Spectral representation of thermal OTO correlators

Chaudhuri, Soumyadeep; Chowdhury, Chandramouli; Loganayagam, R.

doi:10.1007/jhep02(2019)018

Cited by 23 publications

(49 citation statements)

References 60 publications

(99 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These combinations correspond to the retarded advanced (RA) basis within the SK formalism [14,[29][30][31][32][33][34][35][36][37] which is the most convenient in making KMS conditions manifest. In terms of these combinations, we can then write…”

Section: Non-linear Langevin Theorymentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Langevin dynamics via holography

Chakrabarty

Chakravarty

Chaudhuri

et al. 2020

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

In this work, we consider non-linear corrections to the Langevin effective theory of a heavy quark moving through a strongly coupled CFT plasma. In AdS/CFT, this system can be identified with that of a string stretched between the boundary and the horizon of an asymptotically AdS black-brane solution. We compute the Feynman-Vernon influence functional for the heavy quark by evaluating the Nambu-Goto action on a doubled string configuration. This configuration is the linearised solution of the string motion in the doubled black-brane geometry which has been proposed as the holographic dual of a thermal Schwinger-Keldysh contour of the CFT. Our expression for the influence phase passes non-trivial consistency conditions arising from the underlying unitarity and thermality of the bath. The local effective theory obeys the recently proposed non-linear fluctuation dissipation theorem relating the non-Gaussianity of thermal noise to the thermal jitter in the damping constant. This furnishes a non-trivial check for the validity of these relations derived in the weak coupling regime. Contents

show abstract

Section: Non-linear Langevin Theorymentioning

confidence: 99%

“…The vanishing of the all P and all F terms is the hallmark of the retarded advanced basis in the Schwinger-Keldysh formalism [33][34][35][36][37]. On the CFT side, this is a combined consequence of both the largest time equation of SK formalism and the KMS conditions arising from the thermality of the bath.…”

Section: A Influence Phase Of the Heavy Quarkmentioning

confidence: 99%

Nonlinear Langevin dynamics via holography

Chakrabarty

Chakravarty

Chaudhuri

et al. 2020

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…These expressions are obtained from the forms given in tables 2 and 3 by imposing the KMS relations between the spectral functions. Such KMS relations between the bath's correlators were studied in [10] to express the Fourier transforms of all contour-ordered correlators in terms of a different basis of spectral functions which is given below:…”

Section: Relations Between the Oto Effective Couplings And The Bathmentioning

confidence: 99%

“…(19)Plugging these expressions for the quadratic and quartic terms in the influence phase into the path integral given in(15), one can determine the evolution of the reduced density matrix of the particle. The effective action that appears in this path integral can also be used to compute the correlators of the particle 10. From the form of the influence phase in (17), we can see that this effective action is non-local in time.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Out of time ordered effective dynamics of a quartic oscillator

Chakrabarty

Chaudhuri

2019

SciPost Phys.

