arXiv subjects

Karthik Rajeev

Publications and source records attributed to Karthik Rajeev.

At least 19 recordsLinked to original sources

arXiv2026

Thermalization from quenching in coupled oscillators

We introduce a finite-time protocol that thermalizes a quantum harmonic oscillator, initially in its ground state, without requiring a macroscopic bath. The method uses a second oscillator as an effective environment and implements sudden quenches of the oscillator frequencies and coupling. Owing to the Gaussian nature of the dynamics, the thermalization condition reduces to three solvable equations, yielding exact analytic solutions for a dense discrete set of temperatures and numerical solutions in all other cases. Any target temperature can be approximated with arbitrary precision, with a trade-off between speed and accuracy. The simplicity of the protocol makes it a promising tool for rapid, controlled thermalization in quantum thermodynamics experiments and state preparation.

quant-ph↗

arXiv2026

Scattering in strong field QED in a non-null background

We examine scattering amplitudes for an arbitrary number of photons in a class of non-null background electromagnetic fields, studying tree-level and one-loop amplitudes in scalar and spinor quantum-electrodynamics in backgrounds defined by a gauge field $A_μ(\mathfrak{n}\cdot x)$ for $\mathfrak{n}^2\neq 0$. Motivated to account for more physically realistic laser-plasma dispersive properties, our approach overcomes prior work studying such amplitudes in a constant background field and relaxes the familiar null criterion assumed for plane waves. Master Formulae for the $N$-photon amplitudes dressed by the non-null background are constructed using the first-quantised worldline formalism, which can systematically account for all orders in the non-null parameter, $\mathfrak{n}^2$, treated here as an expansion parameter. These are derived from worldline representations of the coordinate and momentum space propagators (and their LSZ-truncated amplitudes) and the effective action, each incorporating the non-null background non-perturbatively. We then outline a partial resummation of their expansions in $\mathfrak{n}^{2}$. A special exactly solvable case of non-null constant crossed fields without photon insertion in the effective action is explored to test the Master Formulae that result. The validity of the presented master formulae is further checked against known expressions for the wavefunction and non-linear Compton scattering in a non-null background to lowest order in the non-null parameter.

hep-th↗

arXiv2026

The ABCs of Amplitudes, Bogoliubov and Crossing

It is now common to describe classical backgrounds involving dynamical black holes with the production of gravitational radiation using the methods of scattering amplitudes. In that light, we revisit the standard formulation of quantum field theory on a background. We discuss the interpretation of Bogoliubov coefficients as generalised amplitudes, and explain how crossing, analyticity, and causality relate the relevant set of amplitudes. When the background is itself a coherent state, we map these statements onto standard results in flat-space quantum field theory.

hep-th↗

arXiv2026

Hawking radiation from the double copy

Gravity and gauge theory are concretely linked by the double copy. Although well-studied at the level of perturbative scattering in vacuum, far less is known about non-perturbative aspects or extensions of the double copy beyond trivial backgrounds. We show here how Hawking radiation in a collapse metric, its associated thermal spectrum, and horizon-dependence, emerges from the double copy of particle production in a background gauge field, where there is no global horizon, nor a thermal spectrum. Our approach combines worldline and amplitudes methods, and allows the unification of several classical and quantum double copy prescriptions for black hole spacetimes.

hep-th↗

arXiv2026

Entanglement scaling and dynamics in the Sauter-Schwinger effect

In quantum field theory, entanglement entropy under spatial bipartitioning serves as a powerful information-theoretic probe of quantum correlations. In this work, we present the first comprehensive numerical study of the dynamical evolution and geometric scaling of entanglement entropy in a nonperturbative, strong-field QED setting -- specifically, in the context of the Sauter-Schwinger effect. While the weak-field regime is dominated by area-law states, we show that the entanglement entropy undergoes a transition from area-law to a volume-law scaling for certain strong-field regimes in the pulse-profile parameter space -- signaling a fundamental shift in the underlying correlation structure induced by nonperturbative pair production. For intermediate regimes, the scaling is a power-law that interpolates between area- and volume-law behavior. Finally, we provide interpretations based on the behavior of the low-energy pair-creation spectrum and discuss how these insights could inform future investigations of related phenomena.

