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Sourav Bhattacharya

Publications and source records attributed to Sourav Bhattacharya.

At least 55 records · Page 3Linked to original sources
arXiv2023

Decoherence and entropy generation in an open quantum scalar-fermion system with Yukawa interaction

We have studied the decoherence mechanism in a fermion and scalar quantum field theory with the Yukawa interaction in the Minkowski spacetime, using the non-equilibrium effective field theory formalism appropriate for open systems. The scalar field is treated as the system whereas the fermions as the environment. As the simplest realistic scenario, we assume that an observer measures only the Gaussian 2-point correlator for the scalar field. The cause of decoherence and the subsequent entropy generation is the ignorance of information stored in higher-order correlators, Gaussian and non-Gaussian, of the system and the surrounding. Using the 2-loop 2-particle irreducible effective action, we construct the renormalised Kadanoff-Baym equations, i.e., the equation of motion satisfied by the 2-point correlators in the Schwinger-Keldysh formalism. These equations contain the non-local self-energy corrections. We then compute the statistical propagator in terms of the 2-point functions. Using the relationship of the statistical propagator with the phase space area, we next compute the von Neumann entropy for the system. We have obtained the variation of the entropy with respect to various relevant parameters. We also discuss the qualitative similarities and differences of our results with the scenario when both the system and the environment are scalar fields.

hep-th↗
arXiv2022

Stationary black holes and stars in the Brans-Dicke theory with $Λ>0$ revisited

It was shown a few years back that for a stationary regular black hole or star solution in the Brans-Dicke theory with a positive cosmological constant $Λ$, endowed with a de Sitter or cosmological event horizon in the asymptotic region, not only there exists no non-trivial field configurations, but also the inverse Brans-Dicke parameter $ω^{-1}$ must be vanishing. This essentially reduces the theory to Einstein's General Relativity. The assumption of the existence of the cosmological horizon was crucial for this proof. However, since the Brans-Dicke field $ϕ$, couples directly to the $Λ$-term in the energy-momentum tensor as well as $Λ$ acts as a source in $ϕ$'s equation of motion, it seems reasonable to ask : can $ϕ$ become strong instead and screen the effect of $Λ$, at very large scales, so that the asymptotic de Sitter structure is replaced by some alternative, yet still acceptable boundary condition? In this work we analytically argue that no such alternative exists, as long as the spacetime is assumed to be free of any naked curvature singularity. We further support this result by providing explicit numerical computations. Thus we conclude that in the presence of a positive $Λ$, irrespective of whether the asymptotic de Sitter boundary condition is imposed or not, a regular stationary black hole or even a star solution in the Brans-Dicke theory always necessitates $ω^{-1}=0$, and thereby reducing the theory to General Relativity. The qualitative differences of this result with that of the standard no hair theorems are also pointed out.

gr-qc↗
arXiv2022

Cross-Attention is all you need: Real-Time Streaming Transformers for Personalised Speech Enhancement

Personalised speech enhancement (PSE), which extracts only the speech of a target user and removes everything else from a recorded audio clip, can potentially improve users' experiences of audio AI modules deployed in the wild. To support a large variety of downstream audio tasks, such as real-time ASR and audio-call enhancement, a PSE solution should operate in a streaming mode, i.e., input audio cleaning should happen in real-time with a small latency and real-time factor. Personalisation is typically achieved by extracting a target speaker's voice profile from an enrolment audio, in the form of a static embedding vector, and then using it to condition the output of a PSE model. However, a fixed target speaker embedding may not be optimal under all conditions. In this work, we present a streaming Transformer-based PSE model and propose a novel cross-attention approach that gives adaptive target speaker representations. We present extensive experiments and show that our proposed cross-attention approach outperforms competitive baselines consistently, even when our model is only approximately half the size.

eess.AS↗
arXiv2022

Massless minimal quantum scalar field with an asymmetric self interaction in de Sitter spacetime