Self Cite

View full text Add to dashboard Cite

We study the dynamics of a quantum Brownian particle weakly coupled to a thermal bath. Working in the Schwinger-Keldysh formalism, we develop an effective action of the particle up to quartic terms. We demonstrate that this quartic effective theory is dual to a stochastic dynamics governed by a non-linear Langevin equation. The Schwinger-Keldysh effective theory, or the equivalent non-linear Langevin dynamics, is insufficient to determine the out of time order correlators (OTOCs) of the particle. To overcome this limitation, we construct an extended effective action in a generalised Schwinger-Keldysh framework. We determine the additional quartic couplings in this OTO effective action and show their dependence on the bath's 4-point OTOCs. We analyse the constraints imposed on the OTO effective theory by microscopic reversibility and thermality of the bath. We show that these constraints lead to a generalised fluctuation-dissipation relation between the non-Gaussianity in the distribution of the thermal noise experienced by the particle and the thermal jitter in its damping coefficient. The quartic effective theory developed in this work provides extension of several results previously obtained for the cubic OTO dynamics of a Brownian particle. Contents SciPost PhysicsSubmission [22,[27][28][29]. Nevertheless, it is interesting to explore the corrections to this effective dynamics by including the cubic and higher degree terms in the analysis. A simple way to obtain such corrections is to extend the Caldeira-Leggett model by introducing a non-linear combination of the bath oscillators' positions in the operator that couples to the particle [29,30].One such extension was discussed in [30] where the oscillators in the bath were divided into two sets (labelled by X and Y). Then apart from the bilinear interactions (which are present in the Caldeira-Leggett model), small cubic interactions were introduced between the particle (q) and pairs of bath oscillators. Each such pair consisted of one oscillator drawn from the set X and the other from the set Y. Due to these cubic interactions, this model was called the 'qXY model'.Introduction of these cubic interactions leads to cubic and higher degree terms in the effective action of the particle. In [30], this effective theory was studied up to the cubic terms in a Markovian limit. It was shown to be dual to a non-linear Langevin dynamics which has perturbative corrections over the linear Langevin dynamics in the Caldeira-Leggett model. The additional parameters in this non-linear dynamics receive contributions from the 3-point correlators of the bath. These 3-point correlators lead to an anharmonicity in the particle's dynamics and a non-Gaussianity in the distribution of the thermal noise experienced by the particle. In addition, they also give rise to thermal jitters 1 in both the frequency and the damping of the particle. The thermal jitter in the damping coefficient and the non-Gaussianity in the noise are connected by a generalised fluctuation-dissipation relation [30...

show abstract

C${\cal C}$osmological G${\cal G}$eometric P${\cal P}$hase F${\cal F}$rom P${\cal P}$ure Q${\cal Q}$uantum S${\cal S}$tates: A Study without/ with having Bell's Inequality Violation

Choudhury

2022

Fortschritte der Physik

View full text Add to dashboard Cite

In this paper, using the concept of Lewis Riesenfeld invariant quantum operator method for finding continuous eigenvalues of quantum mechanical wave functions we derive the analytical expressions for the cosmological geometric phase, which is commonly identified to be the Pancharatnam Berry phase from primordial cosmological perturbation scenario. We compute this cosmological geometric phase from two possible physical situations, (1) In the absence of Bell's inequality violation and (2) In the presence of Bell's inequality violation having the contributions in the sub Hubble region (−kτ≫1$-k\tau \gg 1$), super Hubble region (−kτ≪1$-k\tau \ll 1$) and at the horizon crossing point (−kτ=1$-k\tau = 1$) for massless field (m/scriptH≪1$m/{\cal H}\ll 1$), partially massless field (m/scriptH∼1$m/{\cal H}\sim 1$) and massive/heavy field (m/scriptH≫1$m/{\cal H}\gg 1$), in the background of quantum field theory of spatially flat quasi De Sitter geometry. The prime motivation for this work is to investigate the various unknown quantum mechanical features of primordial universe. To give the realistic interpretation of the derived theoretical results we express everything initially in terms of slowly varying conformal time dependent parameters, and then to connect with cosmological observation we further express the results in terms of cosmological observables, which are spectral index/tilt of scalar mode power spectrum (nζ$n_{\zeta }$) and tensor‐to‐scalar ratio (r). Finally, this identification helps us to provide the stringent numerical constraints on the Pancharatnam Berry phase, which confronts well with recent cosmological observation.

show abstract

Spectral representation of thermal OTO correlators

Cited by 23 publications

References 60 publications

Nonlinear Langevin dynamics via holography

Nonlinear Langevin dynamics via holography

Out of time ordered effective dynamics of a quartic oscillator

C${\cal C}$osmological G${\cal G}$eometric P${\cal P}$hase F${\cal F}$rom P${\cal P}$ure Q${\cal Q}$uantum S${\cal S}$tates: A Study without/ with having Bell's Inequality Violation

Contact Info

Product

Resources

About