scholarly journals QUANTUM INTERFERENCE EFFECTS IN HOŘAVA–LIFSHITZ GRAVITY

2010 ◽  
Vol 25 (37) ◽  
pp. 3115-3127 ◽  
Author(s):  
ABDULLO HAKIMOV ◽  
BOBUR TURIMOV ◽  
AHMADJON ABDUJABBAROV ◽  
BOBOMURAT AHMEDOV
Keyword(s):  
Phase Shift ◽  
Quantum Interference ◽  
Gordon Equation ◽  
Relativistic Quantum ◽  
Sagnac Effect ◽  
Interference Effects ◽  
Nonrelativistic Approximation ◽  
Potential Term ◽  
Klein Gordon ◽  
Neutron Interferometer

The relativistic quantum interference effects in the spacetime of slowly rotating object in the Hořava–Lifshitz gravity as the Sagnac effect and phase shift of interfering particle in neutron interferometer are derived. We consider the extension of Kehagias–Sfetsos (KS) solution48 in the Hořava–Lifshitz gravity for the slowly rotating gravitating object. Using the covariant Klein–Gordon equation in the nonrelativistic approximation, it is shown that the phase shift in the interference of particles includes the gravitational potential term with the KS parameter ω. It is found that in the case of the Sagnac effect, the influence of the KS parameter ω is becoming important due to the fact that the angular velocity of the locally non-rotating observer is increased in Hořava gravity. From the results of the recent experiments50 we have obtained lower limit for the coupling KS constant as ω ≃ 1.25 ⋅10-25 cm -2. Finally, as an example, we apply the obtained results to the calculation of the UCN (ultra-cold neutrons) energy level modification in the gravitational field of slowly rotating gravitating object in the Hořava–Lifshitz gravity.

scholarly journals QUANTUM INTERFERENCE EFFECTS IN SPACETIME OF SLOWLY ROTATING COMPACT OBJECTS IN BRANEWORLD

2010 ◽  
Vol 25 (04) ◽  
pp. 243-256 ◽  
Author(s):  
A. I. MAMADJANOV ◽  
A. A. HAKIMOV ◽  
S. R. TOJIEV
Keyword(s):  
Phase Shift ◽  
Quantum Interference ◽  
Relativistic Quantum ◽  
Additional Term ◽  
Compact Objects ◽  
Sagnac Effect ◽  
Interference Effects ◽  
Upper Limit ◽  
Neutron Interferometer ◽  
Shift Effect

The relativistic quantum interference effects in the spacetime of slowly rotating object in braneworld as the Sagnac effect and phase shift effect of interfering particle in neutron interferometer are derived in unified way. It is found that in the case of the Sagnac effect, the influence of brane parameter is becoming important due to the fact that the angular velocity of the locally non-rotating observer is increased by the brane tension. In the case of neutron interferometry, it is found that an additional term in the phase shift of interfering particle emerges due to the presence of the brane parameter Q*. From the obtained expressions of phase shift in Mach–Zehnder interferometer upper limit for brane parameter has been estimated. From the results of the recent experiments we have obtained upper limit for the tidal charge as Q* ≲ 107 cm 2. Finally, as an example, we apply the obtained results to the calculation of the (ultra-cold neutrons) energy level modification in the gravitational field of slowly rotating gravitating object in the braneworld.

Quantum interference effects in conformal Weyl gravity

2017 ◽  
Vol 32 (19n20) ◽  
pp. 1750116 ◽  
Author(s):  
Abdullo Hakimov ◽  
Ahmadjon Abdujabbarov ◽  
Bakhtiyor Narzilloev
Keyword(s):  
Phase Shift ◽  
Fourth Order ◽  
Quantum Interference ◽  
Order Theory ◽  
Interference Effects ◽  
Nonrelativistic Approximation ◽  
Weyl Space ◽  
Weyl Gravity ◽  
The Earth ◽  
Neutron Interferometer

We investigate the effects of conformal gravity as a phase shift by quantum interference and alternate approach of Sagnac effect which is based on the anisotropy of the coordinate speed of light in the fourth-order theory of conformal Weyl space–time. In the nonrelativistic approximation, it has been shown that the phase shift of the interfering particle in neutron interferometer includes the potential terms with the Weyl parameter of the conformal fourth-order theory. Comparing the results of the measurement of the gravitational redshift by the interferometer in the gravitational field of the earth with our theoretical prediction, it has been obtained upper limit for the Weyl parameter as [Formula: see text].

