arXiv subjects

Sunandan Gangopadhyay

Publications and source records attributed to Sunandan Gangopadhyay.

At least 55 records · Page 3Linked to original sources

arXiv2024

Single and entangled atomic systems in thermal bath and the Fulling-Davies-Unruh effect

In this study, we revisit the Fulling-Davies-Unruh effect in the context of two-level single and entangled atomic systems that are static in a thermal bath. We consider the interaction between the systems and a massless scalar field, covering the scenarios of free space as well as within a cavity. Through the calculation of atomic transition rates and comparing with the results of [\textcolor{blue}{\textit{Phys. Rev. D 108 (2023) 085018}}], it is found that in free space there is an equivalence between the upward and downward transition rates of a uniformly accelerated atom with respect to an observer with that of a single atom which is static with respect to the observer and immersed in a thermal bath, as long as the temperature of the thermal bath matches the Unruh temperature. This equivalence between the upward and downward transition rates breaks down in the presence of a cavity. For two-atom systems, considering the initial state to be in a general pure entangled form, we find that in this case the equivalence between the upward and downward transition rates of the accelerated and static thermal bath scenarios holds only under specific limiting conditions in free space, but breaks down completely in a cavity setup. Though the ratio of the upward and downward transition rates in the thermal bath matches exactly with those of the accelerated systems in free space as well as inside the cavity.

quant-ph↗

arXiv2024

Atom falling into a quantum corrected charged black hole and HBAR entropy

In an earlier analysis \href{https://link.aps.org/doi/10.1103/PhysRevD.105.085007}{Phys. Rev. D 105 (2022) 085007}, we have explored the event of acceleration radiation for an atom freely falling into the event horizon of a quantum-corrected Schwarzschild black hole. We want to explore the acceleration-radiation when the atom is freely falling into the event horizon of a charged quantum-corrected black hole. We consider the quantum effects of the electromagnetic field along with the gravitational field in an asymptotic safety regime. Introducing the quantum improved Reisner-Nordström metric, we have calculated the excitation probability of a two-level atom freely falling into the event horizon of quantum improved charged black hole. Recently, in the case of the braneworld black hole (where the tidal charge has the same dimension as the square of the charge of a Reissner-Nordström black hole in natural units), we have observed from the form of the transition probability that the temperature will have no contribution in the first order of the tidal charge. We observe that for a quantum corrected Reissner-Nordström black hole, there is a second-order contribution in the charge parameter in the temperature that can be read off from the transition probability. Next, we calculate the HBAR entropy in this thought experiment and show that this entropy has a leading order Bekenstein-Hawking entropy term along with some higher order correction terms involving logarithmic as well as fractional terms of the black hole area due to infalling photons. We have finally investigated the validity of Wien's displacement law and compared the critical value of the field wavelength with the general Schwarzschild black hole and its corresponding quantum-corrected case.

gr-qc↗

arXiv2024

Probing the quantum nature of gravity using a Bose-Einstein condensate

The effect of noise induced by gravitons has been investigated using a Bose-Einstein condensate. The gravitational wave perturbation is then considerd as a sum of discrete Fourier modes in the momentum space. Coming to an operatorial representation and quantizing the phase space variables via appropriately introduced canonincal commutation relations between the canonically conjugate variables corresponding to the graviton and bosonic part of the total system, one obtains a proper quantum gravity setup. Then we obtain the Bogoliubov coefficients from the solution of the time-dependent part of the pseudo-Goldstone boson and construct the covariance metric for the bosons initially being in a squeezed state. Using the stochastic average of the Fisher information, we obtain a lower bound on the amplitude parameter of the gravitational wave. As the entire calculation is done at zero temperature, the bosonic system, by construction, will behave as a Bose-Einstein condensate. For a Bose-Einstein condensate with a single mode, we observe that the lower bound of the expectation value of the square of the uncertainty in the amplitude measurement does not become infinite when the total observational term approaches zero. In order to sum over all possible momentum modes, we next consider a noise term with a suitable Gaussian weight factor which decays over time. We then obtain the lower bound on the final expectation value of the square of the variance in the amplitude parameter. Because of the noise induced by the graviton, there is a minimum value of the measurement time below which it is impossible to detect any gravitational wave using a Bose-Einstein condensate. Finally, we consider interaction between the phonon modes of the Bose-Einstein condensate which results in the decoherence. We observe that the decoherence effect becomes significant for gravitons with minimal squeezing.

