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[en] A new method for estimating the matrix elements of the Bogoliubov boson transformation is worked out. The solution given here is based on the following: an arbitrary coefficient (the overlap of a transformed state and an initial one) is related, by an elementary procedure, to a particular one which is subsequently estimated in a simple manner. The cases of the zero momentum bosons and of the non-zero momentum bosons are separately treated. (author)
[en] Regular and dimension-regularized values of three types of the quantities composing vector and axial-vector Ward's identities for the spinor triangle diagrams with an arbitrary Lorentz characteristic of vertices and different masses have been calculated. The effective realization of the Bogolyubov-Parasyuk renormalization scheme and a new version of the dimensional regularization have been applied. It is established that the dimensional-regularized values of these quantities satisfy the canonical Ward identities but the regular values of these quantities satisfy some regular analogs of them. The similarity and difference between them are investigated in detail. (author)
[en] We revisit the Bogoliubov transformation as a representation of the group of unitary operators of Balian and Brezin. We show that the group property is best utilized when we treat successive transformations of quasiparticles and their vacuum at the same time. In particular, we establish a one-to-one correspondence between sets of quasiparticle operators and their vacua using the group property. The correspondence determines the quasiparticle vacuum uniquely including the phase, which is inevitable in treating probability amplitudes in a consistent fashion
[en] The probability of particles creation by a homogeneous scalar field Χ(t) is calculated. Explicit analytical expressions are obtained in two limiting cases in the quasiclassical approximation and in the framework of perturbation theory. In the case when the mass of the created particles is defined by the time-dependent field Χ(t) according to the expression gΧ(t) Ψ-barΨ, where Χ(t)=Χ0cos(ωt), it is shown that the creation probability is suppresed not exponentially, but as ω1/2. Some cosmological consequences of the results are discussed. 13 refs
[en] We apply the Bogoliubov transformations in order to connect two different vacuums, one located at past infinity and another located at future infinity around a black hole inside the scenario of the nonlinear theory of massive gravity. The presence of the extra degrees of freedom changes the behavior of the logarithmic singularity and, as a consequence, the relation between the two Bogoliubov coefficients. This has an effect on the number of particles, or equivalently, on the black hole temperature perceived by observers defining the time arbitrarily.
[en] A recent paper on the application of the Von Mises transformation to the non-linear one-dimensional electron plasma oscillation problem is commented on, completed and corrected. The frequency shift is computed for a water bag model, valid for all k, and found in excellent agreement with the results of computer experiments. (author)
[en] We show that one-way Einstein–Podolsky–Rosen (EPR) steering effects can be generated via the asymmetric dissipation scheme induced by the spontaneously generated coherence (SGC) in a resonantly driven V-type atomic system. According to the dressed atomic states and Bogoliubov transformation, we find that there exist two identical dissipation channels being responsible for the appearance of entanglement and symmetric two-way steering effects in the absence of SGC effect. More interestingly, the one-way EPR steering effect occurs when the population differences between the dressed states are prominently modified by the SGC effect. As a consequence, the symmetry of the two dissipation channels is broken by the quantum interference, leading to the generation of one-way EPR steering effect.
[en] Dynamics of a Dirac particle in general Riemann-Cartan spacetimes is considered. The Hermitian Dirac Hamiltonian is derived and is transformed to the Foldy-Wouthuysen representation for an arbitrary spacetime geometry. The contribution of the torsion field to the Foldy-Wouthuysen Hamiltonian is found. The new bounds on Cartan’s spacetime torsion are obtained.