Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chinese Journal of Physics

Natural Cutoffs and Dynamics of Harmonic Oscillations

Kourosh Nozari, Sepideh Namdari, Javad Vahedi

Published Aug 1, 2012• 3 citations
OpenAlex

Abstract

Different proposed candidates of quantum gravity, such as string theory, noncommutative geometry, loop quantum gravity, and doubly special relativity, all predict the existence of a minimum observable length and/or a maximum observable momentum. These natural cutoffs modify the standard Heisenberg uncertainty principle leading to the so-called Generalized Uncertainty Principle (GUP). In this paper, we study the effects of minimal length and maximal momentum on the dynamics of harmonic oscillations. Within this framework we also study the status of Ehrenfest's theorem with the GUP.

Related papers

COHERENT STATES IN GRAVITATIONAL QUANTUM MECHANICS

Pouria Pedram

We present the coherent states of the harmonic oscillator in the framework of the generalized (gravitational) uncertainty principle (GUP). This form of GUP is consistent with various theories of quantum gravity such as string theory, loop quantum gravity and black-hole physics and implies a minimal measurable length. Using a recently proposed formally self-adjoint representation, we find the GUP-corrected Hamiltonian as a generator of the generalized Heisenberg algebra. Then following Klauder's approach, we construct exact coherent states and obtain the corresponding normalization coefficients, weight functions and probability distributions. We find the entropy of the system and show that it decreases in the presence of the minimal length. These results could shed light on possible detectable Planck-scale effects within recent experimental tests.

arXiv:1204.1524•International Journal of Modern Physics D•Feb 1, 2013•20 citations

Coherent states in minimal-length Quantum Mechanics: inequivalent characterizations and emergent squeezing

Giuseppe Gaetano Luciano, Pasquale Bosso, Daniel Chemisana

Several approaches to quantum gravity suggest the emergence of a fundamental minimal length at the Planck scale. In quantum mechanics, this feature is naturally encoded through deformations of the Heisenberg algebra, leading to the Generalized Uncertainty Principle (GUP). While the phenomenological implications of GUP have been extensively explored, a consistent characterization of coherent states in minimal-length quantum mechanics remains elusive. In this work, we present a systematic analysis of coherent states for the one-dimensional harmonic oscillator. We show that the canonical equivalence among their standard characterizations - as eigenstates of the annihilation operator, displaced vacuum states and minimum-uncertainty wave packets - is generically lost in the presence of a minimal length. We then investigate the dynamical and semiclassical consequences of this inequivalence by comparing the evolution of generalized coherent states with that of states saturating the GUP. In particular, we demonstrate that minimal-length effects induce nontrivial deformations of phase-space trajectories and give rise to an intrinsic squeezing mechanism with no counterpart in ordinary quantum mechanics. These results establish a unified framework for coherence in GUP-based quantum theories and identify distinctive semiclassical signatures of minimal-length physics, opening a new avenue for probing quantum-gravitational effects.

quant-pharXiv:2607.01393•Jul 3, 2026•0 citations

Discriminating quantum gravity models by gravitational decoherence

Eissa Al-Nasrallah, Saurya Das, Fabrizio Illuminati +2 more

Several phenomenological approaches to quantum gravity predict the existence of a minimal measurable length and/or a maximum measurable momentum near the Planck scale. When embedded into the framework of quantum mechanics, such constraints induce a modification of the canonical commutation relations and thus a generalization of the Heisenberg uncertainty relations, commonly referred to as generalized uncertainty principle (GUP). Different models of quantum gravity imply different forms of the GUP. For instance, in the framework of string theory the GUP is quadratic in the momentum operator, while in the context of doubly special relativity it includes an additional linear dependence. Among the possible physical consequences, it was recently shown that the quadratic GUP induces a universal decoherence mechanism, provided one assumes a foamy structure of quantum spacetime close to the Planck length. Along this line, in the present work we investigate the gravitational decoherence associated to the linear-quadratic GUP and we compare it with the one associated to the quadratic GUP. We find that, despite their similarities, the two generalizations of the Heisenberg uncertainty principle yield decoherence times that are completely uncorrelated and significantly distinct. Motivated by this result, we introduce a theoretical and experimental scheme based on cavity optomechanics to measure the different time evolution of nonlocal quantum correlations corresponding to the two aforementioned decoherence mechanisms. We find that the deviation between the two predictions occurs on time scales that are macroscopic and thus potentially amenable to experimental verification. This scenario provides a possible setting to discriminate between different forms of the GUP and therefore different models of quantum gravity.

