We study a consistent infrared and ultraviolet regularization scheme for the cosmological perturbations. The infrared divergences are cured by assuming that the Universe undergoes a transition between a nonsingular preinflationary, radiation-dominated phase and a slow-roll inflationary evolution. The ultraviolet divergences are eliminated via adiabatic subtraction. A consistent regularization o...

It has long been established that for a Positive Displacement (PD) compressor or expander such as reciprocating or rotary screw type, the thermodynamic process is adiabatic when compressor or expander discharge pressure is equal to system back pressure (or 100% internal compression or expansion). At this design point, compressor or expander efficiency and noise are most desirable. But more ofte...

We examine the relationship between three approaches (Hadamard, DeWitt-Schwinger and adiabatic) to renormalization of expectation values field operators acting on a charged quantum scalar field. First, we demonstrate that representation Feynman Green's function is particular case Hadamard representation. Next, restrict attention spatially flat Friedmann-Lemaitre-Robertson-Walker universe with t...

The viscous inhomogeneities of a relativistic plasma determine a further class of entropic modes whose amplitude must be sufficiently small since curvature perturbations are observed to be predominantly adiabatic and Gaussian over large scales. When the viscous coefficients only depend on the energy density of the fluid the corresponding curvature fluctuations are shown to be almost adiabatic. ...

The motion of a muon in two centers coulomb field is one of the interesting problems of quantum mechanics. The adiabatic expansion method is powerful approach to study the muonic three-body system. In this investigation the three-body problem is studied for shortrange interactions. Bound states and energy levels of this system were calculated and compared with their Born-Oppenheimer method coun...

General expressions for the breakup cross sections in the laboratory frame for 1 + 2 reactions are given in terms of the hyperspherical adiabatic basis. The three-body wave function is expanded in this basis and the corresponding hyperradial functions are obtained by solving a set of second order differential equations. The S matrix is computed by using two recently derived integral relations. ...

Ab-initio methods for computing stationary molecular states and radiationless transition probabilities between nonstationary states are discussed. The expansion methods, the molecular Hamiltonians, the adiabatic and dia-batic representations, and the symmetry properties are briefly discussed. As an example, nonadiabatic effects in the V-N spectrum of C2H4 and corresponding V-R, · radiationless ...