scholarly journals QUANTUM INTERFERENCE EFFECTS IN SLOWLY ROTATING NUT SPACE–TIME

2009 ◽  
Vol 18 (01) ◽  
pp. 107-118 ◽  
Author(s):  
V. S. MOROZOVA ◽  
B. J. AHMEDOV
Keyword(s):  
Phase Shift ◽  
Quantum Interference ◽  
Relativistic Quantum ◽  
Additional Term ◽  
Space Time ◽  
Sagnac Effect ◽  
Interference Effects ◽  
General Relativistic ◽  
Shift Effect ◽  
The One

General relativistic quantum interference effects in a slowly rotating NUT space–time, such as the Sagnac effect and the phase shift effect of interfering particles in a neutron interferometer, are considered. It was found that in the case of the Sagnac effect, the influence of the NUT parameter is becoming important due to the fact that the angular velocity of the locally nonrotating observer must be larger than the one in the Kerr space–time. In the case of neutron interferometry, it is found that due to the presence of the NUT parameter, an additional term in the phase shift of interfering particles emerges. This term can be, in principle, detected by a sensitive interferometer and the derived results could be further used in experiments to detect the gravitomagnetic charge. Finally, as an example, we apply the obtained results to the calculation of the UCN (ultra-cold neutrons) energy level modification in a slowly rotating NUT space–time.

BILINEAR FORM AND SOLITON SOLUTIONS FOR THE COUPLED NONLINEAR KLEIN–GORDON EQUATIONS

2012 ◽  
Vol 26 (15) ◽  
pp. 1250057
Author(s):  
HE LI ◽  
XIANG-HUA MENG ◽  
BO TIAN
Keyword(s):  
Field Theory ◽  
Bilinear Form ◽  
Gordon Equation ◽  
Relativistic Quantum ◽  
Soliton Solutions ◽  
Relativistic Quantum Mechanics ◽  
Klein Gordon ◽  
Truncated Painlevé Expansion ◽  
Klein Gordon Equation ◽  
Singular Manifolds

With the coupling of a scalar field, a generalization of the nonlinear Klein–Gordon equation which arises in the relativistic quantum mechanics and field theory, i.e., the coupled nonlinear Klein–Gordon equations, is investigated via the Hirota method. With the truncated Painlevé expansion at the constant level term with two singular manifolds, the coupled nonlinear Klein–Gordon equations are transformed to a bilinear form. Starting from the bilinear form, with symbolic computation, we obtain the N-soliton solutions for the coupled nonlinear Klein–Gordon equations.

scholarly journals APPROXIMATE ℓ-STATE SOLUTIONS TO THE KLEIN–GORDON EQUATION FOR MODIFIED WOODS–SAXON POTENTIAL WITH POSITION DEPENDENT MASS

2009 ◽  
Vol 24 (20n21) ◽  
pp. 3985-3994 ◽  
Author(s):  
ALTUĞ ARDA ◽  
RAMAZAN SEVER
Keyword(s):  
Approximation Scheme ◽  
Gordon Equation ◽  
Saxon Potential ◽  
Radial Part ◽  
Potential Term ◽  
Energy Eigenvalues ◽  
Klein Gordon ◽  
Uvarov Method ◽  
Dependent Mass ◽  
Klein Gordon Equation

The radial part of the Klein–Gordon equation for the generalized Woods–Saxon potential is solved by using the Nikiforov–Uvarov method with spatially dependent mass within the new approximation scheme to the centrifugal potential term. The energy eigenvalues and corresponding normalized eigenfunctions are computed. The solutions in the case of constant mass are also obtained to check out the consistency of our new approximation scheme.