arXiv:2110.10288•Nuclear Physics B•May 26, 2023•6 citations

Modification of Heisenberg’s Uncertainty Relation for a Damped Harmonic Oscillator under the Generalized Uncertainty Principle

Partho Karmaker, S. B. Faruque

We investigate the effects of the Generalized Uncertainty Principle (GUP), which intro- duces a fundamental minimal observable length, on the quantum dynamics of a damped harmonic oscillator. By incorporating a modified Heisenberg algebra into the framework, we derive the altered uncertainty relations for damped quantum systems and examine their dependence on the discrete energy spectrum. Our analysis reveals significant devia- tions from the standard Heisenberg uncertainty relation, demonstrating that the presence of a minimal length scale fundamentally modifies the quantum-classical correspondence in dissipative systems. We present explicit expressions for the modified uncertainty relations and discuss their physical implications for quantum measurements in damped oscillatory systems. These results contribute to our understanding of quantum mechanics at length scales approaching the Planck regime and provide testable predictions for experimental verification of GUP effects in dissipative quantum systems.

SUST Journal of Science and Technology (SUST JST)•Aug 16, 2026•0 citations

Quantum Gravity Simulation: Quantum simulation with a minimum length based on the generalised uncertainty principle

Jack Keable-Elliott, David J. Bacon, Andrew Burbanks +1 more

We present a recipe for simulating one-dimensional quantum systems for low and high energies with $L$ qubits within the framework of first quantisation. Assuming a minimum grid spacing $ΔL$ in the finite-difference method, the generalised uncertainty principle (GUP) is derived analytically and shows distinct properties for low- and high-energy quantum systems. In the low-energy regime, the GUP approaches to the standard Heisenberg uncertainty principle (HUP) for $ ΔL \ll \hbar$. However, for finite $ΔL \neq 0$, the GUP mathematically provides three different regions dependent on the average momentum and suggests that a wavefunction can exhibit a single-point localisation at the finite momentum uncertainty due to lack of grid resolution. We then derive a new expression for the high-energy momentum and focus on two specific cases relevant to relativistic aspects. First, if the HUP is relaxed and the high-energy momentum is matched to the special-relativistic one, the resulting GUP predicts the existence of a minimum length with non-zero mass for high energy despite the continuous limit $ΔL = 0$. Second, enforcing consistency with the HUP allows the recovery of a canonical high-energy representation with no minimum length. But this requirement brings incompatibility with the special-relativistic momentum and suggests a modified energy-momentum equation. Therefore, we believe that the proposed momentum formulation provides a novel pathway to investigate quantum gravity phenomena for high energy using quantum simulation tools.

quant-pharXiv:2607.19602•Jul 23, 2026

A damped harmonic oscillator in the GUP framework

Seyed Davood Sadatian

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.

