arXiv subjects

Sukanta Bhattacharyya

Publications and source records attributed to Sukanta Bhattacharyya.

13 recordsLinked to original sources

arXiv2024

Quantum gravity signatures in gravitational wave detectors placed inside a harmonic trap potential

In this work, we consider a general gravitational wave detector of gravitational wave interacting with an incoming gravitational wave carrying plus polarization only placed inside a harmonic trap. This model can be well acquainted with the description of a resonant detector of gravitational wave as well. The well known detector-gravitational wave interaction scenario uses the method of a semi classical approach where the detector is treated quantum mechanically but the gravitational wave is considered at a classical level. In our analysis, we use a discrete mode decomposition of the gravitational wave perturbation which results in a Hamiltonian involving the position and momentum operators corresponding to the gravitational wave and the harmonic oscillator. We have then calculated the transition probability for the harmonic oscillator-gravitational wave tensor product state for going from an initial state to some unknown final state. Using the energy flux relation of the gravitational waves, we observe that if we consider the total energy as a combination of the number of gravitons in the initial state of the detector then the transition probability for the resonant absorption case scenario takes the analytical form which is exactly similar to the semi-classical absorption case. In case of the emission scenario, we observe a spontaneous emission of a single graviton which was completely absent in the semi-classical analouge of this model. This therefore gives a direct signature of linearized quantum gravity.

hep-th↗

arXiv2024

Resonant detectors of gravitational wave in the linear and quadratic generalized uncertainty principle framework

In this work, we consider a resonant bar detector of gravitational wave in the generalized uncertainty principle (GUP) framework with linear and quadratic momentum uncertainties. The phonon modes in these detectors vibrate due to the interaction with the incoming gravitational wave. In this uncertainty principle framework, we calculate the resonant frequencies and transition rates induced by the incoming gravitational waves on these detectors. We observe that the energy eigenstates and the eigenvalues get modified by the GUP parameters. We also observe non-vanishing transition probabilities between two adjacent energy levels due to the existence of the linear order momentum correction in the generalized uncertainty relation which was not present in the quadratic GUP analysis [http://dx.doi.org/10.1088/1361-6382/abac45, Class. Quantum Grav. 37 (2020) 195006]. We finally obtain bounds on the dimensionless GUP parameters using the form of the transition rates obtained during this analysis.

gr-qc↗

arXiv2022

Path integral action for a resonant detector of gravitational waves in the generalized uncertainty principle framework

The Heisenberg uncertainty principle gets modified by the introduction of an observer independent minimal length. In this work we have considered the resonant gravitational wave detector in the modified uncertainty principle framework where we have used the position momentum uncertainty relation with a quadratic order correction only. We have then used the path integral approach to calculate an action for the bar detector in presence of a gravitational wave and then derived the Lagrangian of the system leading to the equation of motion for the configuration-space position coordinate in one dimension. We then find a perturbative solution for the coordinate of the detector for a circularly polarized gravitational wave leading to a classical solution of the same for given initial conditions. Using this classical form of the coordinate of the detector, we finally obtain the classical form of the on-shell action describing the harmonic oscillator-gravitational wave system. Finally, we have obtained the free particle propagator containing the quantum fluctuation term considering gravitational wave interaction.

gr-qc↗

arXiv2022

Generalized uncertainty principle in bar detectors of gravitational waves

At present the gravitational waves detectors achieve the sensitivity to detect the length variation ($δL$), $\mathcal{O} \approx 10^{-17}-10^{-21}$ meter. Recently a more stringent upperbound on the dimensionless parameter $β_0$, bearing the effect of generalized uncertainty principle has been given which corresponds to the intermediate length scale $l_{im}= \sqrt{β_0} l_{pl} \sim 10^{-23} m$. Hence it becomes quite obvious to search for the generalized uncertainty principle by observing the response of the vibrations of phonon modes in such resonant detectors in the near future. Therefore, we calculate the resonant frequencies and transition rates induced by the incoming gravitational waves on these detectors in the generalized uncertainty principle framework. This presentation is based on the work published in \cite{sb2}.

