Induced Brownian motion by the Friedmann–Robertson–Walker spacetime in the presence of a cosmic string

Abstract

In this paper we investigate the quantum Brownian motion of a massive scalar point particle induced by the FRW spacetime in the presence of a linear topological defect named cosmic string.In addition, we also consider a flat boundary orthogonal to the defect to analyse its effect on the particle's motion. For both cases we found exact expressions for the renormalized mean square deviation of the particle velocity, the quantity that measures the induced Brownian motion, and obtain asymptotic expressions when the point particle is near and far away from the cosmic string and the boundary. Furthermore, in both cases, there appears divergencies in the mean square deviation of the particle velocity coming from a time interval that correspond to a round trip of the massive point particle between its position and the cosmic string/flat boundary. The number of divergencies depends upon the radial position of the particle and the parameter associated with the cosmic string in the case without boundary, and upon this parameter and the radial and z positions of the particle in the case with boundary. * Electronic address: hmota@fisica.ufpb.br † Electronic address: emello@fisica.ufpb.br arXiv:1904.04634v1 [hep-th]

Quantum Brownian motion induced by an inhomogeneous tridimensional space and a $S^1\times R^3$ topological space-time

“…As a result, we note that 0|v i |0 ≡ v i = 0, that is, the velocity mean value of the particle due the quantum vacuum fluctuations vanishes since, by definition, a|0 = 0 and 0|a † = 0. Although the velocity mean value vanishes, the quantum vacuum fluctuations on the velocity can be calculated through the following expression for the renormalized velocity dispersion [14,16]:…”

“…The stochastic motion performed by a point particle when interacting with the quantum vacuum fluctuations of a relativistic field, e.g., scalar or electromagnetic, is also known as Quantum Brownian motion (QBM). This is an example of a phenomena class which arise from quantum vacuum fluctuations and that, over the past several years, has been studied in different scenarios and with different approaches [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. The quantum vacuum fluctuations are always present but only become observable when the vacuum is somehow perturbed, for instance, by considering elements such as boundary conditions, temperature, nontrivial topology and so on.…”

Perturbations to generalized kink-like topological defects in AdS

“…different values. Note that for q = 3, the formula above gives 2, which is the dimensionality of the real irreducible representations of SO (2).…”

“…Two immediate consequences of these equations are that h β ≥ −β 2 and h β ≥ −(β + 1) 2 . Remember that we are in the parameter range β > 0.…”

“…These objects are interesting to study as a possible consequence of symmetry breaking in the early universe leading to cosmological-scale objects such as cosmic strings [1]. In more recent years, some study has gone into how these objects might influence the dynamics of nearby massive objects [2] Our model concerns an SO(l)gauged Higgs-type field theory embedded into AdS q+l with q, l ≥ 1. For convenience, we will often refer to these with the shorthand "(q, l) defect" for the codimension-l topological defect with a worldbrane of AdS q embedded in AdS q+l .…”