arXiv subjects

Karthik Rajeev

Publications and source records attributed to Karthik Rajeev.

24 records · Page 2Linked to original sources

arXiv2020

Complex time route to quantum backreaction

We consider the backreaction of a quantum system $q$ on an effectively classical degree of freedom $C$ that is interacting with it. The backreaction equation based on the standard path integral formalism gives the so-called `in-out' backreaction equation, which has several serious pathologies. One can use a different backreaction prescription, referred to as the `in-in' approach, which resolves all the issues of `in-out' backreaction equation. However, this procedure is usually invoked in a rather ad hoc manner. Here we provide a rigorous path integral derivation of the `in-in' approach by exploiting the concept of quantum evolution along complex time contours. It turns out that, this approach can also be used to study both the `in-in' and `in-out' backreaction equations in a unified manner.

gr-qc↗

arXiv2019

Generalized Schwinger effect and particle production in an expanding universe

We discuss several aspects of particle production in: (a) time dependent electric field and (b) expanding Friedmann background. In the first part of the paper, we provide an algebraic mapping between the differential equations describing these two phenomena. This mapping allows a direct comparison between (a) and (b) and we highlight several interesting features of both cases using this approach. We determine the form of the (equivalent) electric field corresponding to different Friedmann spacetimes and discover, for example, a time-dependent electric field which, in a specific limit, leads to a Planck's spectrum of particles. We also discuss the conditions under which the particle production in an expanding background will be non-analytic in the parameter which encodes the coupling to the curved spacetime, in close analogy with the generalized Schwinger effect. In the second part of the paper, we study the situation in which both time dependent electric field and an expanding background are simultaneously present. We compute particle production rate in this context by several different methods paying special attention to its limiting forms and possible non-analytic behaviour. We also clarify several conceptual issues related to definitions of in-vacuum and out-vacuum in these systems.

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arXiv2019

Quantum Correlators in Friedmann Spacetimes -The omnipresent de Sitter and the invariant vacuum noise

We discuss several aspects of quantum field theory of a scalar field in a Friedmann universe, clarifying and highlighting several conceptual and technical issues. (A) We show that one can map the dynamics of (1) a massless scalar field in a universe with power law expansion to (2) a massive scalar field in the de Sitter spacetime, which allows us to understand several features of either system and clarifies several issues related to the massless limit. (B) We obtain a useful integral representation for the Euclidean Green's function for the de Sitter spacetime, by relating it to the solution of a hypothetical electrostatic problem in five dimensions. This is helpful in the study of several relevant limits. (C) We recover that in any Friedmann universe, sourced by a negative pressure fluid, the Wightman function for a massless scalar field is divergent. This shows that the divergence of Wightman function for the massless field in the de Sitter spacetime is just a special, limiting, case of this general phenomenon. (D) We provide a generally covariant procedure for defining the power spectrum of vacuum fluctuations in terms of the different Killing vectors present in the spacetime. This allows one to study the interplay of the choice of vacuum state and the nature of the power spectrum in different coordinate systems, in the de Sitter universe, in a unified manner. (Truncated Abstract; see the paper for full Abstract.)

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arXiv2018

A comment on generalized Schwinger effect

A spatially homogeneous, time-dependent, electric field can produce charged particle pairs from the vacuum. When the electric field is constant, the mean number of pairs which are produced depends on the electric field and the coupling constant in a non-analytic manner, showing that this result cannot be obtained from the standard perturbation theory of quantum electrodynamics. When the electric field varies with time and vanishes asymptotically, the result may depend on the coupling constant either analytically or non-analytically. We investigate the nature of this dependence in detail. We show that the dependence of particle production on coupling constant is non-analytic for a class of time-dependent electric fields which vanish asymptotically when a specific condition is satisfied. We also demonstrate that for another class of electric fields, which vary rapidly, the dependence of particle production on coupling constant is analytic.

gr-qc↗

arXiv2018

Inverting a normal harmonic oscillator: Physical interpretation and applications

A harmonic oscillator with time-dependent mass $m(t)$ and a time-dependent (squared) frequency $ω^2(t)$ occurs in the modelling of several physical systems. It is generally believed that systems, with $m(t)>0$ and $ω^2(t)>0$ (normal oscillator) are stable while systems with $m(t)>0$ and $ω^2(t)<0$ (inverted oscillator) are unstable. We show that it is possible to represent the \textit{same} physical system either as a normal oscillator or as an inverted oscillator by redefinition of dynamical variables. While we expect the physics to be invariant under such redefinitions, it is not obvious how this invariance actually comes about. We study the relation between these two, normal and inverted, representations of an oscillator in detail both in Heisenberg and Schrödinger pictures to clarify several conceptual and technical issues. The situation becomes more involved when the oscillator is coupled to another (semi)classical degree of freedom $C(t)$ and we want to study the back-reaction of the quantum system $q(t)$ on $C(t)$, in the semi-classical approximation. We provide a simple prescription for the back-reaction based on energy conservation and study that the dynamics of the full system in both normal and the inverted oscillator representation. The physics again remains invariant but there are some extra subtleties which we clarify. The implications of these results for quantum field theory in cosmological backgrounds are discussed briefly in an appendix.

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arXiv2015

An approach to the quantization of black-hole quasi-normal modes

In this work we derive the asymptotic quasi-normal modes of a BTZ black hole using a quantum field theoretic Lagrangian. The BTZ black hole is a very popular system in the context of $2+1$-dimensional quantum gravity. However to our knowledge the quasi-normal modes of the BTZ black hole have been studied only in the classical domain. Here we show a way to quantize the quasi-normal modes of the BTZ black hole by mapping it to the Bateman-Feschbach-Tikochinsky oscillator and the Caldirola-Kanai oscillator. We have also discussed a couple of other black hole potentials to which this method can be applied

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