Free fall in KvN mechanics and Einstein’s principle of equivalence

Sen, Abhijit; Dhasmana, Shailesh; Силагадзе, З. К.

doi:10.1016/j.aop.2020.168302

Cited by 13 publications

(10 citation statements)

References 57 publications

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“…In this paper, we have studied the Wigner functions for the GUP given by the equation (23). The GUP-modified wave function for the harmonic oscillator in configuration space is (34) and, with the help of the Bopp transformation [35] and the use of the equation (37), it allows us to study the corresponding Wigner function W (q, Π).…”

Section: Discussionmentioning

confidence: 99%

“…In this way, it is clear that we recover classicality in the (q, p) sub-space. Further, it is worth noting that there exists transformations [20,23]…”

Section: Classical Mechanics In Hilbert Space Representationmentioning

confidence: 99%

“…of the Eq (26) appears as the extra perturbation term due to the modification in the commutation relation i.e. Eq (23). Hereafter, throughout the calculation, we will only consider these terms which are up to first order in β.…”

Section: Gup Modified Wigner Functionmentioning

confidence: 99%

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GUP modified Wigner function using classical-quantum unified framework

Sen

Parida

2023

Preprint

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The generalized uncertainty principle (GUP) is a natural consequence of many proposed quantum gravity theories which further indicates the modification of the quantum mechanics and classical mechanics. A unified classical-quantum framework also leads to the interpretation of a Winger phase-space distribution of a state as a KvN wave function. In this article, we utilize the classical-quantum unified framework to calculate the expression for the GUP modified Wigner function of a classical harmonic oscillator in the configuration space instead of the conventional approach of utilising the momentum space. Further, we plot the modified Wigner functions and show that they are similar to what has been obtained before in the past literature.

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Section: Discussionmentioning

confidence: 99%

“…In this way, it is clear that we recover classicality in the (q, p) sub-space. Further, it is worth noting that there exists transformations [20,23]…”

Section: Classical Mechanics In Hilbert Space Representationmentioning

confidence: 99%

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GUP modified Wigner function using classical-quantum unified framework

Sen

Parida

2023

Preprint

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“…In the case of pure states, this difficulty was resolved with the demonstration that the Wigner function should be interpreted as a phase space probability amplitude. This is in direct analogy with the Koopman-von Neumann (KvN) representation of classical dynamics [19,[21][22][23][24][25][26][27][28][29][30][31][32][33] which explicitly admits a wavefunction on phase space, and which the Wigner function of a pure state corresponds to in the classical limit. The extension of this interpretation to mixed states has to date been lacking however, given that such states must be described by densities and therefore lack a direct correspondence to wavefunctions.…”

Section: Introductionmentioning

confidence: 93%

The wave operator representation of quantum and classical dynamics

McCaul¹,

Zhdanov²,

Bondar³

2023

Preprint

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The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator representation of quantum dynamics, and explore its connection to standard methods of quantum dynamics, such as the Wigner phase space function. This method takes as its central object the square root of the density matrix, and consequently enjoys several unusual advantages over standard representations. By combining this with purification techniques imported from quantum information, we are able to obtain a number of results. Not only is this formalism able to provide a natural bridge between phase and Hilbert space representations of both quantum and classical dynamics, we also find the wave operator representation leads to novel semiclassical approximations of both real and imaginary time dynamics, as well as a transparent correspondence to the classical limit. This is demonstrated via the example of quadratic and quartic Hamiltonians, while the potential extensions of the wave operator and its application to quantum-classical hybrids is discussed. We argue that the wave operator provides a new perspective that links previously unrelated representations, and is a natural candidate model for scenarios (such as hybrids) in which positivity cannot be otherwise guaranteed.

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“…This old approach is due to Koopman [5] and von Neumann [6]. Whether for derivation of purely classical results or for comparison between quantum and classical mechanics, the Koopman-von Neumann formalism (hereafter abbreviated as KvN) has received increasing attention in the past two decades (see [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]), the possibility of formulating quantum-classical hybrid theories has also increased the interest in this formalism [22,23,24,25]. The existence of the KvN theory raises the question of the classification of the unitary representations of the groups of space-time symmetries in the context of classical mechanics.…”

Section: Introductionmentioning

confidence: 99%

Unitary representation of the Poincaré group for classical relativistic dynamics

Manjarres

2021

Annals of Physics

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Free fall in KvN mechanics and Einstein’s principle of equivalence

Cited by 13 publications

References 57 publications

GUP modified Wigner function using classical-quantum unified framework

GUP modified Wigner function using classical-quantum unified framework

The wave operator representation of quantum and classical dynamics

Unitary representation of the Poincaré group for classical relativistic dynamics

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