gr-qc↗

arXiv2022

Probing the generalized uncertainty principle through quantum noises in optomechanical systems

In this work we have considered a simple mechanical oscillator interacting with a single mode optical field inside a cavity in the generalized uncertainty principle framework (GUP). Our aim is to calculate the modified noise spectrum and observe the effects of the GUP. The commutation relation that we have considered has an extra linear order momentum term along with a quadratic order term. Confronting our theoretical results with the observational results, we observe that we get a much tighter bound on the GUP parameters from the noise spectrum using the values of the system parameters from different experiments.

quant-ph↗

arXiv2021

Path integral action in the generalized uncertainty principle framework

Various gedanken experiments of quantum gravity phenomenology in search of a complete theory of gravity near the Planck scale indicate a modification of the Heisenberg uncertainty principle to the generalized uncertainty principle (GUP). This modification leads to nontrivial contributions on the Hamiltonian of a nonrelativistic particle moving in an arbitrary potential. In this paper we study the path integral representation of a particle moving in an arbitrary potential using the most general form of the GUP containing both the linear and quadratic contributions in momentum. First we work out the action of the particle in an arbitrary potential and hence find an upper bound to the velocity of a free particle. This upper bound interestingly imposes restrictions on the relation between the GUP parameters $α$ and $β$. Analysis shows that $ β> 4 α^2$. We then deduce the mathematical expressions of classical action and the quantum fluctuations for both free particle and the harmonic oscillator systems.

quant-ph↗

arXiv2020

Generalized uncertainty principle in resonant detectors of gravitational waves

With the direct detection of gravitational waves by advanced LIGO detector, a new "window" to quantum gravity phenomenology has been opened. At present, these detectors achieve the sensitivity to detect the length variation ($δL$), $\mathcal{O} \approx 10^{-17}-10^{-21}$ meter. Recently a more stringent upperbound on the dimensionless parameter $β_0$, bearing the effect of generalized uncertainty principle has been given which corresponds to the intermediate length scale $l_{im}= \sqrt{β_0} l_{pl} \sim 10^{-23} m$. Hence the flavour of the generalized uncertainty principle can be realised by observing the response of the vibrations of phonon modes in such resonant detectors in the near future. In this paper, therefore, we calculate the resonant frequencies and transition rates induced by the incoming gravitational waves on these detectors in the generalized uncertainty principle framework. It is observed that the effects of the generalized uncertainty principle bears its signature in both the time independent and dependent part of the gravitational wave-harmonic oscillator Hamiltonian. We also make an upper bound estimate of the GUP parameter.

gr-qc↗

arXiv2020

Phase transitions in Born-Infeld AdS black holes in D-dimensions

In this paper, we have investigated phase transitions in arbitrary spacetime dimensions for Born-Infeld AdS black holes. The phase transition points are characterised from the divergence of heat capacity of the black hole. Two well established techniques, namely, the Ehrenfest scheme and the Ruppeiner state space geometry approach are used to identify the order of phase transition the black hole undergoes. It is observed that the results obtained from these two methods agree with each other. Our analysis reveals that the phase transition is of second order. It is also observed from the variation of the heat capacity with entropy that the small unstable black hole phase becomes more and more stable with increase in the spacetime dimensions. We speculate that this dependence of the stability of the black hole on the spacetime dimension can put an upper limit to the dimension of spacetime from the physical condition of the improbability of the formation of a small stable black hole. We have also derived a Smarr relation in D-spacetime dimensions using scaling arguments and first law of black hole thermodynamics which includes the cosmological constant and the Born-Infeld parameters as thermodynamic variables.

hep-th↗

arXiv2019

Signatures of noncommutativity in bar detectors of gravitational waves

The comparison between the noncommutative length scale $\sqrtθ$ and the length variation $δL=h L$, detected in the GW detectors indicate that there is a strong possibility to detect the noncommutative structure of space in the GW detector set up. We therefore explore how the response of a bar detector gets affected due to the presence of noncommutative structure of space keeping terms upto second order in the gravitational wave perturbation ($h$) in the Hamiltonian. Interestingly, the second order term in $h$ shows a transition between the ground state and one of the perturbed second excited states that was absent when the calculation was restricted only to first order in $h$.

