arXiv subjects

Sujoy K. Modak

Publications and source records attributed to Sujoy K. Modak.

At least 19 recordsLinked to original sources

arXiv2026

Closed form perturbative relativistic modifications to wave-packet dynamics in the quantum harmonic oscillator

We derive closed form expressions of weak relativistic corrections to the wave-packet dynamics of the quantum harmonic oscillator within a perturbative framework. General expressions are derived for the leading-order relativistic contributions to wave-packet parameters, such as the time-dependent widths, variances, and uncertainty relations. Specific calculations are performed for unsqueezed, minimum-uncertainty Gaussian wave packets, valid up to leading order in ($1/c^{2}$). When applied to electron wave packets, the results indicate that relativistic effects become non-negligible for keV-scale harmonic confinement energies: the deviations in variances reach $0.15\% - 1.5\%$ for an electron wave packet confined within the $1-10 \mathrm{keV}$ energy range. We also show that the standard saturation of the uncertainty relation remains unaffected by the leading-order relativistic effect.

quant-ph↗

arXiv2024

Recent Efforts Towards Understanding the Early Universe from a Fundamental Quantum Perspective

The observable universe is fundamentally inhomogeneous and anisotropic. Quantum description of the generation of these inhomogeneities and anisotropies is ill-understood and unsatisfactory. After providing a brief account of the standard approach of the generation of the classical density perturbations starting from the quantum fluctuations of inflaton field, I critically review various assumptions which are crucial for the success of this description, and point out various shortcomings around it. I also discuss the basic ideas and recent works by using an alternative path to overcome those shortcomings which is motivated by the so-called Collapse Model interpretation of quantum mechanics. Inspired by these works, I argue the necessity of constructing a class of manifestly inhomogeneous and anisotropic quantum states after inflation and discuss my recent works which provide one such prescription of building such a state, called the $T-$vacuum, defined in the radiation dominated stage of the early universe.

gr-qc↗

arXiv2023

Anisotropic particle creation from $T-$vacuum in the radiation dominated universe

We further investigate novel features of the $T-$vacuum state, originally defined in the context of quantum field theory in a (1+1) dimensional radiation dominated universe [Modak, JHEP 12, 031 (2020)]. Here we extend the previous work to a realistic (3+1) dimensional set up and show that $T-$vacuum gives rise to an anisotropic particle creation phenomena in the radiation dominated early universe. Unlike the Hawking or Unruh effect, where the particle content is thermal and asymptotically defined, here it is non-thermal and instantaneous. This novel example of particle creation is interesting because these particles are detected in the frame of physical/cosmological observers, who envision $T-$vacuum as a particle excited state. Such results comes with a potential to be eventually compared with the observed anisotropies from the early universe and may provide new insights on cosmological particle creation.

gr-qc↗

arXiv2022

New insights on the quantum-classical division in light of Collapse Models

We argue, in light of Collapse Model interpretation of quantum theory, that the fundamental division between the quantum and classical behaviors is analogous to the division of thermodynamic phases. A specific relationship between the collapse parameter $(\lambda)$ and the collapse length scale ($r_C$) plays the role of the coexistence curve in usual thermodynamic phase diagrams. We further claim that our functional relationship between $\lambda$ and $r_C$ is strongly supported by the existing IGEX collaboration data. This result is preceded by a self-contained discussion of quantum measurement theory and the Ghirardi-Rimini-Weber (GRW) model applied to the free wavepacket dynamics.

quant-ph↗

arXiv2022

Semiclassical gravity with a conformally covariant field in globally hyperbolic spacetimes

We prove that semiclassical gravity in conformally static, globally hyperbolic spacetimes with a massless, conformally coupled Klein-Gordon field is well posed, when viewed as a coupled theory for the dynamical conformal factor of the metric and the Klein-Gordon theory. Namely, it admits unique and stable solutions whenever constrained fourth-order initial data for the conformal factor and suitably defined Hadamard initial data for the Klein-Gordon state are provided on a spacelike Cauchy surface. As no spacetime symmetries are imposed on the conformal factor, the present result implies that, provided constrained initial data exists, there also exist exact solutions to the semiclassical gravity equations beyond the isotropic, homogeneous or static cases.

math-ph↗

arXiv2022

A novel mechanism for probing the Planck scale with wavepackets following general distributions

