Composite system in deformed space with minimal length

Abstract

For composite systems made of $N$ different particles living in a space characterized by the same deformed Heisenberg algebra, but with different deformation parameters, we define the total momentum and the center-of-mass position to first order in the deformation parameters. Such operators satisfy the deformed algebra with new effective deformation parameters. As a consequence, a two-particle system can be reduced to a one-particle problem for the internal motion. As an example, the correction to the hydrogen atom $n$S energy levels is re-evaluated. Comparison with high-precision experimental data leads to an upper bound of the minimal length for the electron equal to $3.3\times 10^{-18}\mathrm{m}$. The effective Hamiltonian describing the center-of-mass motion of a macroscopic body in an external potential is also found. For such a motion, the effective deformation parameter is substantially reduced due to a factor $1/N^2$. This explains the strangely small result previously obtained for the minimal length from a comparison with the observed precession of the perihelion of Mercury. From our study, an upper bound of the minimal length for quarks equal to $2.4\times 10^{-17}\mathrm{m}$ is deduced, which appears close to that obtained for electrons.

22 pages, no figure; small additions in Secs. I, III and VI

References in corpus (11)

• Universality of Quantum Gravity Corrections
• Discreteness of Space from the Generalized Uncertainty Principle
• Hydrogen-atom spectrum under a minimal-length hypothesis
• Lorentz-covariant deformed algebra with minimal length and application to the 1+1-dimensional Dirac oscillator
• Perturbation hydrogen-atom spectrum in deformed space with minimal length
• Modification of Heisenberg uncertainty relations in non-commutative Snyder space-time geometry
• Corrections to the ns-levels of hydrogen atom in deformed space with minimal length
• Dilaton Cosmology, Noncommutativity and Generalized Uncertainty Principle
• Quantum gravity, minimum length and Keplerian orbits
• Orbital magnetic moment of the electron in the hydrogen atom in deformed space with minimal length
• Photoionization Broadening of the 1S-2S Transition in a Beam of Atomic Hydrogen

Cited by in corpus (78)

• Minimal Length Scale Scenarios for Quantum Gravity
• Gravitational tests of the Generalized Uncertainty Principle
• Probing deformed commutators with macroscopic harmonic oscillators
• Lorentz violation and generalized uncertainty principle
• Generalized uncertainty principles and localization in discrete space
• 30 years in: Quo vadis generalized uncertainty principle?
• Deformed Heisenberg algebra with minimal length and equivalence principle
• Composite system in noncommutative space and the equivalence principle
• Hydrogen atom in momentum space with a minimal length
• The deformation parameter of the generalized uncertainty principle
• GUP-based and Snyder Non-Commutative Algebras, Relativistic Particle models and Deformed Symmetries: A Unified Approach
• Composite system in rotationally invariant noncommutative phase space
• Generalized uncertainty principle and Asymptotic Safe gravity
• A new bound on polymer quantization via an opto-mechanical setup
• Weak equivalence principle in noncommutative phase space and the parameters of noncommutativity
• Quantum-optical tests of Planck-scale physics
• Parameters of noncommutativity in Lie-algebraic noncommutative space
• Hydrogen atom in rotationally invariant noncommutative space
• The Soccer-Ball Problem
• Relativistic quantum heat engine from uncertainty relation standpoint
• Deformed Heisenberg algebra and minimal length
• The Classical Limit of Minimal Length Uncertainty Relation:Revisit with the Hamilton-Jacobi Method
• Modification of Schrödinger-Newton equation due to braneworld models with minimal length
• The Constraints and Spectra of a Deformed Quantum Mechanics
• Generalized uncertainty principle and the conformally coupled scalar field quantum cosmology
• Testing Generalised Uncertainty Principles through Quantum Noise
• Minimum-length deformed QM/QFT, issues and problems
• The quantum N-body problem with a minimal length
• Bound on efficiency of heat engine from uncertainty relation viewpoint
• Upper bound on the momentum scale in noncommutative phase space of canonical type
• Quantum-spacetime effects on nonrelativistic Schrödinger evolution
• A squeezed review on coherent states and nonclassicality for non-Hermitian systems with minimal length
• Kinematic variables in noncommutative phase space and parameters of noncommutativity
• Probing quantum gravity effects with quantum mechanical oscillators
• Formulation of the Spinor Field in the Presence of a Minimal Length Based on the Quesne-Tkachuk Algebra
• Lorentz invariant mass and length scales
• Rotationally invariant noncommutative phase space of canonical type with recovered weak equivalence principle
• Detecting the effects of quantum gravity with exceptional points in optomechanical sensors
• The minimal length and the Shannon entropic uncertainty relation
• The Harmonic Oscillator in the Classical Limit of a Minimal-Length Scenario
• Quantum and classical probability distributions for arbitrary Hamiltonian
• Macroscopic body in Snyder space and minimal length estimation
• Improved constraints on minimum length models with a macroscopic low loss phonon cavity
• Dirac $\delta$-function potential in quasiposition representation of a minimal-length scenario
• A framework for nonrelativistic isotropic models based on generalized uncertainty principles
• Deformed Gazeau-Klauder Schrödinger-Cat States with Modified Commutation Relations
• Two-particle system in noncommutative space with preserved rotational symmetry
• Path Integral for Non-Paraxial Optics
• Approximate solutions for N-body Hamiltonians with identical particles in D dimensions
• Squeezed atom laser for Bose-Einstein condensate with minimal length
• Exactly solvable dynamical models with a minimal length uncertainty
• Quantum gravitational decoherence of a mechanical oscillator from spacetime fluctuations
• Relation of deformed nonlinear algebras with linear ones
• Features of free particles system motion in noncommutative phase space
• System of interacting harmonic oscillators in rotationally invariant noncommutative phase space
• Minimal length estimation on the basis of studies of the Sun-Earth-Moon system in deformed space
• Relativistic Approach to the Hydrogen Atom in a Minimal Length Scenario
• Position and momentum uncertainties of a particle in a V-shaped potential under the minimal length uncertainty relation
• Exact solutions for two-body problems in 1D deformed space with minimal length
• Two- and three-body calculations within the dominantly orbital state method
• Effects of a Maximal Energy Scale in Thermodynamics for Photon Gas and Construction of Path Integral
• Kinetic energy properties and weak equivalence principle in a space with GUP
• Reconciling microscopic and macroscopic tests of the Compton-Schwarzschild correspondence
• Minimal momentum estimation in noncommutative phase space of canonical type with preserved rotational and time reversal symmetries
• Towards quantum Mechanics on the curved cotangent bundle
• Short Distance Modification of a Gravitational System and its Optical Analog
• Theory of a many-boson system with deformed Heisenberg algebra
• Features of description of composite system's motion in twist-deformed space-time
• Non-local imprints of gravity on quantum theory
• Regularization of ${\delta }^{\prime }$ potential in general case of deformed space with minimal length
• Effects of underlying topology on quantum state discrimination
• Non-Heisenbergian quantum mechanics
• Refractive index profiles for a $\mathcal{P}\mathcal{T}$-symmetric optical structure
• Constraining the deformed dispersion relation with the hydrogen atom 1S-2S transition
• Upper bounds for critical coupling constants for binding some quantum many-body systems
• Classifying deviation from standard quantum behavior using Kullback Leibler divergence
• GUP/BEB correspondence
• Homogeneous Field and WKB Approximation In Deformed Quantum Mechanics with Minimal Length