Browsing by Author "Sarkar, Tapomoy Guha"

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Adiabatic modulation of driving protocols in periodically driven quantum systems
(ARXIV, 2024-04) Sarkar, Tapomoy Guha; Bandyopadhyay, Jayendra N.
We consider a periodically driven system where the high-frequency driving protocol consists of a sequence of potentials switched on and off at different instants within a period. We explore the possibility of introducing an adiabatic modulation of the driving protocol by considering a slow evolution of the instants when the sequence of potentials is switched on/off. We examine how this influences the long-term dynamics of periodically driven quantum systems. By assuming that the slow and fast timescales in the problem can be decoupled, we derive the stroboscopic (effective) Hamiltonian for a four-step driving sequence up to the first order in perturbation theory. We then apply this approach to a rigid rotor, where the adiabatic modulation of the driving protocol is chosen to produce an evolving emergent magnetic field that interacts with the rotor's spin. We study the emergence of diabolical points and diabolical loci in the parameter space of the effective Hamiltonian. Further, we study the topological properties of the maps of the adiabatic paths in the parameter space to the eigenspace of the effective Hamiltonian. In effect, we obtain a technique to tune the topological properties of the eigenstates by selecting various adiabatic evolution of the driving protocol characterized by different paths in the parameter space. This technique can be applied to any periodic driving protocol to achieve desirable topological effects.
The CMBR ISW and HI 21 cm cross-correlation angular power spectrum
(IOP, 2009-08) Sarkar, Tapomoy Guha
The late-time growth of large scale structures is imprinted in the CMBR anisotropy through the Integrated Sachs Wolfe (ISW) effect. This is perceived to be a very important observational probe of dark energy. Future observations of redshifted 21-cm radiation from the cosmological neutral hydrogen (HI) distribution hold the potential of probing the large scale structure over a large redshift range. We have investigated the possibility of detecting the ISW through cross-correlations between the CMBR anisotropies and redshifted 21-cm observations. Assuming that the HI traces the dark matter, we find that the ISW-HI cross-correlation angular power spectrum at an angular multipole ℓ is proportional to the dark matter power spectrum evaluated at the comoving wave number ℓ/r, where r is the comoving distance to the redshift from which the HI signal originated. The amplitude of the cross-correlation signal depends on parameters related to the HI distribution and the growth of cosmological perturbations. However, the cross-correlation is extremely weak as compared to the CMBR anisotropies and the predicted HI signal. Even in an ideal situation, the cross-correlation signal is smaller than the cosmic variance and a statistically significant detection is not very likely.
CMBR weak lensing and HI 21-cm cross-correlation angular power spectrum
(IOP, 2010-02) Sarkar, Tapomoy Guha
Weak gravitational lensing of the CMBR manifests as a secondary anisotropy in the temperature maps. The effect, quantified through the shear and convergence fields imprint the underlying large scale structure (LSS), geometry and evolution history of the Universe. It is hence perceived to be an important observational probe of cosmology. De-lensing the CMBR temperature maps is also crucial for detecting the gravitational wave generated B-modes. Future observations of redshifted 21-cm radiation from the cosmological neutral hydrogen (HI) distribution hold the potential of probing the LSS over a large redshift range. We have investigated the correlation between post-reionization HI signal and weak lensing convergence field. Assuming that the HI follows the dark matter distribution, the cross-correlation angular power spectrum at a multipole ℓ is found to be proportional to the cold dark matter power spectrum evaluated at ℓ/r, where r denotes the comoving distance to the redshift where the HI is located. The amplitude of the cross-correlation depends on quantities specific to the HI distribution, growth of perturbations and also the underlying cosmological model. In an ideal situation, we found that a statistically significant detection of the cross-correlation signal is possible. If detected, the cross-correlation signal holds the possibility of a joint estimation of cosmological parameters and also may be used to test various CMBR de-lensing estimators.
