Browsing by Author "Mahajan, Gaurang"

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Casimir effect confronts cosmological constant
(Elsevier Science Publishers, 2006-08-23) Mahajan, Gaurang; Sarkar, Sudipta; Padmanabhan, T.
It has been speculated that the zero-point energy of the vacuum, regularized due to the existence of a suitable ultraviolet cut-off scale, could be the source of the on-vanishing cosmological constant that is driving the present acceleration of the universe. We show that the presence of such a cut-off can significantly alter the results for the Casimir force between parallel conducting plates and even lead to repulsive Casimir force when the plate separation is smaller than the cut-off scale length. Using the current experimental data we rule out the possibility that the observed cosmological constant arises from the zero-point energy which is made finite by a suitable cut-off. Any such cut-off which is consistent with the observed Casimir effect will lead to an energy density which is at least about 10¹² times larger than the observed one, if gravity couples to these modes. The implications are discussed.
Casimir effect confronts cosmological constant
(2006-04-02) Mahajan, Gaurang; Sarkar, Sudipta; Padmanabhan, T.
It has been speculated that the zero-point energy of the vacuum, regularized due to the existence of a suitable ultraviolet cut-oﬀ scale, could be the source of the non-vanishing cosmological constant that is driving the present acceleration of the universe. We show that the presence of such a cut-off can signiﬁcantly alter the results for the Casimir force between parallel conducting plates and even lead to repulsive Casimir force when the plate separation is smaller than the cut-off scale length. Using the current experimental data we rule out the possibility that the observed osmological constant arises from the zero-point energy which is made ﬁnite by a suitable cut-off. Any such cut-oﬀ which is consistent with the observed Casimir effect will lead to an energy density which is about 1012 times larger than the observed one, if gravity couples to these modes. The implications are discussed.
Particle creation, classicality and related issues in quantum ﬁeld theory: I. Formalism and toy models
(Springer, 2007-10-16) Mahajan, Gaurang; Padmanabhan, T.
The quantum theory of a harmonic oscillator with a time dependent frequency arises i n s everal important physical problems, especially in the study of quantum ﬁeld theory i n an external background. While the mathematics of t his system is straightforward, several conceptual issues arise i n such a study. We present a general formalism t o address some of t he conceptual issues like the emergence of classicality, deﬁnition of particle content, back reaction etc. I n particular, we parameterize the wave function i n terms of a complex number (which we call excitation parameter) and express all physically relevant quantities in terms it. Many of the notions—like those of particle number density, effective Lagrangian etc., which are usually deﬁned using asymptotic in–out states—are generalized as time-dependent concepts and we show that these generalized deﬁnitions lead to useful and reasonable results. Hav-ing developed the general formalism we apply it to several examples. Exact analytic expressions are found for a particular toy model and approximate analytic solutions are obtained in the extreme cases of adiabatic and highly non-adiabatic evolution. We then work out the exact results numerically for a variety of models and compare them with the analytic results and approximations. The formalism i suseful in addressing the question of emergence of classicality of the quantum state, its relation t o particle production and to clarify several conceptual issues relatedt ot his. In Paper II which is as equel to this, the formalism will be applied to analyze the corresponding issues in the context of quantum ﬁeld theory i n background cosmological models and electric ﬁelds.
Particle creation, classicality and related issues in quantum ﬁeld theory: II. Examples from ﬁeld theory
(Springer, 2007-10-16) Mahajan, Gaurang; Padmanabhan, T.
We adopt the general formalism, which was developed in Paper I to analyze the evolution of a quantized time-dependent oscillator, to address several questions in the context of quantum ﬁeld theory in time dependent external backgrounds. In particular, we study the question of emergence of classicality in terms of the phase space evolution and its relation to particle production, and clarify some conceptual issues. We consider a quantized scalar ﬁeld evolving in a constant electric ﬁeld and in FRW spacetimes which illustrate the two extreme cases of late time adiabatic and highly non-adiabatic evolution. Using t he time-dependent generalizations of various quantities like particle number density, effective Lagrangian etc. introduced in Paper I, we contrast the evolution in these two limits bringing out key differences between the Schwinger effect and evolution in the deSitter background. Further, our examples suggest that the notion of classicality is multifaceted and any one single criterion may not have universal applicability. For example, the peaking of the phase s pace Wigner distribution on t he classical trajectory alone does not imply t ransition to classical behavior. An analysis of the behavior of the classicality parameter, which was intro-duced in Paper I, leads to the conclusion that strong particle production is necessary for the quantum state to become highly correlated in phase space at late times.