Browsing by Author "Sriramkumar, L."

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Does a nonzero tunneling probability imply particle production in time-independent classical electromagnetic backgrounds?
(American Physical Society, 1996-12-15) Sriramkumar, L.; Padmanabhan, T.
In this paper, we probe the validity of the tunneling interpretation that is usually called forth in the literature to explain the phenomenon of particle production by time-independent classical electromagnetic backgrounds. We show that the imaginary part of the effective Lagrangian is zero for a complex scalar ﬁeld quantized in a time-independent, but otherwise arbitrary, magnetic ﬁeld. This result implies that no pair creation takes place in such a background. But we ﬁnd that when the quantum ﬁeld is decomposed into its normal modes in the presence of a spatially conﬁned and time-independent magnetic ﬁeld, there exists a nonzero tunneling prob-ability for the effective Schro¨dinger equation. According to the tunneling interpretation, this result would imply that spatially conﬁned magnetic ﬁelds can produce particles, thereby contradicting the result obtained from the effective Lagrangian. This lack of consistency between these two approaches calls into question the validity of attributing a nonzero tunneling probability for the effective Schro¨dinger equation to the production of particles by the time-independent electromagnetic backgrounds. The implications of our analysis are discussed.
Finite-time response of inertial and uniformly accelerated Unruh–DeWitt detectors
(IOP Publishing, 1996-05-15) Sriramkumar, L.; Padmanabhan, T.
We study the response of inertial and uniformly accelerated Unruh–DeWitt detectors in the Minkowski vacuum when they are coupled to the quantum ﬁeld for a ﬁnite time interval. A ﬁnite-time detector will respond even on an inertial trajectory due to transient effects. Also, the response will depend on the manner in which the detector is switched on and off. We study the response for smooth as well as abrupt switching of the detector. The detectors are switched on and off with window functions whose width, T , determines the effective timescale for which the detector is coupled to the ﬁeld. We work out in detail the response of inertial and uniformly accelerated detectors for Gaussian, exponential and rectangular window functions and also obtain a general formula for the response of these detectors when a window function is speciﬁed. The T ! 0 and T !1 limits are discussed in detail and several subtleties in the limiting procedure are clariﬁed
Hypothesis of path integral duality. II. Corrections to quantum field theoretic results
(American Physical Society, 1998-07-13) Srinivasan, K.; Sriramkumar, L.; Padmanabhan, T.
In the path integral expression for a Feynman propagator of a spinless particle of mass m, the path integral amplitude for a path of proper length R(x,x'\|gμν) connecting events x and x' in a spacetime described by the metric tensor gμν is exp \{-[m R(x,x'\|gμν)]\}. In a recent paper, assuming the path integral amplitude to be invariant under the duality transformation R-->(L2P/R), Padmanabhan has evaluated the modified Feynman propagator in an arbitrary curved spacetime. He finds that the essential feature of this ``principle of path integral duality'' is that the Euclidean proper distance (Δx)2 between two infinitesimally separated spacetime events is replaced by [(Δx)2+4L2P]. In other words, under the duality principle the spacetime behaves as though it has a ``zero-point length'' LP, a feature that is expected to arise in a quantum theory of gravity. In Schwinger's proper time description of the Feynman propagator, the weightage factor for a path with a proper time s is exp [-(m2s)]. Invoking Padmanabhan's ``principle of path integral duality'' corresponds to modifying the weightage factor exp [-(m2s)] to exp \{-[m2s+(L2P/s)]\}. In this paper, we use this modified weightage factor in Schwinger's proper time formalism to evaluate the quantum gravitational corrections to some of the standard quantum field theoretic results in flat and curved spacetimes. In flat spacetime, we evaluate the corrections to (1) the Casimir effect, (2) the effective potential for a self-interacting scalar field theory, (3) the effective Lagrangian for a constant electromagnetic background and (4) the thermal effects in Rindler coordinates. In arbitrary curved spacetime, we evaluate the corrections to (1) the effective Lagrangian for the gravitational field and (2) the trace anomaly. In all these cases, we first briefly present the conventional result and then go on to evaluate the corrections with the modified weightage factor. We find that the extra factor exp [-(L2P/s)] acts as a regulator at the Planck scale thereby ``removing'' the divergences that otherwise appear in the theory. Finally, we discuss the wider implications of our analysis.
Initial state of matter fields and trans-Planckian physics: Can CMB observations disentangle the two?
(American Physical Society, 2005-05-17) Sriramkumar, L.; Padmanabhan, T.
The standard, scale-invariant, inflationary perturbation spectrum will be modified if the effects of trans- Planckian physics are incorporated into the dynamics of the matter field in a phenomenological manner, say, by the modification of the dispersion relation. The spectrum also changes if we retain the standard dynamics but modify the initial quantum state of the matter field. We show that, given any spectrum of perturbations, it is possible to choose a class of initial quantum states which can exactly reproduce this spectrum with the standard dynamics.We provide an explicit construction of the quantum state which will produce the given spectrum. We find that the various modified spectra that have been recently obtained from ‘‘trans-Planckian considerations’’ can be constructed from suitable squeezed states above the Bunch- Davies vacuum in the standard theory. Hence, the CMB observations can, at most, be useful in determining the initial state of the matter field in the standard theory, but it can not help us to discriminate between the various Planck scale models of matter fields.We study the problem in the Schrodinger picture and determine the criterion for negligible back reaction due to modified initial conditions.
