Planck scale effects on some low energy quantum phenomena

Abstract

Almost all theories of Quantum Gravity predict modifications of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle (GUP). Recently it was shown that the GUP gives rise to corrections to the Schrodinger and Dirac equations, which in turn affect all non-relativistic and relativistic quantum Hamiltonians. In this paper, we apply it to superconductivity and the quantum Hall effect and compute Planck scale corrections. We also show that Planck scale effects may account for a (small) part of the anomalous magnetic moment of the muon. We obtain (weak) empirical bounds on the undetermined GUP parameter from present-day experiments.

5 pages. To appear in Physics Letters B

References in corpus (5)

• Universality of Quantum Gravity Corrections
• Discreteness of Space from the Generalized Uncertainty Principle
• A proposal for testing Quantum Gravity in the lab
• Natural extension of the Generalised Uncertainty Principle
• Deformed Special Relativity and Deformed Symmetries in a Canonical Framework

Cited by in corpus (51)

• Minimal Length Scale Scenarios for Quantum Gravity
• Corrections to the thermodynamics of Schwarzschild-Tangherlini black hole and the generalized uncertainty principle
• Quantum corrections to the thermodynamics of Schwarzschild-Tangherlini black hole and the generalized uncertainty principle
• Constraining the generalized uncertainty principle with the gravitational wave event GW150914
• Effects of quantum gravity on black holes
• Relativistic Generalized Uncertainty Principle
• 30 years in: Quo vadis generalized uncertainty principle?
• Semiclassical corrections to black hole entropy and the generalized uncertainty principle
• The Path Integral Quantization corresponding to the Deformed Heisenberg Algebra
• Generalized uncertainty principle or curved momentum space?
• Cosmological constraints on the Generalized Uncertainty Principle from modified Friedmann equations
• Bounds on GUP parameters from GW150914 and GW190521
• Do the Modified Uncertainty Principle and Polymer Quantization predict same physics?
• Quantum field theory with the generalized uncertainty principle I: scalar electrodynamics
• Maximal momentum GUP leads to quadratic gravity
• On the (2+1)-dimensional Dirac equation in a constant magnetic field with a minimal length uncertainty
• The noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios
• Constraining the Generalized Uncertainty Principle with the light twisted by rotating black holes and M87*
• Primordial Power Spectra of Cosmological Fluctuations with Generalized Uncertainty Principle and Maximum Length Quantum Mechanics
• Effective GUP-modified Raychaudhuri equation and black hole singularity: four models
• Quantum field theory with the generalized uncertainty principle II: Quantum Electrodynamics
• Effects of the Modified Uncertainty Principle on the Inflation Parameters
• Black hole thermodynamics and generalized uncertainty principle with higher order terms in momentum uncertainty
• Quantum-spacetime effects on nonrelativistic Schrödinger evolution
• The Effects of Minimal Length, Maximal Momentum and Minimal Momentum in Entropic Force
• Minimal length, maximal momentum and stochastic gravitational waves spectrum generated from cosmological QCD phase transition
• Higher-order generalized uncertainty principle corrections to the Jeans mass
• A Note on Effects of Generalized and Extended Uncertainty Principles on Jüttner Gas
• Constraining the generalized uncertainty principle with neutron interferometry
• Some Implications of Two Forms of the Generalized Uncertainty Principle
• Investigating bounds on the extended uncertainty principle metric through astrophysical tests
• The generalized uncertainty principle impact onto the black hole thermodynamic phase transition
• Collective states of even-even nuclei in gamma-rigid quadrupole Hamiltonian with Minimal Length under the sextic potential
• Hawking radiation and entropy of a BTZ black hole with minimum length
• Comments on the cosmological constant in generalized uncertainty models
• Information Theoretical Approach to Detecting Quantum Gravitational Corrections
• A covariant tapestry of linear GUP, metric-affine gravity, their Poincaré algebra and entropy bound
• HBAR entropy of Infalling Atoms into a GUP-corrected Schwarzschild Black Hole and equivalence principle
• Some consequences of GUP induced ultraviolet wavevector cutoff in one-dimensional Quantum Mechanics
• Generalized Uncertainty Principle, Modified Dispersion Relation and Barrier penetration by a Dirac particle
• Spinning Toroidal Brane Cosmology; A Classical and Quantum Survey
• Generalized uncertainty principle and burning stars
• Effects of Extended Uncertainty Principle on the Relativistic Coulomb Potential
• Transition Rate and the Photoelectric Effect in the Presence of a Minimal Length
• Relativistic Generalized Uncertainty Principle and Its Implications
• Towards quantum Mechanics on the curved cotangent bundle
• Probing DDM and ML quantum concepts in shape phase transitions of $\gamma$-unstable nuclei
• Lorentz Force and Ponderomotive Force in the Presence of a Minimal Length
• Particle in a cavity in one-dimensional bandlimited quantum mechanics
• GUP/BEB correspondence
• Thermomagnetic Ettingshausen-Nernst effect in tachocline, magnetic reconnection phenomenon in lower layers, axion mechanism of solar luminosity variations, coronal heating problem solution and mechanism of ADM variations around BH