Massless minimally coupled quantum scalar field with an asymmetric self interaction, $V(ϕ)=λϕ^4/4!+ βϕ^3/3! $ (with $λ>0$) is considered in the $(3+1)$-dimensional inflationary de Sitter spacetime. This potential is bounded from below irrespective of the sign of $β$. Earlier computations mostly considered the quartic part. Our chief motivation behind this study is to assess the vacuum expectation values of $V(ϕ)$ and $ϕ$, both of which can be negative, and hence may lead to some screening of the inflationary cosmological constant value. First using the in-in formalism, the renormalised quantum correction to the cubic potential appearing in the energy-momentum tensor is computed at two loop, which is the leading order in this case. The quantum correction to the kinetic term at two loop are subleading compared to the above result at late cosmological times. Next, using some of these results we compute the renormalised vacuum expectation value of $ ϕ$, by computing the tadpoles at ${\cal O}(β)$ and ${\cal O}(λβ)$. Due to the appearance of the de Sitter isometry breaking logarithms, the tadpoles cannot be completely renormalised away in this case, unlike the flat spacetime. All these results, as expected, show secularly growing logarithms at late cosmological times. We next use a recently proposed renormalisation group inspired formalism to resum perturbative secular effects, to compute a non-perturbative $\langle ϕ\rangle$ at late cosmological times. $\langle ϕ\rangle$ turns out to be approximately one order of magnitude less compared to the position of the classical minima $ϕ=-3β/λ$ of $V(ϕ)$. Estimation on the possible screening of the inflationary cosmological constant due to this $\langle ϕ\rangle$ is also presented.

hep-th↗
arXiv2022

Vacuum polarisation of Dirac fermions in the cosmological de Sitter-global monopole spacetime

We study the vacuum polarisation effects of the Dirac fermionic field induced by a pointlike global monopole located in the cosmological de Sitter spacetime. First we derive the four orthonormal Dirac modes in this background in a closed form. Quantising the field using these modes, we then compute the fermionic condensate, $\langle 0| \overlineΨ Ψ| 0\rangle$, as well as the vacuum expectation value of the energy-momentum tensor for a massive Dirac field, regularised in a particular way. We have used the Abel-Plana summation formula in order to extract the global monopole contribution to these quantities and have investigated their variations numerically with respect to relevant parameters.

hep-th↗
arXiv2022

Entanglement degradation in multi-event horizon spacetimes

We investigate the degradation of quantum entanglement in the Schwarzschild-de Sitter black hole spacetime, by studying the mutual information and the logarithmic negativity for maximally entangled, bipartite states for massless minimal scalar fields. This spacetime is endowed with a black hole as well as a cosmological event horizon, giving rise to particle creation at two different temperatures. We consider two independent descriptions of thermodynamics and particle creation in this background. The first involves thermal equilibrium of an observer with either of the horizons. We show that as of the asymptotically flat/anti-de Sitter black holes, in this case the entanglement or correlation degrades with increasing Hawking temperatures. The second treats both the horizons combined in order to define a total entropy and an effective equilibrium temperature. We present a field theoretic derivation of this effective temperature and show that unlike the usual cases, the particle creation does not occur here in causally disconnected spacetime wedges but instead in a single region. Using the associated vacua, we show that in this scenario the entanglement never degrades but increases with increasing black hole temperature and holds true no matter how hot the black hole becomes or how small the cosmological constant is. We argue that this phenomenon can have no analogue in the asymptotically flat/anti-de Sitter black hole spacetimes.

hep-th↗
arXiv2021

Fermionic Bell violation in the presence of background electromagnetic fields in the cosmological de Sitter spacetime

The violation of the Bell inequality for Dirac fermions is investigated in the cosmological de Sitter spacetime, in the presence of background electromagnetic fields of constant strengths. The orthonormal Dirac mode functions are obtained and the relevant in-out squeezed state expansion in terms of the Bogoliubov coefficients are found. We focus on two scenarios here : strong electric field and heavy mass limits (with respect to the Hubble constant). Using the squeezed state expansion, we then demonstrate the Bell violations for the vacuum and some maximally entangled initial states. Even though a background magnetic field alone cannot create particles, in the presence of background electric field and or spacetime curvature, it can affect the particle creation rate. Our chief aim thus here is to investigate the role of the background magnetic field strength in the Bell violation. Qualitative differences in this regard for different maximally entangled initial states are shown. Further extension of these results to the so called $α$-vacua are also discussed.