hep-th↗

arXiv2025

Tunnelling amplitudes and Hawking radiation from worldline QFT

We compare Hawking radiation in a collapse background with Schwinger pair creation in an electric field. The comparison is driven by the presence of an analogue horizon in the Schwinger case, which causally divides spacetime for classical particles, but through which quantum fields can tunnel. Amplitudes for tunnelling processes are encoded in the asymptotic behaviour of solutions to the appropriate background-coupled wave equation. We construct these solutions, in both gravity and QED, using the worldline approach, where tunnelling and particle creation manifest as complex saddle points of a real-time path integral. For the Schwinger effect, these saddles correspond to complex worldlines, while for Hawking radiation, the corresponding worldlines are real, but appear complex when extended beyond a certain coordinate patch.

hep-th↗

arXiv2025

Worldline Modeling of Ultra-Intense Lasers for N-photon Scattering Processes

The modeling of present and future ultra-intense lasers demands techniques that go beyond the standard diagrammatic approach to non-perturbatively fully capture the effects of strong fields. We illustrate the first-quantized path integral representation for strong-field quantum electrodynamics as a means of accessing the laser being treated as a background field, which is treated without recourse to perturbation theory. We examine an all-multiplicity construction for $N-$photon scattering processes for complex scalars and spinors, showing compact Master Formulae for tree-level scattering. Several background fields are considering including: plane waves, impulsive PP-waves, non-null fields, and homogeneous fields (constant-crossed fields) with low-energy external photons.

hep-ph↗

arXiv2025

Pair creation, backreaction, and resummation in strong fields

We revisit particle creation in strong fields, and backreaction on those fields, from an amplitudes perspective. We describe the strong field by an initial coherent state of photons which we explicitly evolve in time, thus going beyond the background field approximation, and then consider observables which quantify the effects of backreaction. We present expressions for the waveform, vacuum persistence probability, and number of produced photons at next-to-leading order, all of which are impacted by backreaction, along with the number and statistics of produced pairs. We find that converting between in-out (amplitude) and in-in (expectation value) expressions requires explicit resummation of an infinite number of disconnected loop diagrams.

hep-ph↗

arXiv2024

All-multiplicity amplitudes in impulsive PP-waves from the worldline formalism

We use the worldline formalism to derive Bern-Kosower type Master Formulae for the tree-level scattering of a charged particle and an arbitrary number of photons on impulsive PP-waves, where the coupling of the PP-wave to matter is treated fully non-perturbatively. We show that, in a certain kinematic regime characterised by a semi-classical positive energy condition, both off-shell currents and scattering amplitudes exhibit two novel factorisation structures. First, they may be written as currents in vacuum but with a single additional photon, averaged over the momentum of that photon. This converts the all-orders interaction with the PP-wave into a single effective interaction. Second, the currents and amplitudes may be written as a weighted average of the corresponding quantities in an impulsive plane wave background, with the average taken over all possible field strengths of the plane wave. This generalises a known single-photon result to arbitrary multiplicity.

hep-th↗

arXiv2023

Real-space quantum-to-classical transition of time dependent background fluctuations

Understanding the emergence of classical behavior from a quantum theory is vital to establishing the quantum origin for the temperature fluctuations observed in the Cosmic Microwave Background (CMB). We show that a real-space approach can comprehensively address the quantum-to-classical transition problem in the leading order of curvature perturbations. To this end, we test spatial bipartitions of quadratic systems for the interplay between three different signatures of classical behavior: i) decoherence, ii) peaking of the Wigner function about classical trajectories, and iii) relative suppression of non-commutativity in observables. We extract these signatures from the covariance matrix of a multi-mode Gaussian state and address them primarily in terms of entanglement entropy and log-classicality. Through a phase-space stability analysis of spatial sub-regions via their reduced Wigner function, we ascertain that the underlying cause for the dominance of classicality signatures is the occurrence of gapped inverted mode instabilities. While the choice of conjugate variables enhances some of these signatures, decoherence studied via entanglement entropy is the stronger and more reliable condition for classicality to emerge. We demonstrate the absence of decoherence, which preempts a quantum-to-classical transition of scalar fluctuations in an expanding background in $(1+1)$-dimensions using two examples: i) a Tanh-like expansion and ii) a de-Sitter expansion. We provide connection between log classicality and particle number by studying the evolution of each normal mode at late times. We then extend the analysis to leading order fluctuations in $(3+1)-$dimensions to show that a quantum-to-classical transition occurs in the de-Sitter expansion and discuss the relevance of our analysis in distinguishing cosmological models.

