Helmholtz decomposition of the Lagrangian displacement

Chan, Kwan Chuen

doi:10.1103/physrevd.89.083515

Cited by 25 publications

(29 citation statements)

References 37 publications

(58 reference statements)

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“…In the ZA, Ψ is determined by the gradient of the gravitational potential ∇Φ, which can be expressed in terms of the linearly extrapolated density field. Considering only the scalar contribution Ψ, at first and second order in the matter density field, we have ( [4])…”

Section: A the Zel'dovitch And 2lpt Approximationsmentioning

confidence: 99%

“…In the modelling of cosmological fluid dynamics, a particularly important role is played by the vector displacement field Ψ(q, t), which specifies the trajectory of fluid elements through space (here denoted by a Lagrangian co-ordinate q) and time t. In modelling approaches such as Lagrangian Perturbation Theory, perturbative solutions may be formulated for Ψ and used to construct models for the statistics of the observed density field (e.g. [1][2][3][4])…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Improving reconstruction of the baryon acoustic peak: The effect of local environment

Achitouv¹

2015

Phys. Rev. D

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Precise measurements of the baryon acoustic oscillation (BAO) scale as a standard ruler in the clustering pattern of large-scale structure is a central goal of current and future galaxy surveys. The BAO peak may be sharpened using the technique of density-field reconstruction, in which the bulk displacements of galaxies are estimated using a Zel'dovitch approximation. We use numerical simulations to demonstrate how the accuracy of this approximation depends strongly on local environment, and how this information may be used to construct an improved BAO measurement through environmental re-weighting and using higher-order perturbation theory. We outline further applications of the displacement field for testing cosmological models.

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Section: A the Zel'dovitch And 2lpt Approximationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Improving reconstruction of the baryon acoustic peak: The effect of local environment

Achitouv¹

2015

Phys. Rev. D

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“…This work follows our recent paper [18] (hereafter BSZ), where we studied the perturbative solution for the displacement field of dark matter particles using the appropriate Lagrangian Effective Theory (LEFT) [10] and compared these results against numerical simulations. Tests of LPT at the density field level have also been performed in [19,20] and tests of Effective Field Theory in connection to LPT have been performed in [21,22]. Here we use the density field induced by those displacements and compare it with the same suite of simulations.…”

Section: Introductionmentioning

confidence: 99%

On the reach of perturbative methods for dark matter density fields

Baldauf¹,

Schaan²,

Zaldarriaga³

2016

J. Cosmol. Astropart. Phys.

101

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Abstract. We study the mapping from Lagrangian to Eulerian space in the context of the Effective Field Theory (EFT) of Large Scale Structure. We compute Lagrangian displacements with Lagrangian Perturbation Theory (LPT) and perform the full non-perturbative transformation from displacement to density. When expanded up to a given order, this transformation reproduces the standard Eulerian Perturbation Theory (SPT) at the same order. However, the full transformation from displacement to density also includes higher order terms. These terms explicitly resum long wavelength motions, thus making the resulting density field better correlated with the true non-linear density field. As a result, the regime of validity of this approach is expected to extend that of the Eulerian EFT, and match that of the IR-resummed Eulerian EFT. This approach thus effectively enables a test of the IRresummed EFT at the field level. We estimate the size of stochastic, non-perturbative contributions to the matter density power spectrum. We find that in our highest order calculation, at redshift z = 0 the power spectrum of the density field is reproduced with an accuracy of 1% (10%) up to k = 0.25 hMpc −1 (k = 0.46 hMpc −1 ). We believe that the dominant source of the remaining error is the stochastic contribution. Unfortunately, on these scales the stochastic term does not yet scale as k 4 as it does in the very low k regime. Thus, modeling this contribution might be challenging.

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“…Let's examine the role of the aforementioned assumptions one by one. If assumption (III) at least for one of the reservoirs is relaxed, the dynamics is non-additive [55]. In our work, both reservoirs are independently Markovian, ruling out assumption (III) as the origin of the non-additive dynamics.…”

Section: Resultsmentioning

confidence: 77%

Non-Markovian Dynamics of Macroscopic Quantum Systems in Interaction with Non-equilibrium Environments

2019

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We study the dynamics of a macroscopic superconducting qubit coupled to two independent nonstationary reservoirs by using time-dependent perturbation theory. We show that an equilibrium environment surpasses the coherent evolution of the macroscopic qubit completely. When the qubit couples to two different reservoirs, exemplifying a non-equilibrium environment, the short-time dynamics is affected by the interference between two reservoirs, implying the non-additivity of effects of two reservoirs. The non-additivity can be traced back to a non-Markovian effect, even though two reservoirs are independently assumed to be Markovian. Explicitly, the non-equilibrium environment intensifies both coherent and incoherent parts of the evolution. Therefore, the macroscopic qubit would evolve more coherently but at the price of a shorter decoherence time. INTRODUCTIONAn environment in thermal equilibrium destroys the coherence of a quantum system interacting with it [1][2][3][4]. Such decoherence process is one of the main obstacles in realizing quantum computers [5][6][7][8]. One approach to implement a quantum computer is based on superconductors, where the quantum effects become macroscopic, though at a price of extremely low temperatures [9][10][11][12]. Apart from this straightforward strategy, a number of schemes have been proposed to control the decoherence process by engineering the system-environment interaction (for a rather complete review, see [13]). One of the effective strategies, observed naturally in biological systems [14,15], is engineering non-equilibrium environments. Such an environment has the opportunity to influence the quantum evolution in a manner that is more rich and complex than simply acting to randomize relative phases and dissipate energy.The open quantum systems are mostly examined by Lindblad master equations [3,16,17], which are based on Born and Markov approximations, and depending on the context, an additional uncontrolled approximation [3, 18-20] on the environment. However, in non-equilibrium systems, such approximations may lead to incorrect predictions [21][22][23][26][27][28][29]. One of such predictions is that the effect of two initially uncorrelated environments on the system's dynamics is independent and additive in the weak-coupling limit [30]. The validity of this prediction has been examined in a number of contexts in the literature [22,26,28,[31][32][33][34][35][36][37][38]. In fact, the non-additive effect is not unfolded by Markovian approach, implying the non-Markovian property of the dynamics [39][40][41][42].Apart from the approach employed, among all the works mentioned, the lack of a macroscopic quantum system as the case study is deeply felt. Here, we examine the effective dynamics of a macroscopic superconducting qubit, in interaction with a non-equilibrium environment. To be macroscopic, conceptually, the dynamics should involve macroscopically distinguishable, entangled states [43]. The effective dynamics of the macroscopic superconducting qubit, particularly the p...

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Helmholtz decomposition of the Lagrangian displacement

Cited by 25 publications

References 37 publications

Improving reconstruction of the baryon acoustic peak: The effect of local environment

Improving reconstruction of the baryon acoustic peak: The effect of local environment

On the reach of perturbative methods for dark matter density fields

Non-Markovian Dynamics of Macroscopic Quantum Systems in Interaction with Non-equilibrium Environments

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