Remarks on the Noncommutative Gravitational Quantum Well

Abstract

A planar phase space having both position and momentum noncommutativity is defined in a more inclusive setting than that considered elsewhere. The dynamics of a particle in a gravitational quantum well in this space is studied. The use of the WKB approximation and the virial theorem enable analytic discussions on the effect of noncommutativity. Consistent results are obtained following either commutative space or noncommutative space descriptions. Comparison with recent experimental data with cold neutrons at Grenoble imposes an upper bound on the noncommutative parameter. Also, our results are compared with a recent numerical analysis of a similar problem.

Latex, 17 pages, Title changed, minor modifications, 3 new references added, To appear in Phys. Rev. D

References in corpus (12)

• Noncommutative Field Theory
• Gauge Theory on Noncommutative Spaces
• Quantum mechanics on the noncommutative plane and sphere
• Noncommutative Gravitational Quantum Well
• Measurement of quantum states of neutrons in the Earth's gravitational field
• Study of the neutron quantum states in the gravity field
• Deformed Coordinate Spaces; Derivatives
• Scaling of variables and the relation between noncommutative parameters in Noncommutative Quantum Mechanics
• A Novel Approach to Noncommutativity in Planar Quantum Mechanics
• Noncommutativity from Embedding Techniques
• Deformed relativistic and nonrelativistic symmetries on canonical noncommutative spaces
• Constraint on Quantum Gravitational Well in Noncommutative Space

Cited by in corpus (39)

• Quantum Spacetime Phenomenology
• Topics in Noncommutative Geometry Inspired Physics
• Lie algebraic Noncommutative Gravity
• Berry Phase in the Gravitational Quantum Well and the Seiberg-Witten map
• Deformed Reissner--Nordstrom solutions in noncommutative gravity
• A method to measure the resonance transitions between the gravitationally bound quantum states of neutrons in the GRANIT spectrometer
• Time-Space Noncommutativity in Gravitational Quantum Well scenario
• Noncommutative quantum mechanics of a harmonic oscillator under linearized gravitational waves
• Centrifugal quantum states of neutrons
• Gravitational Collapse of a Homogeneous Scalar Field in Deformed Phase Space
• On the Landau system in noncommutative phase-space
• Particle-like solutions to classical noncommutative gauge theory
• Modified Newton's law, braneworlds, and the gravitational quantum well
• Inflationary Universe in Deformed Phase Space Scenario
• Two-dimensional Noncommutative Gravitational Quantum Well
• Effect of coordinate noncommutativity on the mass of a particle in a uniform field and the equivalence principle
• Modification of Schrödinger-Newton equation due to braneworld models with minimal length
• Noncommutative quantum mechanics of a test particle under linearized gravitational waves
• Quantum engines and the range of the second law of thermodynamics in the noncommutative phase-space
• The quantum N-body problem with a minimal length
• Hydrogen and muonic-Hydrogen Atomic Spectra in Non-commutative Space-Time
• Response of simple quantum systems to different polarizations of gravitational waves in noncommutative phase-space
• Resonant-bar detectors of gravitational wave as possible probe of the noncommutative structure of space
• Galilean symmetry in noncommutative Gravitational Quantum Well
• Non-Hermitian noncommutative quantum mechanics
• On the question of deconfinement in noncommutative Schwinger Model
• Heat flow and noncommutative quantum mechanics in phase-space
• Free-fall in a uniform gravitational field in non-commutative quantum mechanics
• Footprint of spatial noncommutativity in resonant detectors of gravitational wave
• Gaussian fidelity distorted by external fields
• Noncommutative phase-space effects in thermal diffusion of Gaussian states
• Equivalence principle in context of large uniform acceleration - a quantum mechanical perspective
• Noncommutative quantum mechanics of simple matter systems interacting with circularly polarized gravitational waves
• Trace of phase-space noncommutativity in the response of a free particle to linearized gravitational waves
• Quantum mechanics of a charged particle in a background magnetic field interacting with linearized gravitational waves
• Galilei Group with multiple central extension, vorticity and entropy generation: "Exotic" fluid in 3+1-dimensions
• Study on Noncommutative Representations of Galilean Generators
• Interaction of a circularly polarised gravitational wave with a charged particle in a static magnetic background
• Theories on noncommutative spaces and deformed symmetries