Constraining dark energy using the cross correlations of weak lensing with post-reionization probes of neutral hydrogen
(IOP, 2021) Sarkar, Tapomoy Guha
We investigate the prospects of detecting the cross correlation of CMBR weak-lensing convergence field with the large scale tracers of the underlying dark matter distribution in the post-reionization epoch. The cross-correlation is then used to make error projections for dark energy equation of state (EoS)for models with a time evolving dark energy. We study the cross-correlation angular power spectrum of the weak-lensing field with the Lyman-α forest and the redshifted HI 21 cm signal from the post reionization epoch. The angular power spectra is expressed as a line of sight average over the tomographic slices. We find that on using multiple 400 hrs observation with an extended uGMRT like instrument or with a BOSS like survey with quasar (QSO) density of 16 deg−2 the cross-correlation with weak-lensing convergence field covering half the sky can be detected at a very high SNR (> 20). The cross-correlation of weak-lensing with Lyman-α forest allows the 1−σ errors on the dark energy EoS parameters for different parametrizations to be constrained at a level of precision comparable to combined Planck+SNIa+BAO+HST projections. The 21-cm weak-lensing cross-correlation is found to provide strong constraints on the present value of the dark energy EoS parameter at 4% for the 7CPL model. The constraints on wa is comparable (~12%) for models other than the 7CPL model. We also find that the CPL parametrization may not be the best constrained parametrization for dark energy evolution. The cross-correlation of CMBR weak-lensing with the post-reionization probes of neutral hydrogen thus holds the potential to give us valuable understanding about the nature of evolving dark energy.
Constraining large‐scale H i bias using redshifted 21‐cm signal from the post‐reionization epoch
(OUP, 2012-04) Sarkar, Tapomoy Guha
In the absence of complex astrophysical processes that characterize the reionization era, the 21‐cm emission from neutral hydrogen (H i) in the post‐reionization epoch is believed to be an excellent tracer of the underlying dark matter distribution. Assuming a background cosmology, it is modelled through (i) a bias function b(k, z), which relates H i to the dark matter distribution and (ii) a mean neutral fraction (⁠forumla⁠) which sets its amplitude. In this paper, we investigate the nature of large‐scale H i bias. The post‐reionization H i is modelled using gravity only N‐body simulations and a suitable prescription for assigning gas to the dark matter haloes. Using the simulated bias as the fiducial model for H i distribution at z≤ 4, we have generated a hypothetical data set for the 21‐cm angular power spectrum (Cℓ) using a noise model based on parameters of an extended version of the Giant Metrewave Radio Telescope (GMRT). The binned Cℓ is assumed to be measured with S/N ≳ 4 in the range 400 ≤ℓ≤ 8000 at a fiducial redshift z= 2.5. We explore the possibility of constraining b(k) using the principal component analysis on these simulated data. Our analysis shows that in the range 0.2 < k < 2 Mpc−1, the simulated data set cannot distinguish between models exhibiting different k‐dependences, provided 1 ≲b(k) ≲ 2 which sets the 2σ limits. This justifies the use of linear bias model on large scales. The largely uncertain forumla is treated as a free parameter resulting in degradation of the bias reconstruction. The given simulated data are found to constrain the fiducial forumla with an accuracy of ∼4 per cent (2σ error). The method outlined here could be successfully implemented on future observational data sets to constrain b(k, z) and forumla and thereby enhance our understanding of the low‐redshift Universe.
Constraining neutrino mass using the large-scale H i distribution in the post-reionization epoch
(OUP, 2016-07) Sarkar, Tapomoy Guha
The neutral intergalactic medium in the post-reionization epoch allows us to study cosmological structure formation through the observation of the redshifted 21 cm signal and the Lyman α forest. We investigate the possibility of measuring the total neutrino mass through the suppression of power in the matter power spectrum. We investigate the possibility of measuring the neutrino mass through its imprint on the cross-correlation power spectrum of the 21 cm signal and the Lyman α forest. We consider a radio-interferometric measurement of the 21 cm signal with a SKA1-mid-like radio telescope and a BOSS-like Lyman α forest survey. A Fisher matrix analysis shows that at the fiducial redshift z = 2.5, a 10 000 h 21 cm observation distributed equally over 25 radio pointings and a Lyman α forest survey with 30 quasars lines of sights in 1deg2, allows us to measure Ων at a 3.25 per cent level. A total of 25 000 h radio-interferometric observation distributed equally over 25 radio pointings and a Lyman α survey with will allow Ων to be measured at a 2.26 per cent level. This corresponds to an idealized measurement of ∑mν at the precision of (100 ± 2.26)meV and fν = Ων/Ωm at 2.49 per cent level.