hep-th↗

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

Quantum chaos in the presence of non-conformality

The behaviour of a chaotic system and its effect on existing quantum correlation has been holographically studied in presence of non-conformality. Keeping in mind the gauge/gravity duality framework, the non-conformality in the dual field theory has been introduced by considering a Liouville type dilaton potential for the gravitational theory. The resulting black brane solution is associated with a parameter $η$ which represents the deviation from conformality. The parameters of chaos, namely, the Lyapunov exponent and butterfly velocity are computed by following the well-known shock wave analysis. The obtained results reveal that presence of non-conformality leads to suppression of the chaotic nature of a system. Further, for a particular value of the non-conformal parameter $η$, the system achieves Lyapunov stability resulting from the vanishing of both the Lyapunov exponent and as well as butterfly velocity. Interestingly, this particular value of $η$ matches with the previously given upper bound of $η$ known as Gubser bound in the literature. The effects of chaos and non-conformality on the existing correlation of a thermofield doublet state have been quantified by holographically computing the thermo mutual information in both the presence and absence of the shock wave. Furthermore, the entanglement velocity is also computed and the effect of non-conformality on it has been observed. Finally, the obtained results for the Lyapunov exponent and the butterfly velocity have also been computed from the pole-skipping analysis. The results from the two approaches agree with each other.

hep-th↗

arXiv2024

Quantum harmonic oscillator in a time dependent noncommutative background

This work explores the behaviour of a noncommutative harmonic oscillator in a time-dependent background, as previously investigated in [1]. Specifically, we examine the system when expressed in terms of commutative variables, utilizing a generalized form of the standard Bopp-shift relations recently introduced in [2]. We solved the time dependent system and obtained the analytical form of the eigenfunction using the method of Lewis invariants, which is associated with the Ermakov-Pinney equation, a non-linear differential equation. We then obtain exact analytical solution set for the Ermakov-Pinney equation. With these solutions in place, we move on to compute the dynamics of the energy expectation value analytically and explore their graphical representations for various solution sets of the Ermakov-Pinney equation, associated with a particular choice of quantum number. Finally, we determined the generalized form of the uncertainty equality relations among the operators for both commutative and noncommutative cases. Expectedly, our study is consistent with the findings in [1], specifically in a particular limit where the coordinate mapping relations reduce to the standard Bopp-shift relations.

quant-ph↗

arXiv2024

Signatures of quantum geometry from exponential corrections to the black hole entropy

It has been recently shown in [Phys. Rev. Lett. 125 (2020) 041302] that microstate counting carried out for quantum states residing on the horizon of a black hole leads to a correction of the form $\exp(-A/4l_p^2)$ in the Bekenstein-Hawking form of the black hole entropy. In this paper, we develop a novel approach to obtain the possible form of the spacetime geometry from the entropy of the black hole for a given horizon radius. The uniqueness of this solution for a given energy-momentum tensor has also been discussed. Remarkably, the black hole geometry reconstructed has striking similarities to that of noncommutative-inspired Schwarzschild black holes [Phys. Lett. B 632 (2006) 547]. We also obtain the matter density functions using Einstein field equations for the geometries we reconstruct from the thermodynamics of black holes. These also have similarities to that of the matter density function of a noncommutative-inspired Schwarzschild black hole. The conformal structure of the metric is briefly discussed and the Penrose-Carter diagram is drawn. We then compute the Komar energy and the Smarr formula for the effective black hole geometry and compare it with that of the noncommutative-inspired Schwarzschild black hole. We also discuss some astrophysical implications of the solutions. Finally, we propose a set of quantum Einstein vacuum field equations, as a solution of which we obtain one of the spacetime solutions obtained in this work. We then show a direct connection between the quantum Einstein vacuum field equations and the first law of black hole thermodynamics.