Limits on the validity of the semiclassical theory
(2015-01-25) Sriramkumar, L.
For want of a more natural proposal, it is generally assumed that the back-reaction of a quantised matter field on a classical metric is given by the expectation value of its energy-momentum tensor, evaluated in a specified state. This proposal can be expected to be quite sound only when the fluctuations in the energy-momentum tensor of the quantum field are negligible. Based on this condition, a dimensionless criterion has been suggested earlier by Kuo and Ford for drawing the limits on the validity of this semiclassical theory. In this paper, we examine this criterion for the case of a toy model, constructed with two degrees of freedom and a coupling between them that exactly mimics the behaviour of a scalar field in a Friedmann universe. To reproduce the semiclassical regime of the field theory, in the toy model, one of degrees of freedom is assumed to be classical and the other quantum mechanical. Also the back reaction is assumed to be given by the expectation values of the quantum operators involved in the equations of motion for the classical system. Motivated by the same physical reasoning as Kuo and Ford, we, here, suggest another criterion, one which will be shown to perform more reliably as we evaluate these criterions for different states of the quantum system in the toy model. Finally, from the results obtained we conclude that the semiclassical theory being considered for the toy model is reliable, during all stages of its evolution, only if the quantum system is specified to be in coherent like states. The implications of these investigations on field theory are discussed.
Nontrivial classical backgrounds with vanishing quantum corrections
(American Physical Society, 1996-11-15) Sriramkumar, L.; Mukund, R.; Padmanabhan, T.
Vacuum polarization and particle production effects in classical electromagnetic and gravitational back-grounds can be studied by the effective Lagrangian method. Background ﬁeld conﬁgurations for which the effective Lagrangian is zero are special in the sense that the lowest order quantum corrections vanish for such conﬁgurations. We propose here the conjecture that there will be neither particle production nor vacuum polarization in classical ﬁeld conﬁgurations for which all the scalar invariants are zero. We verify this conjec-ture, by explicitly evaluating the effective Lagrangian, for nontrivial electromagnetic and gravitational back-grounds with vanishing scalar invariants. The implications of this result are discussed.
Oscillation in the inflaton potential: Exact numerical analysis and comparison with the recent and forthcoming CMB datasets
(2011-06-15) Aich, Moumita; Hazra, Dhiraj Kumar; Sriramkumar, L.; et al.
Amongst the multitude of inﬂationary models currently available, models that lead to features in the primordial scalar spectrum are drawing increasing attention, since certain features have been found to provide a better ﬁt to the CMB data than the conventional, nearly scale invariant, primordial spectrum. In this work, we carry out an exact numerical analysis of two models that lead to oscillations over all scales in the scalar power spectrum. We consider the model described by a quadratic potential which is superposed by a sinusoidal modulation and the recently popular axion monodromy model. Since the oscillations continue even onto smaller scales, in addition to the WMAP data, we also compare the models with the small scale data from ACT. Though, both the models, broadly, result in oscillations in the spectrum, interestingly, we ﬁnd that, while the monodromy model leads to a considerably better ﬁt to the data in comparison to the standard power law spectrum, the quadratic potential superposed with a sinusoidal modulation does not improve the ﬁt to a similar extent. We also carry out forecasting of the parameters using simulated Planck data for both the models. We show that the Planck mock data performs better in constraining the model parameters as compared to the presently available CMB datasets.
Path integral duality modiﬁed propagators in spacetimes with constant curvature
(American Physical Society, 2009-08-10) Kothawala, Dawood; Sriramkumar, L.; Shankaranarayanan, S.; Padmanabhan, T.
The hypothesis of path integral duality provides a prescription to evaluate the propagator of a free, quantum scalar field in a given classical background, taking into account the existence of a fundamental length, say, the Planck length LP in a locally Lorentz invariant manner. We use this prescription to evaluate the duality modified propagators in spacetimes with constant curvature (exactly in the case of one spacetime, and in the Gaussian approximation for another two), and show that (i) the modified propagators are ultraviolet finite, (ii) the modifications are nonperturbative in LP, and (iii) LP seems to behave like a "zero point length" of spacetime intervals such that σ2(x,x') =[σ2(x,x')+O(1)LP2], where σ(x,x') is the geodesic distance between the two spacetime points x and x', and the angular brackets denote (a suitable) average over the quantum gravitational fluctuations. We briefly discuss the implications of our results.
Plane waves viewed from an accelerated frame: Quantum physics in a classical setting
(American Physical Society, 1997-04-14) Srinivasan, K.; Sriramkumar, L.; Padmanabhan, T.