Constraining warm dark matter power spectrum using the cross-correlation of HI 21 cm signal and the Lyman-α forest
(IOP, 2019-12) Sarkar, Tapomoy Guha
We have considered the prospects for measuring the cross Warm Dark Matter (WDM) power spectrum of the redshifted HI 21-cm signal and the Lyman-α forest and thereby constraining WDM mass using observations with upcoming radio-interferometers—the Ooty Wide Field Array (OWFA) and SKA1-mid, and a spectroscopic survey of the quasars. We have considered a quasar survey with a mean observed quasar number density of bar nQ = 48 deg−2 over a collecting area of 14455 deg2, and a mean spectroscopic SNR = 5. Our analysis with OWFA shows that it is possible to measure the WDM power spectrum in several k-bins at k ⩽ 0.45 Mpc−1 with SNR > 5 using observations of 200 hours each in 100 different fields-of-view for mWDM = 0.25 keV . Considering the possibility of the joint measurement of the parameters, the warm dark matter density parameter ΩWDM, and the dark energy density parameter ΩΛ0, we find that the relative error on the 1−σ measurement of the parameter ΩWDM is ∼ 0.8 for a fiducial mWDM = 0.25 keV . However, we find that OWFA is not sensitive towards measuring the suppression of the WDM power spectrum, and therefore, cannot be used to constrain the WDM mass. Considering the analysis with SKA I mid, we find that for a fiducial mWDM= 0.25 keV, the suppression in the cross power spectrum can be measured at ∼ 10 − σ around k ∼ 0.2 Mpc−1 for a total observing time of 20000 hours distributed uniformly over 50 independent pointings where we have binned the available k-range as Δ k = k/5.
Conversion of Emitted Axionic Dark Matter to Photons for Non-Rotating Magnetized Neutron Stars
(ARXIV, 2024-02) Sarkar, Tapomoy Guha; Mishra, Madhukar
We attempt to find the impact of a modified Tolman Oppenheimer Volkoff (TOV) system of equations on the luminosities of direct photons, neutrinos and axions for a particular axion mass in the presence of a magnetic field. We employ two different equation of states (EoSs) namely APR and FPS to generate the profiles of mass and pressure for spherically symmetric and non-rotating Neutron stars (NSs). We then compute the axions and neutrino emission rates by employing the Cooper-pair-breaking and formation process (PBF) in the core using the NSCool code. We also examine the possibility of axion to photon conversion in the magnetosphere of NSs. Furthermore, we investigate the impact of the magnetic field on the actual observables, such as the energy spectrum of axions and axion-converted photon flux for three different NSs. Our comparative study indicates that axions energy spectrum and axion-converted photon flux changes significantly due to an intense magnetic field.
Cosmology and Astrophysics using the Post-Reionization HI
(Springer, 2016-11) Sarkar, Tapomoy Guha
We discuss the prospects of using the redshifted 21-cm emission from neutral hydrogen in the post-reionization epoch to study our Universe. The main aim of the article is to highlight the efforts of Indian scientists in this area with the SKA in mind. It turns out that the intensity mapping surveys from SKA can be instrumental in obtaining tighter constraints on the dark energy models. Cross-correlation of the HI intensity maps with the Ly α forest data can also be useful in measuring the BAO scale.