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↗

arXiv2024

Bose-Einstein condensate as a quantum gravity probe; "Erste Abhandlung"

We consider a Bose-Einstein condensate interacting with a gravitational wave for the case when the gravitational fluctuations are quantized in order to incorporate quantum gravity effects into the theory. We observe that the solution of the time-dependent part of the pseudo-Goldstone boson has infusions from the noise induced by gravitons and the corresponding differential equation of motion is Langevin-like. Using this result, we obtain the quantum gravity modified Fisher information which has been termed as the quantum gravitational Fisher information (QGFI). The inverse square root of the stochastic average of the QGFI gives the minimum uncertainty in the measurement of the gravitational wave amplitude. The minimum uncertainty does not go to infinity as the measurement time approaches zero in a quantum gravity setup rather it has a measurable finite value for gravitons with high squeezing. Finally, we observe the effect of decoherence due to interacting phonon modes in the QGFI and observe a less obvious decoherence effect for higher squeezing of the initial graviton.

hep-th↗

arXiv2024

Uncertainty principle from the noise of gravitons

The effect of the noise induced by gravitons in the case of a freely falling particle from the viewpoint of an external observer has been recently calculated in \href{https://link.aps.org/doi/10.1103/PhysRevD.107.066024}{Phys. Rev. D 107 (2023) 066024}. There the authors have calculated the quantum gravity modified Newton's law of free fall where the spacetime has been considered to be weakly curved. In our work, we extend this work by calculating the variance in the velocity and eventually the momentum of the freely falling massive particle. From this simple calculation, we observe that the product of the standard deviation in the position with that of the standard deviation in momentum picks up a higher order correction which is proportional to the square of the standard deviation in momentum. We also find out that in the Planck limit (both Planck length and Planck mass), this uncertainty product gives the well-known form of the generalized uncertainty principle. We then calculate a similar uncertainty product when the graviton is in a squeezed state, and eventually, we get back the same uncertainty product. Finally, we extend our analysis for the gravitons being in a thermal state and obtain a temperature-dependent uncertainty product. If one replaces this temperature with the Planck temperature and the mass of the particle by the Planck mass, the usual uncertainty product appears once again. We also obtain an upper bound of the uncertainty product thereby giving a range of the product of the variances in position and momentum.

hep-th↗

arXiv2023

Mixed state entanglement measures for the dipole deformed supersymmetric Yang-Mills theory

Two different entanglement measures for mixed states, namely, the entanglement of purification and entanglement negativity has been holographically computed for the dipole deformed supersymmetric Yang-Mills (SYM) theory by considering its gravity dual. The dipole deformation induces non-locality in the SYM theory which is characterized by a length-scale $a=λ^{\frac{1}{2}}\tilde{L}$. Considering a strip like subsystem of length $\frac{l}{a}$ (in dimensionless form), we first analytically calculate the holographic entanglement entropy for and compare the obtained results with that of obtained numerically.~The analytical calculations have been carried out by considering $au_t \leq 1$,~$1\leq au_t < au_b$ and $au_t\sim au_b$, where $au_b$ is the UV cut-off. The choice of these regions enable us to identify the expansion parameters needed to carry out binomial expansions. The entanglement measures expectedly displays a smooth behaviour with respect to the subsystem size as the geometry has a smooth transition between the mentioned regions. Using these results, the holographic mutual information is then computed for two disjoint subsystems $A$ and $B$. Based upon the $E_{P}=E_{W}$ duality, the entanglement of purification ($E_{P}$) is then computed and the effects of dipole deformation in this context have been studied. Finally, we proceed to compute entanglement negativity for this theory and compare the obtained result with that of the standard SYM theory in order to get a better understanding about the effects of the non-locality.

hep-th↗

arXiv2023

Lewis and Berry phases for a gravitational wave interacting with a quantum harmonic oscillator

