arXiv subjects
Publications and source records attributed to Arundhati Dasgupta.
We suggest that quantum algorithms can be used to model classical stochastic simulations as the measurement process is inherently random. To illustrate, we solve the classical Lorenz system with stochastic behavior using a Python random number generator. We compare the classical stochasticity of the Lorenz system with the measured output of the system obtained using quantum algorithms.
Quark-Gluon Plasma (QGP), a strongly interacting state of the early universe, exhibits remarkably fluid-like behavior despite its underlying non-Abelian dynamics. Motivated by these features, we explore time-dependent SU(2) Yang-Mills condensates as non-linear classical background fields to model QGP. We first study quarks in gluon backgrounds and show that quark back-reaction can break the isotropy of the condensate for certain initial conditions. We then compute the one-loop finite-temperature effective action using the background-field method and heat-kernel expansion. The resulting thermodynamic pressure increases with temperature but exhibits an approximately logarithmic dependence. This is expected, as this is the de-confined phase of QGP; it is not exactly an ideal gas due to self-interaction. We also perform lattice calculations for the system to contrast continuum and lattice perspectives. We then add the GW to the thermodynamic QGP model and show that certain frequencies of the GW can induce instabilities in the QGP. Our analysis explores the limitations and role of non-perturbative, time-dependent backgrounds in semi-classical description of Yang-Mills dynamics.
We discuss the effect of `Rindler like' transformation in superspace on the WKB wavefunction in cosmology. In the transformed frame we find the density matrix of the WKB wavefunction is mixed, and this is the sign of a thermal system. This background independent result does not have the same interpretations of a particle thermalization in accelerated frames. One can however show the super space transformation is similar to a double Rindler transformation of real space-time coordinates in the semi-classical regime. We also discuss the implications of the super-space transformation in loop quantum cosmology.
In this article, we investigate the interactions of a Yang-Mills (YM) wave fluctuation of a classical isotropic, homogeneous YM condensate, which models gluon plasma, with a Gravitational Wave (GW). We re-analyse the study of fluctuations of the gluon plasma using vector decomposition of the gauge field into scalar, longitudinal, and transverse modes. We find that there is an energy transfer between isotropic gluon condensate and plasmon modes, but the effect is delayed, and dependent on the initial conditions. We also studied quarks in the background of YM condensate and GW. We find that the quarks break the isotropy of the condensate and the GW couples quarks of different flavours of the SU(2) group. The GW induces flavour fluctuations, and this has interesting implications for experimental observations and quark-gluon plasma physics.
We develop a hybrid classical-quantum method for solving the Lorenz system. We use the forward Euler method to discretize the system in time, transforming it into a system of equations. This set of equations is solved using the Variational Quantum Linear Solver (VQLS) algorithm. We present numerical results comparing the hybrid method with the classical approach for solving the Lorenz system. The simulation results demonstrate that the VQLS method can effectively compute solutions comparable to classical methods. The method is easily extended to solving similar nonlinear differential equations.
In this paper, we discuss the interaction of non-Abelian SU(2) Yang-Mills progressive waves with gravitational waves. We solve and obtain some interesting solutions to pure Yang-Mills equations in different backgrounds, and perturbative solutions induced due to gravitational waves. These perturbations show `beat patterns' and depending on boundary conditions, changes in frequency. In flat space-time, when the Yang-Mills fields and the gravitational waves are in the same direction there is no interaction, unless there is self interaction of the Yang-Mills fields. In the system with non-zero self interaction the amplitudes of the perturbation are inversely proportional to the Yang-Mills coupling constant. In a cosmological background, the Yang-Mills fields and the gravitational wave interact when they are in the same direction even without self interaction of the Yang-Mills progressive fields. We find that in the electroweak symmetry broken phase of the gauge fields, the interactions are perturbative only for an infinitesimal time.
We discuss the semi-classical gravitational wave corrections to Gauss's law, and obtain an explicit solution for the electromagnetic potential. The Gravitational Wave perturbs the Coulomb potential with a function which propagates to the asymptotics.