gr-qc↗

arXiv2019

Path integral action of a particle with the generalized uncertainty principle and correspondence with noncommutativity

The existence of an observer independent minimum length scale can lead to the modification of the Heisenberg uncertainty principle to the generalized uncertainty principle. This in turn would be responsible for the modification of the Hamiltonian describing a non-relativistic particle moving in the presence of an arbitrary potential. In this work we carry out a path integral formulation to compute the transition amplitude for this particle. The formalism yields the action of such a particle in an arbitrary potential. Interestingly, the action indicates that there is an upper bound to the velocity that a particle can have which depends on the generalized uncertainty principle parameter. We then compute explicitly the propagator of a free particle and particle moving in a harmonic oscilltor potential using the path integral representation of the transition amplitude. We observe that there exists a curious connection between the transition amplitude of the free particle in the generalized uncertainty priciple framework with the corresponding result in noncommutative space found from the path integral formulation in \cite{sgprl}. From the harmonic oscillator result for the transition amplitude, we calculate the ground state energy of the harmonic oscillator. The result shows that the ground state energy of the harmonic oscillator in the framework of the Heisenberg uncertainty principle gets augmented by the presence of the generalized uncertainty principle and also depends on the mass of the particle. We also demonstrate that the result agrees with that obatined using the operatorial approach.

quant-ph↗

arXiv2018

Footprint of spatial noncommutativity in resonant detectors of gravitational wave

The present day gravitational wave (GW) detectors strive to detect the length variation $δL = h L$, which, owing to the smallness of the metric perturbation $\sim h$, is an extremely small length $\mathcal{O} \sim 10^{-18} - 10^{-21}$ meter. The recently proposed noncommutative structure of space has a characteristic length-scale $\sqrtθ$ which has an estimated upper-bound in similar length-scale range. We therefore propose that GW data can be used as an effective probe of noncommutative structure of space and demonstrate how spatial noncommutativity modifies the responding frequency of the resonant mass detectors of GW and also the corresponding probabilities of GW induced transitions that the phonon modes of the resonant mass detectors undergo. In this paper we present the complete perturbative calculation involving both time-independent and time-dependent perturbation terms in the Hamiltonian.

gr-qc↗

arXiv2018

Rainbow black hole thermodynamics and the generalized uncertainty principle

We study the phase transition of rainbow inspired higher dimensional Schwarzschild black hole incorporating the effects of the generalized uncertainty principle. First, we obtain the relation between the mass and Hawking temperature of the rainbow inspired black hole taking into account the effects of the modified dispersion relation and the generalized uncertainty principle. The heat capacity is then computed from this relation which reveals that there are remnants. The entropy of the black hole is next obtained in $3+1$ and $4+1$-dimensions and is found to have logarithmic corrections only in $3+1$-dimensions. We further investigate the local temperature, free energy and stability of the black hole in an isothermal cavity. From the analysis of the free energy, we find that there are two Hawking-Page type phase transitions in $3+1$ and $4+1$-dimensions if we take into account the generalized uncertainty principle. However, in the absence of the generalized uncertainty principle, only one Hawking-Page type phase transition exists in spacetime dimensions greater than four.

gr-qc↗

arXiv2017

Equivalence principle in context of large uniform acceleration - a quantum mechanical perspective

We study the effect of large acceleration of an uniformly accelerated frame on the validity of weak equivalence principle. Specifically we demonstrate how the behaviour of free quantum particle, as observed by an observer with large uniform acceleration, completely changes from that of a quantum particle emmarsed in a uniform gravitational field. We also extend our analysis to the simplest noncommutative space scenario to show that while spatial noncommutativity does not affect the quantum particle in a gravitational field, it does alter the energy eigenvalues of a quantum particle as seen from a frame with very large uniform acceleration.

quant-ph↗