Cosmological particle creation

Abstract

Comments and AddendaThe section Comments and Addenda is for short communications which are not appropriate for regular articles. It includes only the following types o f communications: (1) Comments on papers previously published in The Physical Review or Physical Review Letters.(2) Addenda to papers previously published in The Physical Review or Physical Review Letters, in which the addit~onal information can be presented without the need for writing a complete article. Manuscripts intended for this section must be accompanied by a brief abstract for information-retrieval purposes. Accepted manuscripts follow the same publication schedule as articles in this journal, and page proofs are sent to authors.We present a simple alternative derivation of cosmological particle production in models with an initial singularity using the Lewis invariant for the time-dependent harmonic oscillator.

Anisotropic Bose-Einstein condensates and completely integrable dynamical systems

“…In (22), c is an arbitrary numerical constant. Taking a positive c prevents ρ from changing sign, which is a convenient property for our purposes.…”

“…Other theoretical studies on Ermakov systems concerns its Lie symmetry structure [19,20], the existence of additional constants of motion [21] and the extension of the Ermakov systems concept to higher dimensions [19]. From the physical point of view, Ermakov systems have found applications in several problems, such as cosmological particle creation [22], nonlinear optics [23,24] and propagation of shallow water waves [25].…”

Algebraic Structure and Poisson’s Integral Theory of f(R) Cosmology

“…It is well known that many methods, such as Ermakov technique [4,5], Lutzky's approach [6,7], group transformation method [8][9][10], dynamical algebraic method [11][12][13], and algebraic structure and Poisson's method for constrained mechanical systems [14][15][16], have been developed to seek invariants of mechanical and physical systems. Among these methods, the invariants of the mechanical systems studied by using Lie group of transformation seem to have an extra advantage of a straightforward extension to the corresponding quantum mechanics, cosmological models and f (R) cosmology [17][18][19][20][21][22].…”

The damped Pinney equation and its applications to dissipative quantum mechanics

“…As is well-known, the Pinney equation [1] is ubiquitous in nonlinear dynamics. A partial list of applications includes the exact solution for the classical and quantum harmonic oscillators [2,3], the search for invariants (constants of motion) [4,5,6], the stability analysis of charged particle motion in accelerators [7,8], the propagation of gravitational waves [9], the amplitude-phase representation of quantum mechanics [10], the derivation of the Feynman propagator for variable-mass problems [11], numerical solutions for non relativistic quantum problems [12], cosmological particle-creation models [13], cosmological models for the Friedmann-Robertson-Walker metric [14], isotropic, four-dimensional cosmological theories [15,16], rotating shallow water-wave systems [17], curve flows in affine geometries [18], the stabilizer set of Virasoro orbits [19], Bose-Einstein condensates with timedependent traps and/or time-dependent scattering length [20,21], discretized Pinney models [22,23] and nonlinear oscillations of transversally isotropic hyperelastic tubes [24].…”