hep-th↗
arXiv2021

Defensive Tensorization

We propose defensive tensorization, an adversarial defence technique that leverages a latent high-order factorization of the network. The layers of a network are first expressed as factorized tensor layers. Tensor dropout is then applied in the latent subspace, therefore resulting in dense reconstructed weights, without the sparsity or perturbations typically induced by the randomization.Our approach can be readily integrated with any arbitrary neural architecture and combined with techniques like adversarial training. We empirically demonstrate the effectiveness of our approach on standard image classification benchmarks. We validate the versatility of our approach across domains and low-precision architectures by considering an audio classification task and binary networks. In all cases, we demonstrate improved performance compared to prior works.

cs.LG↗
arXiv2021

The maximum turnaround radius for axisymmetric cosmic structures

Three simple idealised models are studied in order to develop some intuition about the leading order effect of non-sphericity on the maximum turnaround size $R_{\rm TA,max}$ of large scale bound cosmic structures. Two of them describe intrinsically axisymmetric static mass distributions whereas the other is the Kerr-de Sitter metric where the axisymmetry is generated due to the rotation of the structure. In all the cases the fractional change $δR_{\rm TA,max}(θ)/R^{(0)}_{\rm TA,max}$ of $R_{\rm TA,max}$ of a given structure, compared to a spherical one with the same mass $M$, depends on the polar angle $θ$ and is proportional to the product of the relevant eccentricity parameter, times the square of a small quantity. This quantity in the static examples is the ratio of two characteristic length scales, while in the spinning case it is the ratio $v_{\rm out}/c$ of the azimuthal speed of the outmost members of the structure, over the speed of light. Furthermore, the angular average $\langle δR_{\rm TA,max}(θ)/R^{(0)}_{\rm TA,max}\rangle$ is zero in the two static cases, while it is negative and proportional to ${\cal O}(v^2_{\rm out}/c^2)$ for the Kerr-de Sitter. Thus, $δR_{\rm TA,max}(θ)/R^{(0)}_{\rm TA,max}$ for an axisymmetric structure is very small for practically any value of the eccentricity parameter. We speculate about some possible further implications of our result on the maximum turn around radius of realistic cosmic structures.

gr-qc↗
arXiv2021

Unruh-DeWitt detector responses for complex scalar fields in de Sitter spacetime

We derive the response function for a comoving, pointlike Unruh-DeWitt particle detector coupled to a complex scalar field $ϕ$, in the $(3+1)$-dimensional cosmological de Sitter spacetime. The field-detector coupling is taken to be proportional to $ϕ^{\dagger} ϕ$. We address both conformally invariant and massless minimally coupled scalar field theories, respectively in the conformal and the Bunch-Davies vacuum. The response function integral for the massless minimal complex scalar, not surprisingly, shows divergences and accordingly we use suitable regularisation scheme to find out well behaved results. The regularised result also contains a de Sitter symmetry breaking logarithm, growing with the cosmological time. Possibility of extension of these results with the so called de Sitter $α$-vacua is discussed. While we find no apparent problem in computing the response function for a real scalar in these vacua, a complex scalar field is shown to contain some possible ambiguities in the detector response. The case of the minimal and nearly massless scalar field theory is also briefly discussed.

hep-th↗
arXiv2021

Unicritical Laminations

Thurston introduced \emph{invariant (quadratic) laminations} in his 1984 preprint as a vehicle for understanding the connected Julia sets and the parameter space of quadratic polynomials. Important ingredients of his analysis of the angle doubling map $σ_2$ on the unit circle $\mathbb{S}^1$ were the Central Strip Lemma, non-existence of wandering polygons, the transitivity of the first return map on vertices of periodic polygons, and the non-crossing of minors of quadratic invariant laminations. We use Thurston's methods to prove similar results for \emph{unicritical} laminations of arbitrary degree $d$ and to show that the set of so-called \emph{minors} of unicritical laminations themselves form a \emph{Unicritical Minor Lamination} $\mathrm{UML}_d$. In the end we verify the \emph{Fatou conjecture} for the unicritical laminations and extend the \emph{Lavaurs algorithm} onto $\mathrm{UML}_d$.

math.DS↗
arXiv2020

Some measures for fermionic entanglement in the cosmological de Sitter spacetime

We investigate two measures of quantum correlations and entanglement, namely the violation of the Bell-Mermin-Klyshko inequalities and the quantum discord, for Dirac fermions in the cosmological de Sitter background of dimension four. The BMK violation is focussed on the vacuum for two and four mode squeezed states and it is shown to increase with the number of modes. For the quantum discord, we investigate a maximally entangled in-vacuum state. Qualitative similarities as well as differences of our results with that of different coordinatisations of de Sitter in the context of scalar and fermionic field theory is discussed.