It was also shown recently that GUP predicts potentially measurable corrections to the `doubling time' of freely moving Gaussian atomic and molecular wavepackets with a favorable combination of three parameters, {\it e.g.} mass, initial width and mean velocity of a travelling wavepacket. However, it is well known that such wavepackets can come with various shapes which correspond to variety of distributions. In this article, we generalize our earlier work for an {\it arbitrary distribution} and thereby accommodate any shape of the wavepacket. Mathematically, we build this formalism by exploiting a duality between quantum and statistical mechanics, by which (quantum mechanical) expectation values of the momentum operator can be expressed in terms of the derivatives of the characteristic functions of the dual statistical description. Equipped with this result, we go one step further and numerically study a few physical distributions. We find that large organic (TPPF152) wavepacket following the generalized normal distribution with parameter $\kappa=0.5$ offers one of the best-case scenarios, effectively scanning the whole GUP parameter space with current technologies. Although we do not say that the minimal length has to be near or at the Planck value, we mange improving our previous studies to scan the minimal length signatures down to hundred times the Planck value.

gr-qc↗

arXiv2021

Quantum field theory in a de Sitter universe transiting to the radiation stage

We study some physical aspects of quantum field theory in a two stage universe starting from the inflationary de Sitter and transiting into the radiation dominated stage. We look into the time evolution of the primordial vacuum states, associated with the (i) comoving and (ii) Bunch-Davies modes. We show how the power spectrum for a comoving observer, obtained from the excitation of the aforementioned states defined in the de Sitter stage, changes as the universe transits into the radiation stage. In addition, we also develop a methodology to transfer the well known result of particle creation in the static de Sitter frame, originating from the aforementioned vacuum states, while the universe makes a transition to the next (radiation dominated) stage.

gr-qc↗

arXiv2021

Cosmological Particle Creation Beyond de Sitter

Over the years, de Sitter spacetime has been a central focus, in studies involving quantum fields, for its importance in the early and late expansion stages of the universe. While de Sitter spacetime closely mimics characteristics of the inflationary and dark energy dominated universe it does not help to understand the radiation and matter dominated expansions. In this review, we revisit some recent works, involving the author, which study gravitational particle creation beyond the de Sitter stage. Specifically, we present novel aspects of particle creation in the radiation dominated universe, and then provide an analysis of time evolution of the primordial (Bunch-Davies) vacuum state, its particle excitation and quantum versus classical behavior of field modes, in a multi stage universe, comprising of, (i) the inflationary de Sitter, (ii) the radiation dominated and, (iii) the late dark energy dominated stages.

gr-qc↗

arXiv2021

A novel mechanism for probing the Planck scale

The Planck or the quantum gravity scale, being $16$ orders of magnitude greater than the electroweak scale, is often considered inaccessible by current experimental techniques. However, it was shown recently by one of the current authors that quantum gravity effects via the Generalized Uncertainty Principle affects the time required for free wavepackets to double their size, and this difference in time is at or near current experimental accuracies [1, 2]. In this work, we make an important improvement over the earlier study, by taking into account the leading order relativistic correction, which naturally appears in the systems under consideration, due to the significant mean velocity of the travelling wavepackets. Our analysis shows that although the relativistic correction adds nontrivial modifications to the results of [1, 2], the earlier claims remain intact and are in fact strengthened. We explore the potential for these results being tested in the laboratory.

gr-qc↗

arXiv2020

Physical observers, $T$-vacuum and Unruh like effect in the radiation dominated early universe

We report the existence of an Unruh like effect, for physical observers (cosmological and comoving observers) in the radiation dominated early universe, which is possible due to the discovery of a new vacuum state (referred here as the $T-$vacuum). Both the comoving and the cosmological observers, who are crucial in our understanding of cosmology, observe this $T-$vacuum as a particle excited state and are able to detect radiation due to particle creation. We draw a robust analogy with the Unruh effect, whereby -- (i) the physical observers here are closely analogous to the accelerated (Rindler) observers in the flat spacetime, and (ii) the $T-$vacuum plays the role of the Minkowski vacuum state which contains particles when viewed from the physical observers frame. Our analogy is further supported by a proof of well-defined (hadamard) behavior of the $T-$vacuum in the entire spacetime. All our analysis of the particle creation process is done here within a two dimensional set up.

gr-qc↗

arXiv2019

Indirect Probe of Quantum Gravity using Molecular Wave-packets

The most obvious obstacle behind a direct test of Quantum Gravity (QG) is its energy scale ($10^{19}$ GeV), which remains well outside of any human made machine. The next best possible approach is to provide indirect tests on effective theories of QG which can be performed in a lower energy scale. This paper is aimed in this direction, and shows a promising path to test the existence of the fundamental minimal length scale of Nature by measuring the dispersion of free, large molecular wave-packets. The existence of the minimal length is believed to be the reason for a modified commutation relationship between the position and momentum operators and, in this paper, we show that such a modification of the commutator has a profound effect on the dispersion rate of free wave-packets, and precise measurement on the broadening times of large molecular wave-packets (such as $C_{60}$, $C_{176}$ and large organic molecules) provide a promising path for an indirect test of quantum gravity, in a laboratory setting.

gr-qc↗

arXiv2019

Minimal length effect on the broadening of free wave-packets and its physical implications

