Simulations of “tunnelling of the 3rd kind”

Mou, Zong-Gang; Saffin, Paul M.; Tognarelli, Paul; Tranberg, Anders

doi:10.1007/jhep07(2017)015

Cited by 6 publications

(11 citation statements)

References 14 publications

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“…The numerical challenge we encounter here also reflects the fact that the pure quantum tunnelling effect is hard to simulate, as it is accompanied with exponential suppression of the evolution across the barrier, for instance as in [52]. To have a sensible signal of tunnelling, a reasonably-sized coupling constant is required.…”

Section: Results With the Thimble Approachmentioning

confidence: 99%

Quantum tunnelling, real-time dynamics and Picard-Lefschetz thimbles

Mou

Saffin

Tranberg

2019

J. High Energ. Phys.

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We follow up the work, where in light of the Picard-Lefschetz thimble approach, we split up the real-time path integral into two parts: the initial density matrix part which can be represented via an ensemble of initial conditions, and the dynamic part of the path integral which corresponds to the integration over field variables at all later times. This turns the path integral into a two-stage problem where, for each initial condition, there exits one and only one critical point and hence a single thimble in the complex space, whose existence and uniqueness are guaranteed by the characteristics of the initial value problem. In this paper, we test the method for a fully quantum mechanical phenomenon, quantum tunnelling in quantum mechanics. We compare the method to solving the Schrödinger equation numerically, and to the classical-statistical approximation, which emerges naturally in a well-defined limit. We find that the Picard-Lefschetz result matches the expectation from quantum mechanics and that, for this application, the classical-statistical approximation does not.-1 -There are a number of ways to try and sidestep this problem. One is to solve for the time evolution of the fields, or correlators of the fields, through some effective, systematically truncated, evolution equations. Good examples include the classical statistical approximation, where an ensemble mimicking the quantum initial density matrix are evolved using straightforward classical equations of motion. In cases where the occupation numbers are large, and the system is far from thermal equilibrium, this is a powerful and easily implementable approximation (see for instance [3][4][5][6][7]). Truncated Schwinger-Dyson equations for two-or higher-point correlators have been used to good effects for the approach to equilibrium, as well as in cosmological applications involving scalar and fermion fields (see [8][9][10][11]). Stochastic equations have also proven a valuable tool for concrete cases, that allow for a mapping of the full dynamics to such a description in a systematic way (see for instance [12,13]).In some cases, however, one must return to the direct computation of the path integral (1.2), but standard Monte-Carlo techniques, routinely and effectively applied to euclidean systems in QCD, fall short. A number of ways to try and resolve this sign problem have been proposed. Stochastic quantization is particularly promising, providing a Langevin type equation to sample the field space [14-16]. For a real-time path integral, the procedure leads to complex Langevin equations, driving the field φ away from the real axis sampling the entire complex plane. This effective doubling of the degrees of freedom helps to significantly improve convergence and one may show that under sensible assumptions, the correct physical result is achieved .Another remedy for the sign problem is to again complexify the real integration variables φ, but rather than doubling the dimensionality of field space R n → C n , we constrain the field variables to live on a...

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Section: Results With the Thimble Approachmentioning

confidence: 99%

Quantum tunnelling, real-time dynamics and Picard-Lefschetz thimbles

Mou

Saffin

Tranberg

2019

J. High Energ. Phys.

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“…As the Higgs potential becomes unstable later, the fields roll down in random directions, leading to non-trivial Higgs configurations. In the presence of CP-violation, this might produce a baryon asymmetry, which is referred to as cold electroweak baryogenesis [50][51][52][53], and has been studied extensively with simulations [54][55][56][57]. Such a process might also be a source of primordial magnetic fields [58,59] and stochastic gravitational waves [60].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

A possible mass distribution of primordial black holes implied by LIGO-Virgo

Deng

2021

Preprint

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The LIGO-Virgo Collaboration has so far detected around 90 black holes, some of which have masses larger than what were expected from the collapse of stars. The mass distribution of LIGO-Virgo black holes appears to have a peak at ∼ 30M and two tails on the ends. By assuming that they all have a primordial origin, we analyze the GWTC-1 (O1&O2) and GWTC-2 (O3a) datasets by performing maximum likelihood estimation on a broken power law mass function f (m), with the result f ∝ m 1.2 for m < 35M and f ∝ m −4 for m > 35M . This appears to behave better than the popular log-normal mass function. Surprisingly, such a simple and unique distribution can be realized in our previously proposed mechanism of PBH formation, where the black holes are formed by vacuum bubbles that nucleate during inflation via quantum tunneling. Moreover, this mass distribution can also provide an explanation to supermassive black holes formed at high redshifts.

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“…One may then expect a baryon asymmetry to be generated there as well. This is currently under investigation [27].…”

Section: A Lattice Implementationmentioning

confidence: 97%

“…The field dynamics however also becomes more complicated. We will address this in a future publication [27], and proceed here with a hand-made quench, keeping in mind the energy loss for slow quenches.…”

Section: Energymentioning

confidence: 99%

Simulations of Cold Electroweak Baryogenesis: Hypercharge U(1) and the creation of helical magnetic fields

Mou,

Saffin,

Tranberg

2017

Preprint

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We perform numerical simulations of Cold Electroweak Baryogenesis, including for the first time in the Bosonic sector the full electroweak gauge group SU(2)×U(1) and CP-violation. We find that the maximum generated baryon asymmetry is reduced by a factor of three relative to the SU(2)-only model of [1], but that the quench time dependence is very similar. In addition, we compute the magnitude of the helical magnetic fields, and find that it is proportional to the strength of CP-violation and dependent on quench time, but is not proportional to the magnitude of the baryon asymmetry as proposed in [2,3]. Astrophysical signatures of primordial magnetic helicity can therefore not in general be used as evidence that electroweak baryogenesis has taken place.

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Simulations of “tunnelling of the 3rd kind”

Cited by 6 publications

References 14 publications

Quantum tunnelling, real-time dynamics and Picard-Lefschetz thimbles

Quantum tunnelling, real-time dynamics and Picard-Lefschetz thimbles

A possible mass distribution of primordial black holes implied by LIGO-Virgo

Simulations of Cold Electroweak Baryogenesis: Hypercharge U(1) and the creation of helical magnetic fields

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