The cross-correlation of redshited 21-cm signal and Lyman-α forest: A cosmological probe
(IOP, 2014) Sarkar, Tapomoy Guha
We have investigated the cross-correlation of the Lyman-α forest and redshifted 21-cm emission as a new observational probe of the large scale structures in the post-reionization era, with a significant advantage that the problems of continuum subtraction and foreground removal, and other systematics are expected to be considerably less servere in comparison to the respective auto-correlation signals. In this paper, we have explored the possibility of detecting the baryon acoustic oscillation in the cross-correlation signal. We have developed a formalism to calculate the expected cross-correlation signal and its covariance. We have used this to predict the expected signal and noise for a range of observational parameters.
Cross-correlation of the H i 21-cm signal and Lyα forest: a probe of cosmology
(OUP, 2011-01) Sarkar, Tapomoy Guha
Separating the cosmological redshifted 21-cm signal from foregrounds is a major challenge. We present the cross-correlation of the redshifted 21-cm emission from neutral hydrogen (H i) in the post-reionization era with the Lyα forest as a new probe of the large-scale matter distribution in the redshift range z= 2–3 without the problem of foreground contamination. Though the 21-cm and the Lyα forest signals originate from different astrophysical systems, they are both expected to trace the underlying dark matter distribution on large scales. The multifrequency angular cross-correlation power spectrum estimator is found to be unaffected by the discrete quasar sampling, which only affects the noise in the estimate.
Disentangling the growth rate of perturbations from the HI bias using only clustering data from galaxy surveys
(2025-06) Sarkar, Tapomoy Guha
This work serves two-fold purpose. Firstly, we provide an alternative to the traditional method of determining the growth rate of density perturbations . In usual practice, can not be directly measured from tracer clustering at some redshift without knowledge of the bias. While the bayron acoustic oscillation (BAO) imprint allows the determination of , redshift space anisotropy (RSD) allows the measurement of a quantity . To extract from , one usually requires some other data set. We show that precise BAO and RSD measurements in and around some key redshifts themselves can solely reconstruct without requiring any other data sets. Secondly, we extend this approach to another tracer, namely the post-reionization 21-cm brightness temperature intensity maps. We demonstrate that the measured from purely redshift space clustering allows us to measure the 21-cm bias, which is a largely unknown quantity. This may help interpret the observed intensity mapping signal in the future.
The dynamics of background cosmological evolution and structure formation in phase space: a semi-cosmographic reconstruction
(Elsevier, 2025-11) Sarkar, Tapomoy Guha
The Baryon Acoustic Oscillation (BAO) feature, imprinted in the transverse and radial clustering of dark matter tracers, enables the simultaneous measurement of the angular diameter distance DA(z) and the Hubble parameter H(z) at a given redshift. Further, measuring the redshift space anisotropy (RSD) allows us to measure the combination f8(z) ≡ fσ8(z). Motivated by this, we simultaneously study the dynamics of background evolution and structure formation in an abstract phase space of dynamical quantities , , and f8. We adopt a semi-cosmographic approach, whereby we do not pre-assume any specific dark energy model to integrate the dynamical system. The Luminosity distance is expanded as a Padé rational approximation in the variable . The dynamical system is solved by using a semi-cosmographic equation of state, which incorporates the dark matter density parameter along with the parameters of the Padé expansion. The semi-cosmographic DA(z), H(z) and fσ8(z), thus obtained, are fitted with BAO and RSD data from the SDSS IV. The reconstructed phase trajectories in the 3D (x, p, f8) space are used to reconstruct some diagnostics of background cosmology and structure formation. At low redshifts, a discernible departure from the ΛCDM model is observed. The geometry of the phase trajectories in the projected spaces allows us to identify three key redshifts where future observations may be directed for a better understanding of cosmic tensions and anomalies.
