Classical versus quantum evolution for a universe with a positive cosmological constant

Brizuela, David

doi:10.1103/physrevd.91.085003

Cited by 7 publications

(5 citation statements)

References 46 publications

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“…Writing these expressions in terms of moments, as performed in ( 33)- (34), and truncating the series at secondorder, one ends up with five constants of motion for five variables and the system is thus completely determined. Note that, for convenience, we have defined the conserved quantities as expectation values of powers of differences, like ( Ri − R i ) 2 , instead of expectation values of powers, like R2 i , and with a symmetric ordering of R 1 and R 2 .…”

Section: B Conserved Quantitiesmentioning

confidence: 99%

Quantum Kasner transition in a locally rotationally symmetric Bianchi II universe

Alonso-Serrano,

Brizuela,

Uria

2021

Preprint

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The Belinski-Khalatnikov-Lifshitz (BKL) conjecture predicts a chaotic alternation of Kasner epochs in the evolution of generic classical spacetimes towards a spacelike singularity. As a first step towards understanding the full quantum BKL scenario, we analyze a vacuum Bianchi II model with local rotational symmetry, which presents just one Kasner transition. During the Kasner epochs, the quantum state is coherent and it is thus characterized by constant values of the different quantum fluctuations, correlations and higher-order moments. By computing the constants of motion of the system we provide, for any peaked semiclassical state, the explicit analytical transition rules that relate the parametrization of the asymptotic coherent state before and after the transition. In particular, we obtain the modification of the transition rules for the classical variables due to quantum back-reaction effects. This analysis is performed by considering a high-order truncation in moments (the full computations are performed up to fifth-order, which corresponds to neglecting terms of an order 3 ), providing a solid estimate about the quantum modifications to the classical model. Finally, in order to understand the dynamics of the state during the transition, we perform some numerical simulations for an initial Gaussian state, that show that the initial and final equilibrium values of the quantum variables are connected by strong and rapid oscillations.

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Section: B Conserved Quantitiesmentioning

confidence: 99%

Quantum Kasner transition in a locally rotationally symmetric Bianchi II universe

Alonso-Serrano,

Brizuela,

Uria

2021

Preprint

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“…However, as we mentioned above, there is a particular semiclassical formalism in which a quantum mechanical system can be studied as a classical Hamiltonian system but in an infinite dimensional phase space, where the additional degrees of freedom are directly related to the expectation values of all the infinitely many quantum dispersions [6]. This general formalism was applied to simple models of loop quantum cosmology to show the existence of a quantum bounce at the beginning of the Universe [47][48][49][50]. However, it has also been studied in other systems such as anharmonic oscillators [51], and also two-dimensional systems such as the quantum Kepler problem [52].…”

Section: Effective Equations For the Dynamics Of The Quantum Falling ...mentioning

confidence: 99%

Effective dynamics of the quantum falling particle

Chacón‐Acosta¹,

Hernandez-Hernandez²,

Velázquez³

2020

Eur. J. Phys.

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We analyze the problem of a quantum particle falling under the influence of a one-dimensional constant gravitational field, also known as the bouncing ball, employing a semiclassical approach for the effective equations of motion for the quantum system. In this formalism, the quantum evolution is described through a dynamical system of infinite dimensions for the position, the momentum, and all dispersions. Usually, the system is truncated to reduce it to a finite-dimensional one; however, in this case, equations of motion decouple and the system can be solved exactly. For a specific set of initial conditions, we find that the time-dependent dispersion in position follows the classical trajectory; however, for large times, it grows enough to allow a non-classical behavior for the rebounds. We also propose the study of an effective potential in terms of a pair of canonical variables for dispersions.

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“…However, as we mentioned above, there is a particular semiclassical formalism in which a quantum mechanical system can be studied as a classical Hamiltonian system but in a infinite dimensional phase space, where the additional degrees of freedom are directly related to the expectation values of all the infinite many quantum dispersions [3]. This formalism was first applied to soluble models of loop quantum cosmology to show the existence of a quantum bounce at the beginning of the universe [13][14][15][16]. However, it has also been studied in other systems such as anharmonic oscillators [17], and also two dimensional systems as the quantum Kepler problem [18].…”

Section: Momentous Effective Formulation Of the Quantum Falling Particlementioning

confidence: 99%

Effective Quantum Mechanics of a falling particle

Chacón‐Acosta¹,

Hernandez-Hernandez²,

Velázquez³

2019

Preprint

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We analyze the problem of one dimensional quantum particle falling in a constant gravitational field, also known as the bouncing ball, employing a semiclassical approach known as momentous effective quantum mechanics. In this formalism the quantum evolution is described through a dynamical system of infinite dimension for the position, the momentum and all dispersions. Usually the system is truncated to have a finite dimensional one, however, in this case equations of motion decouple and the system can be solved. For a specific set of initial conditions we find that the time dependent dispersion in position is always around the classical trajectory.

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Classical versus quantum evolution for a universe with a positive cosmological constant

Cited by 7 publications

References 46 publications

Quantum Kasner transition in a locally rotationally symmetric Bianchi II universe

Quantum Kasner transition in a locally rotationally symmetric Bianchi II universe

Effective dynamics of the quantum falling particle

Effective Quantum Mechanics of a falling particle

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