Monte Carlo Study of Real Time Dynamics on the Lattice

Alexandru, Andrei; Başar, Gökçe; Bedaque, Paulo F.; Vartak, Sohan; Warrington, Neill C.

doi:10.1103/physrevlett.117.081602

Cited by 115 publications

(93 citation statements)

References 36 publications

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“…The most pressing one is perhaps the extension to the thermodynamic limit, with the goal of determining whether the contribution of any other thimble survives this limit. Also, our group has recently developed similar technology to that described in this paper to study the real time dynamics of a simple quantum mechanical model [23]. We look forward to combining the experience acquired in the present paper to study the real time dynamics of the Bose gas with an eye towards the computation of transport coefficients.…”

Section: Discussionmentioning

confidence: 91%

Study of symmetry breaking in a relativistic Bose gas using the contraction algorithm

Alexandru¹,

Başar²,

Bedaque³

et al. 2016

Phys. Rev. D

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A relativistic Bose gas at finite density suffers from a sign problem that makes direct numerical simulations not feasible. One possible solution to the sign problem is to re-express the path integral in terms of Lesfschetz thimbles. Using this approach we study the relativistic Bose gas both in the symmetric phase (low-density) and the spontaneously broken phase (high-density). In the high-density phase we break explicitly the symmetry and determine the dependence of the order parameter on the breaking. We study the relative contributions of the dominant and sub-dominant thimbles in this phase. We find that the sub-dominant thimble only contributes substantially when the explicit symmetry breaking is small, a regime that is dominated by finite volume effects. In the regime relevant for the thermodynamic limit, this contribution is negligible.

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Section: Discussionmentioning

confidence: 91%

Study of symmetry breaking in a relativistic Bose gas using the contraction algorithm

Alexandru¹,

Başar²,

Bedaque³

et al. 2016

Phys. Rev. D

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“…We also notice that the localization technique is applicable in CP N −1 QM to compute the first order ground state energy E (1) but not the second order. Recent results on volume independence [41] should be useful in extending our study to QFT, which may also require more refined thimble analysis as has been studied intensively [64][65][66][67][68].…”

Section: Summary and Discussionmentioning

confidence: 99%

“…We will show that the contributions from an infinite tower of multi-bion solutions yield all these nonperturbative exponentials. This is the first result revealing the thimble structure of all the complex saddle points, which is useful not only to understand the resurgence structure in quantum theories but also to study complex path integrals including real-time formalism and finite-density systems in condensed and nuclear matters [63][64][65][66][67][68].…”

Section: Introductionmentioning

confidence: 99%

Exact resurgent trans-series and multibion contributions to all orders

et al. 2017

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The full resurgent trans-series is found exactly in near-supersymmetric CP 1 quantum mechanics. By expanding in powers of the SUSY breaking deformation parameter, we obtain the first and second expansion coefficients of the ground state energy. They are absolutely convergent series of nonperturbative exponentials corresponding to multi-bions with perturbation series on those backgrounds. We obtain all multi-bion exact solutions for finite time interval in the complexified theory. We sum the semi-classical multi-bion contributions that reproduce the exact result supporting the resurgence to all orders. We also discuss the similar resurgence structure in CP N−1 (N > 2) models. This is the first result in the quantum mechanical model where the resurgent trans-series structure is verified to all orders in nonperturbative multi-bion contributions.

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“…However, when there exists more than one thimbles, the transition from one to another does not occur during the Monte Carlo simulation and hence the ergodicity is violated in this limit. Therefore, there is an optimal flow time in general [23][24][25]. (See refs.…”

Section: Jhep06(2017)023mentioning

confidence: 99%

Combining the complex Langevin method and the generalized Lefschetz-thimble method

Nishimura

Shimasaki

2017

J. High Energ. Phys.

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Abstract:The complex Langevin method and the generalized Lefschetz-thimble method are two closely related approaches to the sign problem, which are both based on complexification of the original dynamical variables. The former can be viewed as a generalization of the stochastic quantization using the Langevin equation, whereas the latter is a deformation of the integration contour using the so-called holomorphic gradient flow. In order to clarify their relationship, we propose a formulation which combines the two methods by applying the former method to the real variables that parametrize the deformed integration contour in the latter method. Three versions, which differ in the treatment of the residual sign problem in the latter method, are considered. By applying them to a single-variable model, we find, in particular, that one of the versions interpolates the complex Langevin method and the original Lefschetz-thimble method.

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Monte Carlo Study of Real Time Dynamics on the Lattice

Cited by 115 publications

References 36 publications

Study of symmetry breaking in a relativistic Bose gas using the contraction algorithm

Study of symmetry breaking in a relativistic Bose gas using the contraction algorithm

Exact resurgent trans-series and multibion contributions to all orders

Combining the complex Langevin method and the generalized Lefschetz-thimble method

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