The effect of the w-term on the visibility correlation and power spectrum estimation
(OUP, 2010-07) Sarkar, Tapomoy Guha
The visibility–visibility correlation has been proposed as a technique for the estimation of the power spectrum, and used extensively for small field of view observations, where the effect of the w-term is usually ignored. We consider power spectrum estimation from large field of view observations, where the w-term can have a significant effect. Our investigation shows that a non-zero w manifests itself as a modification of the primary aperture function of the instrument. Using a Gaussian primary beam, we show that the modified aperture is an oscillating function with a Gaussian envelope. We show that the two-visibility correlation (visibility variance) reproduces the power spectrum beyond a certain baseline given by the width, Uw, of the modified aperture. Further, for a given interferometer, the maximum Uw remains independent of the frequencies of observation. This suggests that the incorporation of a large field of view in radio interferometric observations has a greater effect for larger observing wavelengths.
Effective time-independent analysis for quantum kicked systems
(APS, 2015-03) Bandyopadhyay, Jayendra N.; Sarkar, Tapomoy Guha
We present a mapping of potentially chaotic time-dependent quantum kicked systems to an equivalent approximate effective time-independent scenario, whereby the system is rendered integrable. The time evolution is factorized into an initial kick, followed by an evolution dictated by a time-independent Hamiltonian and a final kick. This method is applied to the kicked top model. The effective time-independent Hamiltonian thus obtained does not suffer from spurious divergences encountered if the traditional Baker-Cambell-Hausdorff treatment is used. The quasienergy spectrum of the Floquet operator is found to be in excellent agreement with the energy levels of the effective Hamiltonian for a wide range of system parameters. The density of states for the effective system exhibits sharp peaklike features, pointing towards quantum criticality. The dynamics in the classical limit of the integrable effective Hamiltonian shows remarkable agreement with the nonintegrable map corresponding to the actual time-dependent system in the nonchaotic regime. This suggests that the effective Hamiltonian serves as a substitute for the actual system in the nonchaotic regime at both the quantum and classical level.
Emission properties of non-rotating neutron stars with magnetic field using modified TOV equations
(Springer, 2024-07) Mishra, Madhukar; Sarkar, Tapomoy Guha
Emission properties of the Astrophysical objects such as Neutron Stars are found using mass, pressure profile and thermal cooling rate. In this current work, we determine the cooling rate of spherically symmetric neutron star as a function of time and distance from the star’s centre using NSCool code. Here we first find the mass, pressure and baryon number density profile of the non-rotating neutron stars using modified Tolman-Oppenheimer-Volkoff (TOV) system of equations in the presence of intense magnetic field. We used here a constant value of magnetic field and a distance dependent magnetic field in TOV equations to obtain the profile. We employ three different equation of states to solve the TOV equations by assuming that the core of Neutron Stars is composed of a hadronic matter. By employing above profile, we obtain the cooling rate with and without magnetic field to examine the effect of magnetic field for three different equations of states. Observed temperature of a few Neutron Stars have also been plotted along with calculated values for comparison. Finally, emissivity of axions as a dark matter candidates has been calculated as a result of the nucleon Bremsstrahlung mechanism with and without magnetic field.
Floquet analysis of a fractal-spectrum-generating periodically driven quantum system
(APS, 2018-10) Bandyopadhyay, Jayendra N.; Sarkar, Tapomoy Guha
We employ Floquet analysis to study the spectral properties of a double-kicked top (DKT) system. This is a classically nonintegrable dynamical system, which also shows chaos. However, even for the underlying classically chaotic dynamics, the quantum quasienergy spectrum of this system does not follow the random matrix conjecture which was proposed for the quantum spectrum of any classically chaotic systems. Instead the quasienergy spectrum of the DKT system shows a butterfly-like self-similar fractal spectrum. Here we investigate the relation between the quasienergy spectrum and the energy spectrum of the corresponding time-independent Floquet Hamiltonian. This Hamiltonian is determined by factorizing the Floquet time-evolution operator into three terms: an initial kick and a final kick, and in between a time-independent evolution dictated by a time-independent Hermitian operator which is called the Floquet Hamiltonian. Like any other generic systems, the Floquet Hamiltonian of the DKT system is also not possible to determine exactly. We apply a recently proposed perturbation theory to obtain the approximate Floquet Hamiltonian at the high-frequency driving limit. We then study the parameter regime where the quasienergy spectrum of the Floquet time-evolution operator matches the energy spectrum of the approximate Floquet Hamiltonian. We have also done a comparative analysis of how the two butterfly spectra disappear with the variation of a system parameter. Finally, we also explore the self-similar property of the energy spectrum of the approximate Floquet Hamiltonian and find its connection with the Farey sequence. Unlike all previous studies, here we have extensively investigated the self-similar property of the whole DKT butterfly.