In this work, we consider a gravitational wave interacting with a quantum harmonic oscillator in the transverse-traceless gauge. We take the gravitational wave to be carrying the signatures of both plus and cross polarization at first. We then try to obtain a suitable form of the Lewis invariant using the most general form possible while considering only quadratic order contributions from both position and momentum variables. In order to progress further, we then drop the cross terms obtaining a separable Hamiltonian in terms of the first and the second spatial coordinates. We then obtain two Lewis invariants corresponding to each separable parts of the entire Hamiltonian of the system. Using both Lewis invariants, one can obtain two Ermakov-Pinney equations, from which we finally obtain the corresponding Lewis phase and eventually the Berry phase for the entire system. Finally, we obtain some explicit expressions of the Berry phase for a plane polarized gravitational wave with different choices of the harmonic oscillator frequency.

hep-th↗

arXiv2023

Horizon brightened accelerated radiation in the background of braneworld black holes

The concept of horizon brightened acceleration radiation (HBAR) has brought to us a distinct mechanism of particle production in curved spacetime. In this manuscript we examine the HBAR phenomena for a braneworld black hole (BBH) which emerges as an effective theory in our $(3+1)$ dimensional universe due to the higher dimensional gravitational effects. Despite being somewhat similar to the Reissner-Nordstr$\ddot{\rm o}$m solution in general relativity, the BBH is unique with respect to its charge term which is rather the tidal charge. In this background, we study the transition probability of the atom due to the atom-field interaction and the associated HBAR entropy. Both the quantities acquire modifications over the standard Schwarzschild results and turn out to be the function of the tidal charge. This modifications appear solely due to the bulk gravitational effects as induced on the 3-brane. Studying the Wien's displacement, we observe an important feature that the wavelengths of HBAR corresponding to the Schwarzschild and the BBH, deviate from each other depending on their masses. This deviation is found to be more pronounced for the mass values slightly greater or comparable to the Planck mass.

gr-qc↗

arXiv2023

Minimal length scale correction in the noise of gravitons

In this paper we have considered a quantized and linearly polarized gravitational wave interacting with a gravitational wave detector (interferometer detector) in the generalized uncertainty principle (GUP) framework. Following the analysis in Phys. Rev. Lett. 127 (2021) 081602 (https://link.aps.org/doi/10.1103/PhysRevLett.127.081602), we consider a quantized gravitational wave interacting with a gravitational wave detector (LIGO/VIRGO etc.) using a path integral approach. Although the incoming gravitational wave was quantized, no Planck-scale quantization effects were considered for the detector in earlier literatures. In our work, we consider a modified Heisenberg uncertainty relation with a quadratic order correction in the momentum variable between the two phase space coordinates of the detector. Using a path integral approach, we have obtained a stochastic equation involving the separation between two point-like objects. It is observed that random fluctuations (noises) and the correction terms due to the generalized uncertainty relation plays a crucial role in dictating such trajectories. Finally, we observe that the solution to the stochastic equation leads to time dependent standard deviation due to the GUP insertion, and for a primordial gravitational wave (where the initial state is a squeezed state) both the noise effect and the GUP effects exponentially enhance which may be possible to detect in future generation of gravitational wave detectors. We have also given a plot of the dimensionless standard deviation with time depicting that the GUP effect will carry a distinct signature which may be detectable in the future space based gravitational wave observatories.

gr-qc↗

arXiv2023

Lorentzian path integral in Kantowski-Sachs anisotropic cosmology

Motivated by the recent development in quantum cosmology, we revisit the anisotropic Kantowski-Sachs model in the light of a Lorentzian path integral formalism. Studies so far have considered the Euclidean method where the choice of the lapse integration contour is constrained by certain physical considerations rather than mathematical justification. In this paper, we have studied the Hartle-Hawking no-boundary proposal along with the use of Picard-Lefschetz theory in performing the lapse integration. In an isotropic limit, we show our results agree with the studies made in FLRW cosmology. We also observe that in the large scale structure the no-boundary proposal tends towards a conical singularity at the beginning of time. We have also performed a massless scalar perturbation analysis with no back reaction. This reveals that if there were any perturbation present at the beginning of the universe then that would flare up at the final boundary.