In this brief article we discuss the corrections to the photon orbits of a non-rotating black hole due to semiclassical fluctuations of the metric. It is found that the photon orbit impact parameter differences with the critical impact parameter become of the order of the semiclassical fluctuations. We calculate the effect of the semi-classical fluctuations on the photon orbits and show that instead of circulating the black hole infinite number of times at the critical orbit, the photons bounce off the semiclassical geometry.
With the discovery of gravitational waves, the search for the quantum of gravity, the graviton, is imminent. We discuss the current status of the bounds on graviton mass from experiments as well as the theoretical understanding of these particles. We provide an overview of current experiments in astrophysics such as the search for Hawking radiation in gamma-ray observations and neutrino detectors, which will also shed light on the existence of primordial black holes. Finally, the semiclassical corrections to the image of the event horizon are discussed.
It is important to re-examine some of the interactions of gravitational waves with matter due to the recent discovery of the waves in LIGO. In a previous paper with Morales, interaction of gravitational waves was studied with scalar and neutrino fields in Minkowski space-time. In this paper, we find that electromagnetic waves have a similar interaction with gravitational wave in a flat background, and we comment on the implications of this for a gravitational wave detector. Primordial gravitational waves were generated in the early universe and thus it is important to study interaction of the gravitational waves in cosmological backgrounds. In this paper we discuss the interaction of electromagnetic waves and gravitational waves in a de-Sitter background. We find that the electromagnetic wave is perturbed and modulated. This result is new and will be useful in studying inhomogeneities in Cosmic Microwave Background.
Given that gravitational waves are the future probes of the universe, it is important to test various physical effects of these on matter. This article explores the first-order perturbation, caused by a planar gravitational wave, on massless scalar and chiral fermions. We find a new propagating mode for the perturbed fields with a new dispersion relation by solving inhomogeneous differential equations. We also discuss the massive scalar field, and find interesting effects due to the gravitational wave. Our results have physical implications for early universe cosmology and also for ground-based observations, where the new mode might be able to help in the gravitational waves' detection on earth.
In this paper we re-investigate the Bogoliubov transformations which relate the Minkowski inertial vacuum to the vacuum of an accelerated observer. We implement the transformation using a non-unitary operator used in formulations of irreversible systems by Prigogine. We derive a Lyapunov function which signifies an irreversible time flow. We extend the formalism to the black hole space-time which has similar near-horizon geometry of an accelerated observer, and in addition show that thermalization is due to presence of black hole and white hole regions. Finally we discuss an attempt to generalize quantum field theory for accelerated frames using this new connection to Prigogine transformations.
In this article we explore the origin of black hole thermodynamics using semiclassical states in loop quantum gravity. We re-examine the case of entropy using a density matrix for a coherent state and describe correlations across the horizon due to SU(2) intertwiners. We further show that Hawking radiation is a consequence of a non-Hermitian term in the evolution operator, which is necessary for entropy production or depletion at the horizon. This non-unitary evolution is also rooted in formulations of irreversible physics.
We re-examine vacuum polarisation of a scalar field in a quasi-local volume including the horizon. We find that Hawking radiation rate is derived as a pure decay of vacuum due to scalar field interaction with classical gravity exactly in the same way as the origin of vacuum polarisation effect in Electrodynamics.
Using a new effective action predicted from quantum gravity where the sign of the Euclidean Einstein action is reversed we discuss WKB solutions in quantum cosmology and predict that this sign change might explain the origin of phantom scalars.
In this article a description is given of the measure in Euclidean path-integral in quantum gravity, and recent results using the Faddeev-Popov method of gauge fixing. The results suggest that the effective action is finite and positive.
We study semiclassical corrections to the Schwarzchild metric, and their effects on unstable orbits.
A density matrix is defined using coherent states for space-times with apparent horizons. Evolving the density matrix in time gives the origin of Hawking radiation.