Floquet analysis of pulsed Dirac systems: a way to simulate rippled graphene
(Springer, 2015-09) Sarkar, Tapomoy Guha; Bandyopadhyay, Jayendra N.
The low energy continuum limit of graphene is effectively known to be modeled using the Dirac equation in (2 + 1) dimensions. We consider the possibility of using a modulated high frequency periodic driving of a two-dimensional system (optical lattice) to simulate properties of rippled graphene. We suggest that the Dirac Hamiltonian in a curved background space can also be effectively simulated by a suitable driving scheme in an optical lattice. The time dependent system yields, in the approximate limit of high frequency pulsing, an effective time independent Hamiltonian that governs the time evolution, except for an initial and a final kick. We use a specific form of 4-phase pulsed forcing with suitably tuned choice of modulating operators to mimic the effects of curvature. The extent of curvature is found to be directly related to ω −1 the time period of the driving field at the leading order. We apply the method to engineer the effects of curved background space. We find that the imprint of curvilinear geometry modifies the electronic properties, such as LDOS, significantly. We suggest that this method shall be useful in studying the response of various properties of such systems to non-trivial geometry without requiring any actual physical deformations.
Floquet topological phase transitions in a kicked Haldane-Chern insulator
(APS, 2018-02) Bandyopadhyay, Jayendra N.; Sarkar, Tapomoy Guha
We consider a periodically δ-kicked Haldane type Chern insulator with the kicking applied in the ˆz direction. This is known to behave as an inversion symmetry breaking perturbation, since it introduces a time-dependent staggered sublattice potential. We study here the effects of such driving on the topological phase diagram of the original Haldane model of a Hall effect in the absence of a net magnetic field. The resultant Floquet band topology is again that of a Chern insulator with the driving parameters—frequency and amplitude— influencing the inversion breaking mass M of the undriven Haldane model. A family of such periodically related “Semenoff masses” is observed to occur, which support a periodic repetition of Haldane like phase diagrams along the inversion breaking axis of the phase plots. Out of these it is possible to identify two in-equivalent masses in the reduced zone scheme of the Floquet quasienergies, which form the centers of two inequivalent phase diagrams. Further, variation in the driving amplitude's magnitude alone is shown to effect the topological properties by linearly shifting the phase diagram of the driven model about the position of the undriven case, a phenomenon that allows the study of Floquet topological phase transitions in the system. Finally, we also discuss some issues regarding the modifications to Haldane's condition for preventing band overlaps at the Dirac point touchings in the Brillouin zone, in the presence of kicking.
Gravitational-wave detection using redshifted 21-cm observations
(APS, 2009-06) Sarkar, Tapomoy Guha
A gravitational-wave traversing the line of sight to a distant source produces a frequency shift which contributes to redshift space distortion. As a consequence, gravitational waves are imprinted as density fluctuations in redshift space. The gravitational-wave contribution to the redshift space power spectrum has a different μ dependence as compared to the dominant contribution from peculiar velocities. This, in principle, allows the two signals to be separated. The prospect of a detection is most favorable at the highest observable redshift z. Observations of redshifted 21-cm radiation from neutral hydrogen hold the possibility of probing very high redshifts. We consider the possibility of detecting primordial gravitational waves using the redshift space neutral hydrogen power spectrum. However, we find that the gravitational-wave signal, though present, will not be detectable on superhorizon scales because of cosmic variance and on subhorizon scales where the signal is highly suppressed.