluctuations of the physical vacuum as a relic of the process of permanent inflation according to Linde. Based on the assumption of the self-measurement of the Universe, the quantum Zeno effect, and Hawking’s idea of the Universe being a quantum object with the Nth sum of Feynman stories, it is assumed that the history of the Universe is deterministic. From the perspective of the orthogonality of the electromagnetic field vectors E and B, the Heisenberg equation of the form Δp × Δx = ħ/2 is considered. A thought experiment is considered showing the complexity in describing the interaction of a photon with an electron of an atom from the point of view of the classical interaction of an electromagnetic wave with an antenna device. It is proposed to consider the absorption of a photon by an electron as its inertial collapse on an atom.

Influence of the dissipation on the N-level atom interacting with a two two-level atoms in presence of qubit–qubit interaction

The interacting of two qubits and an N-level atom based on su(2) Lie algebra in the presence of both qubit–qubit interaction and dissipation term is considered. The effects of the qubit–qubit interaction and the dissipation term on the dynamics of the proposed system are discussed in detail for certain values of the number of levels. The dynamical expressions of the observable operators are obtained using the Heisenberg equation of motion. The population inversion and linear entropy, as well as the concurrence formula as a measure of entanglement between the two qubits are calculated and discussed. The roles of the number of levels, the qubit–qubit coupling parameter and the dissipation rate on these quantities are also discussed. We explore the sudden birth and sudden death of the entanglement phenomena with and without the dissipation term.

Magnetism and magnetoresistance in the critical region of a dilute ferromagnet

We present detailed experimental measurements and simulations of the field-dependent magnetization and magnetoresistance in the vicinity of the Curie temperature in the highly disordered dilute ferromagnetic semiconductor (Ga,Mn)As. The observed dependence of the magnetization on external magnetic field and temperature is consistent with three-dimensional Heisenberg equation of state calculations including a narrow distribution of critical temperatures. The magnetoresistance shows a peak at the Curie temperature due to the suppression of magnetic scattering in an applied magnetic field, which is well-described by considering changes in the square of the magnetization induced by the magnetic field.

Lagrangian description of Heisenberg and Landau–von Neumann equations of motion

An explicit Lagrangian description is given for the Heisenberg equation on the algebra of operators of a quantum system, and for the Landau–von Neumann equation on the manifold of quantum states which are isospectral with respect to a fixed reference quantum state.

Influence of classical field on entanglement and photon statistics of n-level atom interacting with a two two-level atom

In this study, we consider three interacting atoms, one of them represented by N-level atom based on SU(2) Lie algebra and the other represented by a two two-level atom in presence of the external field. The effect of the external field on the dynamics of the proposed system is discussed in detail for certain values for the external field. The dynamical expression of the observable operators is obtained by using the Heisenberg equation of motion. The general solution via solving Schrodinger equation is obtained. The fidelity and concurrence formula as a measure of entanglement between two two-level atom are calculated and discussed in detail. We explore the sudden death and sudden birth phenomena with and without the presence of external field. Finally, we compare the results of the fidelity, concurrence and second-order correlation function for some values of the initial state and the external field parameters.