We report here an analogue for the vacuum state in classical field theory and its Planckian nature with respect to uniformly accelerated observers. We find that when a real, monochromatic mode of a classical field is Fourier transformed with respect to the proper time of a uniformly accelerating observer, the resulting power spectrum has three separate terms none of which have a simple classical meaning. But they bear a striking resemblance to the quantum mechanical description. Specifically, the three terms are (i) a factor (1/2) that is typical of the ground state energy of a quantum oscillator, (ii) a Planckian distribution N(Ω) and, most importantly, (iii) a term proportional to √N(N+1), which is the root mean square fluctuations about the Planckian distribution. The implications of this result are discussed.
Possible quantum interpretation of certain power spectra in classical field theory
(World Scientific Publication Company, 1997-03-13) Srinivasan, K.; Sriramkumar, L.; Padmanabhan, T.
In this paper we report an analogue for the vacuum state in classical field theory and its Planckian nature with respect to uniformly accelerated observers. When a real, monochromatic, mode of a scalar field is Fourier analyzed with respect to the proper time of a uniformly accelerating observer, the resulting power spectrum consists of three terms none of which have a simple classical meaning. Specifically, the three terms are (i) a factor (1/2) that is typical of the ground state energy of a quantum ascillator, (ii) a Planckian distribution N(Ω) and — most importantly — (iii) a term , which is the root mean aquare fluctuations about the Planckian distribution. It is the appearance of the root mean square fluctuations that motivates us to attribute a "thermal" nature to the power spectrum. Such a power spectrum also arises when we Fourier analyze a real, monochromatic, plane electromagnetic wave in the frame of a uniformly accelerating observer. We also present a model of a detector whose response is the Fourier spectrum of the field with respect to its proper time, which illustrates that it should, in principle, be possible to physically measure the power spectrum we have obtained. These results show that some of the "purely" quantum mechanical results might have a classical analogue.
Probes of the vacuum structure of quantum fields in classical backgrounds
(2000-11-12) Sriramkumar, L.; Padmanabhan, T.
We compare the diﬀerent approaches presently available in literature to probe the vacuum structure of quantum ﬁelds in classical electromagnetic and gravitational backgrounds. We compare the results from the Bogolubov transformations and the eﬀective Lagrangian approach with the response of monopole detectors (of the Unruh-DeWitt type) in non-inertial frames in ﬂat spacetime and in inertial frames in diﬀerent types of classical electromagnetic backgrounds. We also carry out such a comparison in inertial and rotating frames when boundaries are present in ﬂat spacetime. We ﬁnd that the results from these diﬀerent approaches do not, in general, agree with each other. We attempt to identify the origin of these diﬀerences and then go on to discuss its implications for classical gravitational backgrounds.
Probes of vacuum structure of quantum fields in classical backgrounds
(World Scientiﬁc Publishing Company, 2000-10-04) Sriramkumar, L.; Padmanabhan, T.
We compare the different approaches presently available in literature to probe the vacuum structure of quantum fields in classical electromagnetic and gravitational back- grounds. We compare the results from the Bogolubov transformations and the effective Lagrangian approach with the response of monopole detectors (of the Unruh - DeWitt type) in noninertial frames in ﬂat spacetime and in inertial frames in different types of classical electromagnetic backgrounds. We also carry out such a comparison in inertial and rotating frames when boundaries are present in ﬂat spacetime. We find that the results from these different approaches do not, in general, agree with each other. We attempt to identify the origin of these differences and then go on to discuss its implications for classical gravitational backgrounds.
Scalar bi-spectrum in the Starobinsky model
(2011-08-12) Sriramkumar, L.
Tensor-to-scalar ratio in punctuated inflation
(2009-01-01) Jain, Rajeev Kumar; Chingangbam, Pravabati; Sriramkumar, L.
Recently, we have shown that scalar spectra with lower power on large scales and certain other features naturally occur in punctuated inﬂation, i.e. the scenario wherein a brief period of rapid roll is sandwiched between two stages of slow roll inﬂation. Such spectra gain importance due to the fact that they can lead to a better ﬁt of the observed Cosmic Microwave Background (CMB) anisotropies, when compared to the conventional, featureless, power law spectrum. In this paper, with examples from the canonical scalar ﬁeld as well as the tachyonic models, we illustrate that, in punctuated inﬂation, a drop in the scalar power on large scales is always accompanied by a rise in the tensor power and, hence, an even more pronounced increase in the tensor-to-scalar ratio ron these scales. Interestingly, we ﬁnd that r actually exceeds well beyond unity over a small range of scales. To our knowledge, this work presents for the ﬁrst time, examples of single scalar ﬁeld inﬂationary models wherein r ≫ 1. This feature opens up interesting possibilities. For instance, we show that the rise in r on large scales translates to a rapid increase in the angular power spectrum, CBB ℓ , of the B-mode polarization of the CMB at the low multipoles. We discuss the observational implications of these results.