SELF-COUPLING OF EXCITED ATOMS IN CURVED SPACE–TIME

2005 ◽  
Vol 14 (12) ◽  
pp. 2271-2277
Author(s):  
FABRIZIO PINTO
Keyword(s):  
Gravitational Field ◽  
Excited Atom ◽  
Energy Shift ◽  
Gravitational Acceleration ◽  
Curved Space ◽  
Excited Atoms ◽  
Hertz Potential ◽  
Homogeneous Gravitational Field ◽  
Self Force ◽  
Atom Interferometers

It is well known that an excited atom, placed near a boundary, such as a mirror, undergoes an energy shift due to its interaction with the reflected field. In this paper, we use a generalized Hertz potential to prove that a radiating dipole embedded in a continuously inhomogeneous medium also experiences a position-dependent self-interaction energy shift and a corresponding self-force. Consequently, an excited atom inside a cylindrical cavity embedded in a quasi-homogeneous gravitational field, which acts as an effective "soft" boundary, is shown to experience an effective gravitational acceleration dependent on the atomic quantum state. We predict that excited trapped atom interferometers will thus provide an unexpected tool for ground-based experimentation on radiation backscattering in a Schwarzschild background.

A spatially homogeneous gravitational field

1966 ◽  
Vol 62 (1) ◽  
pp. 87-89 ◽  
Author(s):  
V. Joseph
Keyword(s):  
Gravitational Field ◽  
Canonical Form ◽  
Riemann Tensor ◽  
Vacuum Field ◽  
Type I ◽  
Field Equations ◽  
Parameter Group ◽  
Spatially Homogeneous ◽  
Homogeneous Gravitational Field ◽  
Type V

AbstractA solution of Einstein's vacuum field equations, apparently new, is exhibited. The metric, which is homogeneous (that is, admits a three-parameter group of motions transitive on space-like hypersurfaces), belongs to Taub Type V. The canonical form of the Riemann tensor, which is of Petrov Type I, is determined.

scholarly journals WKB FORMALISM AND A LOWER LIMIT FOR THE ENERGY EIGENSTATES OF BOUND STATES FOR SOME POTENTIALS

2007 ◽  
Vol 22 (35) ◽  
pp. 2675-2687 ◽  
Author(s):  
LUIS F. BARRAGÁN-GIL ◽  
ABEL CAMACHO
Keyword(s):  
Quantum Mechanics ◽  
Gravitational Field ◽  
Lower Bound ◽  
Harmonic Oscillator ◽  
Approximation Method ◽  
Bound States ◽  
The Other ◽  
Homogeneous Gravitational Field ◽  
Definition Of ◽  
Ground Energy

In this work the conditions appearing in the so-called WKB approximation formalism of quantum mechanics are analyzed. It is shown that, in general, a careful definition of an approximation method requires the introduction of two length parameters, one of them always considered in the textbooks on quantum mechanics, whereas the other is usually neglected. Afterwards we define a particular family of potentials and prove, resorting to the aforementioned length parameters, that we may find an energy which is a lower bound to the ground energy of the system. The idea is applied to the case of a harmonic oscillator and also to a particle freely falling in a homogeneous gravitational field, and in both cases the consistency of our method is corroborated. This approach, together with the so-called Rayleigh–Ritz formalism, allows us to define an energy interval in which the ground energy of any potential, belonging to our family, must lie.

Relativistic quantum bouncing particles in a homogeneous gravitational field

2021 ◽  
pp. 2150098
Author(s):  
Ar Rohim ◽  
Kazushige Ueda ◽  
Kazuhiro Yamamoto ◽  
Shih-Yuin Lin
Keyword(s):  
Gravitational Field ◽  
Relativistic Effect ◽  
Relativistic Quantum ◽  
Energy Levels ◽  
Nonrelativistic Limit ◽  
Wave Functions ◽  
Dirac Equations ◽  
Rindler Coordinates ◽  
Klein Gordon ◽  
Homogeneous Gravitational Field

In this paper, we study the relativistic effect on the wave functions for a bouncing particle in a gravitational field. Motivated by the equivalence principle, we investigate the Klein–Gordon and Dirac equations in Rindler coordinates with the boundary conditions mimicking a uniformly accelerated mirror in Minkowski space. In the nonrelativistic limit, all these models in the comoving frame reduce to the familiar eigenvalue problem for the Schrödinger equation with a fixed floor in a linear gravitational potential, as expected. We find that the transition frequency between two energy levels of a bouncing Dirac particle is greater than the counterpart of a Klein–Gordon particle, while both are greater than their nonrelativistic limit. The different corrections to eigen-energies of particles of different nature are associated with the different behaviors of their wave functions around the mirror boundary.

A surface gravity traverse on Mars indicates low bedrock density at Gale crater

Science ◽  
2019 ◽  
Vol 363 (6426) ◽  
pp. 535-537 ◽  
Author(s):  
Kevin W. Lewis ◽  
Stephen Peters ◽  
Kurt Gonter ◽  
Shaunna Morrison ◽  
Nicholas Schmerr ◽  
...  
Keyword(s):  
Gravitational Field ◽  
Precise Measurement ◽  
Attitude Determination ◽  
Sedimentary Rocks ◽  
Gravitational Acceleration ◽  
High Porosity ◽  
Rock Density ◽  
Gravitational Fields ◽  
Gale Crater ◽  
Curiosity Rover

Gravimetry, the precise measurement of gravitational fields, can be used to probe the internal structure of Earth and other planets. The Curiosity rover on Mars carries accelerometers normally used for navigation and attitude determination. We have recalibrated them to isolate the signature of the changing gravitational acceleration as the rover climbs through Gale crater. The subsurface rock density is inferred from the measured decrease in gravitational field strength with elevation. The density of the sedimentary rocks in Gale crater is 1680 ± 180 kilograms per cubic meter. This value is lower than expected, indicating a high porosity and constraining maximum burial depths of the rocks over their history.

VAN DER WAALS FORCES IN CURVED SPACE AS A QUANTUM TOOL TO TEST GENERAL RELATIVITY THEORY

2005 ◽  
Vol 14 (06) ◽  
pp. 995-1008 ◽  
Author(s):  
FABRIZIO PINTO
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Experimental Test ◽  
Point Charge ◽  
Van Der Waals ◽  
Atom Interferometry ◽  
Relativity Theory ◽  
Spherically Symmetric ◽  
General Relativity Theory ◽  
Curved Space

It has been known shortly after the introduction of the general relativity theory that the electrostatic Coulomb potential of a point charge supported in a gravitational field is not spherically symmetric and becomes warped in curved space. Under ordinary laboratory conditions, this effect is quite small and has never been directly observed. Surprisingly, this distortion causes the appearance of a hitherto unknown, topologically complex non-central van der Waals force whose detection is well within range of existing trapped atom interferometry techniques. This will allow for an unexpected experimental test of gravity theory by means of quantum-electro-dynamical interatomic forces.

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