Topological quantum scattering under the influence of a nontrivial boundary condition

2016 ◽  
Vol 31 (11) ◽  
pp. 1650074 ◽  
Author(s):  
Herondy Mota
Keyword(s):  
Boundary Condition ◽  
Phase Shift ◽  
Gordon Equation ◽  
Scattering Problem ◽  
Quantum Scattering ◽  
Topological Quantum ◽  
Klein Gordon ◽  
Bohm Effect ◽  
Aharonov Bohm

We consider the quantum scattering problem of a relativistic particle in (2 + 1)-dimensional cosmic string spacetime under the influence of a nontrivial boundary condition imposed on the solution of the Klein–Gordon equation. The solution is then shifted as consequence of the nontrivial boundary condition and the role of the phase shift is to produce an Aharonov–Bohm-like effect. We examine the connection between this phase shift and the electromagnetic and gravitational analogous of the Aharonov–Bohm effect and compare the present results with previous ones obtained in the literature, also considering non-relativistic cases.

scholarly journals Supersymmetry of Relativistic Hamiltonians for Arbitrary Spin

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1590
Author(s):  
Georg Junker
Keyword(s):  
Quantum Dynamics ◽  
Gordon Equation ◽  
Relativistic Quantum ◽  
Arbitrary Spin ◽  
Negative Energy ◽  
Diagonal Form ◽  
Proca Equation ◽  
Klein Gordon ◽  
Block Diagonal Form ◽  
Supersymmetric Structure

Hamiltonians describing the relativistic quantum dynamics of a particle with an arbitrary but fixed spin are shown to exhibit a supersymmetric structure when the even and odd elements of the Hamiltonian commute. Here, the supercharges transform between energy eigenstates of positive and negative energy. For such supersymmetric Hamiltonians, an exact Foldy–Wouthuysen transformation exists which brings it into a block-diagonal form separating the positive and negative energy subspaces. The relativistic dynamics of a charged particle in a magnetic field are considered for the case of a scalar (spin-zero) boson obeying the Klein–Gordon equation, a Dirac (spin one-half) fermion and a vector (spin-one) boson characterised by the Proca equation. In the latter case, supersymmetry implies for the Landé g-factor g=2.

Relativistic quantum motion of spin-0 particles with a Cornell-type potential in (1 + 2)-dimensional Gürses spacetime backgrounds

2019 ◽  
Vol 34 (38) ◽  
pp. 1950314 ◽  
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Quantum Dynamics ◽  
Gordon Equation ◽  
Relativistic Quantum ◽  
Scalar Potential ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Klein Gordon ◽  
Quantum Motion ◽  
Type Potential ◽  
Klein Gordon Equation

In this work, we investigate the relativistic quantum dynamics of spin-0 particles in the background of (1 + 2)-dimensional Gürses spacetime [M. Gürses, Class. Quantum Grav. 11, 2585 (1994)] with interactions. We solve the Klein–Gordon equation subject to Cornell-type scalar potential in the considered framework, and evaluate the energy eigenvalues and corresponding wave functions, in detail.

Discrete phase space and continuous time relativistic quantum mechanics II: Peano circles, hyper-tori phase cells, and fiber bundles

2021 ◽  
Vol 36 (35) ◽  
Author(s):  
Anadijiban Das ◽  
Rupak Chatterjee
Keyword(s):  
Phase Space ◽  
State Space ◽  
Continuous Time ◽  
Gordon Equation ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Fiber Bundles ◽  
Phase Cell ◽  
Klein Gordon ◽  
Discrete Phase

The discrete phase space and continuous time representation of relativistic quantum mechanics are further investigated here as a continuation of paper I.1 The main mathematical construct used here will be that of an area filling Peano curve. We show that the limit of a sequence of a class of Peano curves is a Peano circle denoted as [Formula: see text], a circle of radius [Formula: see text] where [Formula: see text]. We interpret this two-dimensional (2D) Peano circle in our framework as a phase cell inside our 2D discrete phase plane. We postulate that a first quantized Planck oscillator, being very light, and small beyond current experimental detection, occupies this phase cell [Formula: see text]. The time evolution of this Peano circle sweeps out a 2D vertical cylinder analogous to the worldsheet of string theory. Extending this to 3D space, we introduce a [Formula: see text]-dimensional phase space hyper-tori [Formula: see text] as the appropriate phase cell in the physical dimensional discrete phase space. A geometric interpretation of this structure in state space is given in terms of product fiber bundles. We also study free scalar Bosons in the background [Formula: see text]-dimensional discrete phase space and continuous time state space using the relativistic partial difference-differential Klein–Gordon equation. The second quantized field quanta of this system can cohabit with the tiny Planck oscillators inside the [Formula: see text] phase cells for eternity. Finally, a generalized free second quantized Klein–Gordon equation in a higher [Formula: see text]-dimensional discrete state space is explored. The resulting discrete phase space dimension is compared to the significant spatial dimensions of some of the popular models of string theory.

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