gr-qc↗

arXiv2023

Near horizon approximation and beyond for a two-level atom falling into a Kerr-Newman black hole

In this work we investigate the phenomena of acceleration radiation for a two-level atom falling into the event horizon of a Kerr-Newman black hole. In https://link.aps.org/doi/10.1103/PhysRevD.104.065006 (Phys. Rev. D 104 (2021) 065006), it has been shown that conformal quantum mechanics has a connection to the generated Planck-like spectrum due to acceleration radiation. In this particular aspect, the near horizon approximation played a significant role. In https://link.aps.org/doi/10.1103/PhysRevD.106.025004 (Phys. Rev. D 106 (2022) 025004), we have used the beyond near horizon approximation to show that the excitation probability attains a Planck-like spectrum irrespective of the non-existence of an underlying conformal symmetry for a general class of static spherically symmetric black holes. In our analysis we have gone beyond the near horizon approximation for the rotating and charged case and even without the consideration of the conformal symmetry we observe a similar Planck-like spectrum. However, the coefficient of the spectrum is significantly different from the near horizon case. We have then considered a different scenario where a two-level atom emits multiple photons while freely falling into the event horizon of the Kerr-Newman black hole. It is observed that the Planck factor in the excitation probability is significantly small than that of the case of single-photon emission (for large number of simultaneously emitted photons from the two-level atom). Finally, we have computed the von-Neumann entropy which is also known as the horizon brightened acceleration radiation entropy or the HBAR entropy. We have carried out our analysis for a scalar field only to see the effect of the charge and rotation of the black hole in this particular scenario.

gr-qc↗

arXiv2023

Entanglement degradation as a tool to detect signatures of quantum gravity

We investigate entanglement degradation in the vicinity of a quantum corrected black hole. We consider a biprtite system (Alice-Rob) with Alice freely falling (radially) into the event horizon of a quantum corrected black hole and Rob being in the vicinity of the event horizon of the black hole. We consider a maximally entangled state (in the Fock basis) and start with the basic assumption that Rob is an uniformly accelerated observer. We then give a pedagogical analysis of the relation involving the Minkowski vaccum state and Rindler number states. Following the analogy given in https://link.aps.org/doi/10.1103/PhysRevD.82.064006 {Phys. Rev. D 82 (2010) 064006}, we establish the relation between the Hartle-Hawking vacuum state and Boulware and Anti-Bouware number states from the Minkowski-Rindler relation. We then write down the quantum corrected black hole metric by making use of the near horizon approximation in an appropriate form. Next, we obtain the analytical forms of logarithmic negativity and mutual information and plot as a function of Rob's distance from the $r=0$ point. We observe that the entanglement degradation slows down due to the incorporation of quantum gravity corrections in the Schwarzschild black hole. This observation may lead to identification of quantum gravity signatures in future generation of advanced observational scenarios. We can also interpret this effect as a noisy quantum channel with an operator sum representation of a completely positive and trace preserving (CPTP) map. We then finally obtain the entanglement fidelity using this operator sum representation.

hep-th↗

arXiv2023

Entropic force for quantum particles

Entropic force has been drawing the attention of theoretical physicists following E. Verlinde's work in 2011 to derive Newton's second law and Einstein's field equations of general relativity. In this paper, we extend the idea of entropic force to the distribution of quantum particles. Starting from the definition of Shannon entropy for continuous variables, here we have derived quantum osmotic pressure as well as the consequent entropic forces for bosonic and fermionic particles. The entropic force is computed explicitly for a pair of bosons and fermions. The low temperature limit of this result show that the entropic force for bosons is similar to Hooke's law of elasticity revealing the importance of this idea in the formation of a Bose-Einstein condensate. For fermions, the low temperature limit boils down to the well known Neumann's radial force and also reveals the Pauli's exclusion principle. The classical limit of the entropic force between quantum particles is then discussed. As a further example, the entropic force for quantum particles in noncommutative space is also computed. The result reveals a violation of the Pauli exclusion principle for fermions in noncommutative space.

quant-ph↗