We study the Generalized Uncertainty Principle (GUP) modified time evolution for the width of wave-packets for a scalar potential. Free particle case is solved exactly where the wave-packet broadening is modified by a coupling between the GUP parameter and higher order moments in the probability distribution in momentum space. We consider two popular forms of deformations widely used in the literature - one of which modifies the commutator with a quadratic term in momentum, while the other modifies it with terms both linear and quadratic in momentum. Unlike the standard case, satisfying Heisenberg uncertainty, here the GUP modified broadening rates, for both deformations, not only depend on the initial size (both in position and momentum space) of the wave-packet, but also on the initial probability distribution and momentum of the particle. The new rates of wave-packet broadening, for both situations, are modified by a handful of new terms - such as the skewness and kurtosis coefficients, as well as the (constant) momentum of the particle. Comparisons with the standard Heisenberg Uncertainty Principle (HUP)-based results show potentially measurable differences in the rates of free wave-packet broadening for physical systems such as the $C_{60}$ and $C_{176}$ molecules, and more so for large organic molecular wave-packets. In doing so, we open a path to scan the GUP parameter space by several orders of magnitude inside the best existing upper bounds for both forms of GUP.

gr-qc↗

arXiv2018

New geometric and field theoretic aspects of a radiation dominated universe

The homogeneous and isotropic radiation dominated universe, following the inflationary stage, is expressed as a spherically symmetric and inhomogeneous spacetime upon a power law type conformal transformation of the null (cosmological) coordinates. This new spacetime metric has many interesting properties. While the static observers, at a fixed position in this new spacetime, do not see any horizon, some non-static observers encounter a horizon due to their motion which is analogous to the situation of Rindler observers in Minkowski spacetime. The symmetry of the new metric offers a unitarily inequivalent quantization of the massless scalar field and provides a new example of particle creation. We calculate the particle content of the cosmological vacuum state with respect to the static observer in this new spacetime who, with respect to cosmological time, is freely falling in asymptotic past and future but accelerated in between.

gr-qc↗

arXiv2018

Does gravity cause disentanglement?

Inspired by our recent works on information paradox in black holes, which exploit various foundational intricacies of quantum mechanics, here we propose a novel connection between the spacetime geometry and quantum entanglement of matter fields "living" in that geometry. We highlight, as a natural consequence of those studies, that gravitational field might have a natural tendency of reducing entanglement between two quantum states.

gr-qc↗

arXiv2017

Collapse of the wavefunction, the information paradox and backreaction

We consider the black hole information problem within the context of collapse theories in a scheme that allows the incorporation of the backreaction to the Hawking radiation. We explore the issue in a setting of the two dimensional version of black hole evaporation known as the Russo-Susskind-Thorlacius model. We summarize the general ideas based on the semiclassical version of Einstein's equations and then discuss specific modifications that are required in the context of collapse theories when applied to this model.

gr-qc↗

arXiv2017

Modelling non-paradoxical loss of information in black hole evaporation

We give general overview of a novel approach, recently developed by us, to address the issue black hole information paradox. This alternative viewpoint is based on theories involving modifications of standard quantum theory, known as "spontaneous dynamical state reduction" or "wave-function collapse models" which were historically developed to overcome the notorious foundational problems of quantum mechanics known as the "measurement problem". We show that these proposals, when appropriately adapted and refined for this context, provide a self-consistent picture where loss of information in the evaporation of black holes is no longer paradoxical.

gr-qc↗

arXiv2016

Relativistic collapse dynamics and black hole information loss

We study a proposal for the resolution of the black hole information puzzle within the context of modified versions of quantum theory involving spontaneous reduction of the quantum state. The theories of this kind, which were developed in order to address the so called "measurement problem" in quantum theory have, in the past, been framed in a non-relativistic setting and in that form they were previously applied to the black hole information problem. Here, and for the first time, we show in a simple toy model, a treatment of the problem within a fully relativistic setting. We also discuss the issues that the present analysis leaves as open problems to be dealt with in future refinements of the present approach.

gr-qc↗

arXiv2015

Black Holes: Information Loss But No Paradox

The process of black hole evaporation resulting from the Hawking effect has generated an intense controversy regarding its potential conflict with quantum mechanics' unitary evolution. In a recent couple of works of a collaboration involving one of us, we have revised the controversy with the aims of, on the one hand, clarifying some conceptual issues surrounding it, and, at the same time, arguing that collapse theories have the potential to offer a satisfactory resolution of the so-called paradox. Here we show an explicit calculation supporting this claim using a simplified model of black hole creation and evaporation, known as the CGHS model, together with a dynamical reduction theory, known as CSL, and some speculative, but seemingly natural ideas about the role of quantum gravity in connection with the would-be singularity. This work represents a specific realization of general ideas first discussed in [1].

gr-qc↗