gr-qc↗

arXiv2023

Master Formulae for $N$-photon tree level amplitudes in plane wave backgrounds

The presence of strong electromagnetic fields adds huge complexity to QED Feynman diagrams, such that new methods are required to calculate higher-loop and higher-multiplicity scattering amplitudes. Here we use the worldline formalism to present `Master Formulae' for all tree level amplitudes of two massive particles and an arbitrary number of photons, in a plane wave background, in both scalar and spinor QED. The plane wave is treated without approximation throughout, meaning in particular that our formulae are valid in the strong-field regime of current theoretical and experimental interest. We check our results against literature expressions obtainable at low multiplicity via direct Feynman diagram calculations.

hep-th↗

arXiv2022

Effective-one-body formalism for leading-order radiative effects in the post-linear framework

In recent years, significant progress has been made in the computation of conservative and dissipative scattering observables using the post-Minkowskian approach to gravitational dynamics. However, for accurate modeling of unbound orbits, an appropriate effective-one-body (EOB) resummation of the post-Minkowski results that also accounts for dissipative dynamics is desirable. As a step in this direction, we consider the electromagnetic analog of this problem here. We show that a six-parameter equation of motion encapsulates the effective-one-body dynamics for the electromagnetic scattering problem appropriate to third-order in the coupling constant. Three of these six parameters describe the conservative part of the dynamics, while the rest correspond to the radiation-reaction effects. Here we show that only two radiation-reaction-related parameters are important at the desired order, making the effective number of parameters in our formalism to be five. We compute the explicit forms of these five parameters by matching EOB scattering observables to that of the original two-body ones computed by [Saketh et al., Phys.Rev.Res. 4 (2022) 1]. Interestingly, our formalism leads to a conjecture for the sub-leading angular momentum loss, for which no precise computations exist. In addition, we demonstrate that the bound-orbit observables computed using our method are in perfect agreement with those calculated using unbound-to-bound analytical continuation techniques. Lastly, we qualitatively discuss the extension of our formalism to gravity.

gr-qc↗

arXiv2022

Wave function of the Universe as a sum over eventually inflating universes

We consider a proposal to define the wave function of the Universe as a sum over spacetimes that eventually inflate. In the minisuperspace model, we explicitly show that a simple family of initial conditions, parametrized by a positive real number $a_0$, can be imposed to realise this prescription. The resulting wave function is found to be proportional to the Hartle-Hawking wave function and its dependence on $a_0$ is only through an overall phase factor. Motivated by this observation, we ask whether it is possible to analytically extend $a_0$ to an extended region $\bar{\mathcal{D}}$ in complex $a_0-$plane, while retaining the Hartle-Hawking form of the wave function. We use the condition for convergence of path integral and a recent theorem due to Kontsevich and Segal, further extended by Witten, to explicitly find $\bar{\mathcal{D}}$. Interestingly, a special point on the boundary of $\bar{\mathcal{D}}$ recovers the exact no-boundary wave function. Following that, we show that our prescription leads to a family of quantum states for the perturbations, which give rise to scale-invariant power spectra. If we demand, as an extra ingredient to our prescription, a matching condition at the "no-boundary point" in $\bar{\mathcal{D}}$, we converge on a unique quantum state for the perturbations.

gr-qc↗

arXiv2022

New Kind of Echo from Quantum Black Holes

We propose that a quantum black hole can produce a new kind of late-time gravitational echoes, facilitated by a near-horizon process analogous to Andreev reflection in condensed matter systems. In comparison to the traditional echo scenarios where the near-horizon region is treated as an ordinary reflector, we argue that, consequent to near-horizon gravitational scattering, this region is better described by an Andreev reflector. Such interactions lead to a novel contribution to gravitational echoes with a characteristic phase difference, an effect which is analogous to how Andreev reflections lead to propagating particle-like and hole-like components with a relative phase in certain condensed matter scenarios. Moreover, this novel contribution to the echo signal encodes information about the `near-horizon quantum state', hence offering a possible new window to probe the quantum nature of black holes.

