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GUP modified Wigner function using classical-quantum unified framework

Abhijit Sen, Bikram Keshari Parida

Published May 17, 2023• 0 citations
Publisher

Abstract

Abstract 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.

DOI
10.21203/rs.3.rs-2598396/v2

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Abstract 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.
Abstract 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.
The generalized uncertainty principle (GUP) is a modification of Heisenberg's Principle predicted by several theories of quantum gravity. It consists of a modified commutator between the position and momentum. In this work, we compute potentially observable effects that GUP implies for the harmonic oscillator, coherent, and squeezed states in quantum mechanics. In particular, we rigorously analyze the GUP-perturbed harmonic oscillator Hamiltonian, defining new operators that act as ladder operators on the perturbed states. We use these operators to define the new coherent and squeezed states. We comment on potential applications.
The Generalized Uncertainty Principle (GUP) is a modification of Heisenberg's Uncertainty Principle predicted by several theories of quantum gravity. In this work, we compute GUP corrections to the well-known Jaynes-Cummings Model (JCM) with the aim of eventually observing quantum gravity effects in quantum optical systems. To this end, we first analytically solve the GUP-corrected JCM and obtain the corrected Rabi frequency in the quadratic GUP model. Following this, we calculate the effects of a dispersive interaction with light in a coherent state and show that this gives rise to photon-added coherent states that were first studied by Agarwal and Tara in 1991. The latter causes a change in the value of the Wigner function, which if detected in the laboratory, would in effect be a signature of quantum gravity.
Harmonic oscillator is significantly important in quantum gravity for its dynamical properties. Dynamics of the harmonic oscillator can be modified by inserting a modified uncertainty relation considered in quantum cosmology models such as string theory and quantum loop gravity theory. In this paper, the equation of damped quantum harmonic oscillator has been solved with respect to the modified uncertainty relation and the effects of this modification have been probed in the case of the damped oscillating system.
In this paper, dynamics and quantum mechanical coherent states of a simple harmonic oscillator are considered in the framework of the Generalized Uncertainty Principle (GUP). Equations of motion for the simple harmonic oscillator are derived and some of their new implications are discussed. Then, coherent states of the harmonic oscillator in the case of the GUP are compared with the relative situation in ordinary quantum mechanics. It is shown that in the framework of GUP there is no considerable difference in definition of coherent states relative to ordinary quantum mechanics. But, considering expectation values and variances of some operators, based on quantum gravitational arguments, one concludes that although it is possible to have complete coherency and vanishing broadening in usual quantum mechanics, gravitational induced uncertainty destroys complete coherency in quantum gravity and it is not possible to have a monochromatic ray in principle.