Iranian Journal of Physics Research•Oct 1, 2019•0 citations
Different proposed candidates of quantum gravity, such as string theory, noncommutative geometry, loop quantum gravity, and doubly special relativity, all predict the existence of a minimum observable length and/or a maximum observable momentum. These natural cutoffs modify the standard Heisenberg uncertainty principle leading to the so-called Generalized Uncertainty Principle (GUP). In this paper, we study the effects of minimal length and maximal momentum on the dynamics of harmonic oscillations. Within this framework we also study the status of Ehrenfest's theorem with the GUP.
We present the coherent states of the harmonic oscillator in the framework of the generalized (gravitational) uncertainty principle (GUP). This form of GUP is consistent with various theories of quantum gravity such as string theory, loop quantum gravity and black-hole physics and implies a minimal measurable length. Using a recently proposed formally self-adjoint representation, we find the GUP-corrected Hamiltonian as a generator of the generalized Heisenberg algebra. Then following Klauder's approach, we construct exact coherent states and obtain the corresponding normalization coefficients, weight functions and probability distributions. We find the entropy of the system and show that it decreases in the presence of the minimal length. These results could shed light on possible detectable Planck-scale effects within recent experimental tests.
Several approaches to quantum gravity suggest the emergence of a fundamental minimal length at the Planck scale. In quantum mechanics, this feature is naturally encoded through deformations of the Heisenberg algebra, leading to the Generalized Uncertainty Principle (GUP). While the phenomenological implications of GUP have been extensively explored, a consistent characterization of coherent states in minimal-length quantum mechanics remains elusive. In this work, we present a systematic analysis of coherent states for the one-dimensional harmonic oscillator. We show that the canonical equivalence among their standard characterizations - as eigenstates of the annihilation operator, displaced vacuum states and minimum-uncertainty wave packets - is generically lost in the presence of a minimal length. We then investigate the dynamical and semiclassical consequences of this inequivalence by comparing the evolution of generalized coherent states with that of states saturating the GUP. In particular, we demonstrate that minimal-length effects induce nontrivial deformations of phase-space trajectories and give rise to an intrinsic squeezing mechanism with no counterpart in ordinary quantum mechanics. These results establish a unified framework for coherence in GUP-based quantum theories and identify distinctive semiclassical signatures of minimal-length physics, opening a new avenue for probing quantum-gravitational effects.
Several phenomenological approaches to quantum gravity predict the existence of a minimal measurable length and/or a maximum measurable momentum near the Planck scale. When embedded into the framework of quantum mechanics, such constraints induce a modification of the canonical commutation relations and thus a generalization of the Heisenberg uncertainty relations, commonly referred to as generalized uncertainty principle (GUP). Different models of quantum gravity imply different forms of the GUP. For instance, in the framework of string theory the GUP is quadratic in the momentum operator, while in the context of doubly special relativity it includes an additional linear dependence. Among the possible physical consequences, it was recently shown that the quadratic GUP induces a universal decoherence mechanism, provided one assumes a foamy structure of quantum spacetime close to the Planck length. Along this line, in the present work we investigate the gravitational decoherence associated to the linear-quadratic GUP and we compare it with the one associated to the quadratic GUP. We find that, despite their similarities, the two generalizations of the Heisenberg uncertainty principle yield decoherence times that are completely uncorrelated and significantly distinct. Motivated by this result, we introduce a theoretical and experimental scheme based on cavity optomechanics to measure the different time evolution of nonlocal quantum correlations corresponding to the two aforementioned decoherence mechanisms. We find that the deviation between the two predictions occurs on time scales that are macroscopic and thus potentially amenable to experimental verification. This scenario provides a possible setting to discriminate between different forms of the GUP and therefore different models of quantum gravity.
We investigate the effects of the Generalized Uncertainty Principle (GUP), which intro- duces a fundamental minimal observable length, on the quantum dynamics of a damped harmonic oscillator. By incorporating a modified Heisenberg algebra into the framework, we derive the altered uncertainty relations for damped quantum systems and examine their dependence on the discrete energy spectrum. Our analysis reveals significant devia- tions from the standard Heisenberg uncertainty relation, demonstrating that the presence of a minimal length scale fundamentally modifies the quantum-classical correspondence in dissipative systems. We present explicit expressions for the modified uncertainty relations and discuss their physical implications for quantum measurements in damped oscillatory systems. These results contribute to our understanding of quantum mechanics at length scales approaching the Planck regime and provide testable predictions for experimental verification of GUP effects in dissipative quantum systems.
We present a recipe for simulating one-dimensional quantum systems for low and high energies with LLL qubits within the framework of first quantisation. Assuming a minimum grid spacing ΔLΔLΔL in the finite-difference method, the generalised uncertainty principle (GUP) is derived analytically and shows distinct properties for low- and high-energy quantum systems. In the low-energy regime, the GUP approaches to the standard Heisenberg uncertainty principle (HUP) for $ ΔL \ll \hbar$. However, for finite ΔL≠0ΔL \neq 0ΔL=0, the GUP mathematically provides three different regions dependent on the average momentum and suggests that a wavefunction can exhibit a single-point localisation at the finite momentum uncertainty due to lack of grid resolution. We then derive a new expression for the high-energy momentum and focus on two specific cases relevant to relativistic aspects. First, if the HUP is relaxed and the high-energy momentum is matched to the special-relativistic one, the resulting GUP predicts the existence of a minimum length with non-zero mass for high energy despite the continuous limit ΔL=0ΔL = 0ΔL=0. Second, enforcing consistency with the HUP allows the recovery of a canonical high-energy representation with no minimum length. But this requirement brings incompatibility with the special-relativistic momentum and suggests a modified energy-momentum equation. Therefore, we believe that the proposed momentum formulation provides a novel pathway to investigate quantum gravity phenomena for high energy using quantum simulation tools.
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.