gr-qc↗

arXiv2022

Bouncing with shear: Implications from quantum cosmology

We consider the introduction of anisotropy in a class of bouncing models of cosmology. The presence of anisotropy often spells doom on bouncing models, since the energy density due to the anisotropic stress outweighs that of other matter components, as the universe contracts. Different suggestions have been made in the literature to resolve this pathology, classically. Here, we introduce a family of bouncing models, in which the shear density can be tuned to either allow or forbid classical bouncing scenarios. Following this, we show that quantum cosmological considerations can drastically change the above scenario. Most importantly, we find that quantum effects can enable a bounce, even when the anisotropic stress is large enough to forbid the same classically. We employ the solutions of the appropriate mini-superspace Wheeler-DeWitt equation for homogeneous, but anisotropic cosmologies, with the boundary condition that the universe is initially contracting. Intriguingly, the solution to the Wheeler-DeWitt equation exhibit an interesting phase transition-like behaviour, wherein, the probability to have a bouncing universe is precisely unity before the shear density reaches a critical value and then starts to decrease abruptly as the shear density increases further. We verified our findings using the tools of the Lorentzian quantum cosmology, along with the application of the Picard-Lefschetz theory. In particular, the semi-classical probability for a bounce has been re-derived from the imaginary component of the on-shell effective action, evaluated at the complex saddle points. Implications and future directions have also been discussed.

gr-qc↗

arXiv2021

Lorentzian worldline path integral approach to Schwinger effect

We demonstrate that the positive frequency modes for a complex scalar field in a constant electric field (Schwinger modes), in three different gauges, can be represented as exact Lorentzian worldline path integral amplitudes. Although the mathematical forms of the mode functions differ in each gauge, we show that a simple prescription for Lorentzian worldlines' boundary conditions dispenses the Schwinger modes in all three gauges (that we considered) in a unified manner. Following that, using our formalism, we derive the exact Bogoliubov coefficients and, hence, the particle number, \textit{without} appealing to the well-known connection formulas for parabolic cylinder functions. This result is especially relevant in view of the fact that in a general electromagnetic field configuration, one does not have the luxury of closed-form solutions. We argue that the real time worldline path integral approach may be a promising alternative in such non-trivial cases. We also demonstrate, using Picard-Lefschetz theory, how the so-called worldline instantons emerge naturally from relevant saddle points that are complex.

hep-th↗

arXiv2021

No-boundary Wave Function, Wheeler-DeWitt Equation and Path Integral Analysis of the Bouncing `Quantum' Cosmology

Bouncing models are alternatives to inflationary cosmology that replace the initial Big-Bang singularity by a `bouncing' phase. A deeper understanding of the initial conditions of the universe, in these scenarios, requires knowledge of quantum aspects of bouncing models. In this work, we propose two classes of bouncing models that can be studied with great analytical ease and hence, provide test-bed for investigating more profound problems in quantum cosmology of bouncing universes. Our model's two key ingredients enable us to do straightforward analytical calculations: (i) a convenient parametrization of the minisuperspace of FRLW spacetimes and (ii) two distinct choices of the effective perfect fluids that source the background geometry of the bouncing universe. We study the quantum cosmology of these models using both the Wheeler-de Witt equations and the path integral approach. In particular, we found a bouncing model analogue of the no-boundary wavefunction and presented a Lorentzian path integral representation for the same. We also discuss the introduction of real scalar perturbations.

gr-qc↗

arXiv2020

Exploring the Rindler vacuum and the Euclidean Plane

In flat spacetime, two inequivalent vacuum states which arise rather naturally are the Rindler vacuum (R) and the Minkowski vacuum (M). We disuss several aspects of the Rindler vacuum, concentrating on the propagator and Schwinger (heat) kernel defined using R, both in the Lorentzian and Euclidean sectors. We start by exploring an intriguing result due to Candelas and Raine , viz., that $G_{R}$, the Feynman propagator corresponding to R, can be expressed as a curious integral transform of $G_{M}$, the Feynman propagator in M. We show that, this relation actually follows from the well known result that, $G_{M}$ can be written as a periodic sum of $G_{R}$, in the Rindler time $τ$, with the period $2πi$. We further show that, the integral transform result holds for a wide class of pairs of bi-scalars $(F_{M},F_{R})$, provided $F_{M}$ can be represented as a periodic sum of $F_{R}$ with period $2πi$. We provide an explicit procedure to retrieve $F_{R}$ from its periodic sum $F_{M}$, for a wide class of functions. An example of particular interest is the pair of Schwinger kernels $(K_{M},K_{R})$, corresponding to the Minkowski and the Rindler vacua. We obtain explicit expression for $K_{R}$ and clarify several conceptual and technical issues related to these biscalars both in the Euclidean and Lorentzian sector. In particular we address the issue of retrieving the information contained in all the four wedges of the Rindler frame in the Lorentzian sector, starting from the Euclidean Rindler (polar) coordinates. This is possible but require four different types of analytic continuations, based on one unifying principle. Our procedure allows generalisation of these results to any (bifurcate Killing) horizon in curved spacetime.

gr-qc↗