hep-th↗
arXiv2020

Bunched LPCNet : Vocoder for Low-cost Neural Text-To-Speech Systems

LPCNet is an efficient vocoder that combines linear prediction and deep neural network modules to keep the computational complexity low. In this work, we present two techniques to further reduce it's complexity, aiming for a low-cost LPCNet vocoder-based neural Text-to-Speech (TTS) System. These techniques are: 1) Sample-bunching, which allows LPCNet to generate more than one audio sample per inference; and 2) Bit-bunching, which reduces the computations in the final layer of LPCNet. With the proposed bunching techniques, LPCNet, in conjunction with a Deep Convolutional TTS (DCTTS) acoustic model, shows a 2.19x improvement over the baseline run-time when running on a mobile device, with a less than 0.1 decrease in TTS mean opinion score (MOS).

eess.AS↗
arXiv2020

Iterative Compression of End-to-End ASR Model using AutoML

Increasing demand for on-device Automatic Speech Recognition (ASR) systems has resulted in renewed interests in developing automatic model compression techniques. Past research have shown that AutoML-based Low Rank Factorization (LRF) technique, when applied to an end-to-end Encoder-Attention-Decoder style ASR model, can achieve a speedup of up to 3.7x, outperforming laborious manual rank-selection approaches. However, we show that current AutoML-based search techniques only work up to a certain compression level, beyond which they fail to produce compressed models with acceptable word error rates (WER). In this work, we propose an iterative AutoML-based LRF approach that achieves over 5x compression without degrading the WER, thereby advancing the state-of-the-art in ASR compression.

cs.LG↗
arXiv2020

Background magnetic field and quantum correlations in the Schwinger effect

In this work we consider two complex scalar fields distinguished by their masses coupled to constant background electric and magnetic fields in the $(3+1)$-dimensional Minkowski spacetime and subsequently investigate a few measures quantifying the quantum correlations between the created particle-antiparticle Schwinger pairs. Since the background magnetic field itself cannot cause the decay of the Minkowski vacuum, our chief motivation here is to investigate the interplay between the effects due to the electric and magnetic fields. We start by computing the entanglement entropy for the vacuum state of a single scalar field. Second, we consider some maximally entangled states for the two-scalar field system and compute the logarithmic negativity and the mutual information. Qualitative differences of these results pertaining to the charge content of the states are emphasised. Based upon these results, we suggest some possible effects of a background magnetic field on the degradation of entanglement between states in an accelerated frame, for charged quantum fields.

hep-th↗
arXiv2020

Dirac fermion, cosmological event horizons and quantum entanglement

We discuss the field quantisation of a free massive Dirac fermion in the two causally disconnected static patches of the de Sitter spacetime, by using mode functions that are normalisable on the cosmological event horizon. Using this, we compute the entanglement entropy of the vacuum state corresponding to these two regions, for a given fermionic mode. Further extensions of this result to more general static spherically symmetric and stationary axisymmetric spacetimes are discussed. For the stationary axisymmetric Kerr-de Sitter spacetime in particular, the variations of the entanglement entropy with respect to various eigenvalues and spacetime parameters are depicted numerically. We also comment on such variations when instead we consider the non-extremal black hole event horizon of the same spacetime.

hep-th↗
arXiv2019

Very badly ordered cycles of interval maps

We prove that a periodic orbit $P$ with coprime over-rotation pair is an over-twist periodic orbit iff the $P$-linear map has the over-rotation interval with left endpoint equal to the over-rotation number of $P$. We then show that this result fails if the over-rotation pair of $P$ is not coprime. Examples of patterns with non-coprime over-rotation pairs are given so that these patterns have no block structure over over-twists but have over-rotation number equal to the left endpoint of the forced over-rotation interval (such patterns are called \emph{very badly ordered}). This presents a situation in which the results about over-rotation numbers on the interval and those about classical rotation numbers for circle degree one maps are different. In the end we elucidate a rigorous description of the strongest unimodal pattern that corresponds to a given over-rotation interval and use it to construct unimodal very badly ordered patterns with arbitrary non-coprime over-rotation pair.

math.DS↗