scholarly journals Tunneling Quantum Dynamics in Ammonia

2021 ◽  
Vol 22 (15) ◽  
pp. 8282
Author(s):  
Ciann-Dong Yang ◽  
Shiang-Yi Han
Keyword(s):  
Nitrogen Atom ◽  
Quantum Dynamics ◽  
Equations Of Motion ◽  
Quantum Probability ◽  
Quantum Mechanical ◽  
Quantum Trajectories ◽  
Experimental Measurements ◽  
Hamilton Equations ◽  
Usual Quantum ◽  
Tunneling Phenomenon

Ammonia is a well-known example of a two-state system and must be described in quantum-mechanical terms. In this article, we will explain the tunneling phenomenon that occurs in ammonia molecules from the perspective of trajectory-based quantum dynamics, rather than the usual quantum probability perspective. The tunneling of the nitrogen atom through the potential barrier in ammonia is not merely a probability problem; there are underlying reasons and mechanisms explaining why and how the tunneling in ammonia can happen. Under the framework of quantum Hamilton mechanics, the tunneling motion of the nitrogen atom in ammonia can be described deterministically in terms of the quantum trajectories of the nitrogen atom and the quantum forces applied. The vibrations of the nitrogen atom about its two equilibrium positions are analyzed in terms of its quantum trajectories, which are solved from the Hamilton equations of motion. The vibration periods are then computed by the quantum trajectories and compared with the experimental measurements.

APPLICATION OF THE FINITE STRIP METHOD TO MODELING OF VIBRATIONS OF COLLECTING ELECTRODES

2013 ◽  
Vol 13 (07) ◽  
pp. 1340001 ◽  
Author(s):  
IWONA ADAMIEC-WÓJCIK ◽  
ANDRZEJ NOWAK ◽  
STANISŁAW WOJCIECH
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Geometrical Parameters ◽  
Experimental Measurements ◽  
Newmark Method ◽  
Algebraic Equations ◽  
Finite Strip ◽  
Strip Method ◽  
Finite Strip Method ◽  
Large Length

The paper presents an application of the finite strip method to modeling of vibrations of the collecting electrodes, which are shells with large length (up to 16 m), width of 0.5 m and thickness of 0.002 m. The models and computer programs have been worked out and validated. Comparison of results obtained from numerical simulations and experimental measurements are presented and discussed. The equations of motion have been solved using methods for solution of sparse algebraic equations and Newmark method. The strip method has proved to be numerically effective. The programs enable us to carry out calculations for a system with several hundred thousands of degrees of freedom with time of analysis requiring thousand integration steps during less than 90 min on a PC computer. High numerical efficiency enables the geometrical parameters of the collecting electrodes to be selected in order to ensure large accelerations caused by a beater to be spread evenly over the surface of the electrodes. Conclusions concerning the influence of length of the collecting electrodes on the normal and tangentz accelerations are formulated.

Novel Technique for Quantum-Mechanical Eigenstate and Eigenvalue Calculations based on Seke's Self-Consistent Projection-Operator Method

1997 ◽  
Vol 11 (06) ◽  
pp. 245-258 ◽  
Author(s):  
J. Seke ◽  
A. V. Soldatov ◽  
N. N. Bogolubov
Keyword(s):  
Projection Operator ◽  
Equations Of Motion ◽  
Operator Method ◽  
Approximation Order ◽  
Quantum Mechanical ◽  
Approximation Technique ◽  
Operator Structure ◽  
Projection Operator Method ◽  
Self Consistent ◽  
Effective Hamiltonians

Seke's self-consistent projection-operator method has been developed for deriving non-Markovian equations of motion for probability amplitudes of a relevant set of state vectors. This method, in a Born-like approximation, leads automatically to an Hamiltonian restricted to a subspace and thus enables the construction of effective Hamiltonians. In the present paper, in order to explain the efficiency of Seke's method in particular applications, its algebraic operator structure is analyzed and a new successive approximation technique for the calculation of eigenstates and eigenvalues of an arbitrary quantum-mechanical system is developed. Unlike most perturbative techniques, in the present case each order of the approximation determines its own effective (approximating) Hamiltonian ensuring self-consistency and formal exactness of all results in the corresponding approximation order.

scholarly journals Dynamics of an orbital polarization of twisted electron beams in electric and magnetic fields

2019 ◽  
Vol 204 ◽  
pp. 10008
Author(s):  
Alexander J. Silenko ◽  
Pengming Zhang ◽  
Liping Zou
Keyword(s):  
Magnetic Field ◽  
Electron Beam ◽  
Magnetic Fields ◽  
Quantum Dynamics ◽  
Electron Beams ◽  
Equations Of Motion ◽  
Vortex Beam ◽  
Dirac Particles ◽  
Electric And Magnetic Fields ◽  
Average Projection

Relativistic classical and quantum dynamics of twisted (vortex) Dirac particles in arbitrary electric and magnetic fields is constructed. The relativistic Hamiltonian and equations of motion in the Foldy-Wouthuysen representation are derived. Methods for the extraction of an electron vortex beam with a given orbital polarization and for the manipulation of such a beam are developed. The new effect of a radiative orbital polarization of a twisted electron beam in a magnetic field resulting in a nonzero average projection of the intrinsic orbital angular momentum on the field direction is predicted.

Calculations of the development of an undular bore

1966 ◽  
Vol 25 (2) ◽  
pp. 321-330 ◽  
Author(s):  
D. H. Peregrine
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Solitary Wave ◽  
Equations Of Motion ◽  
Experimental Measurements ◽  
Order Of Approximation ◽  
Undular Bore ◽  
Finite Difference Approximations ◽  
Difference Approximations ◽  
Long Wave

If a long wave of elevation travels in shallow water it steepens and forms a bore. The bore is undular if the change in surface elevation of the wave is less than 0·28 of the original depth of water. This paper describes the growth of an undular bore from a long wave which forms a gentle transition between a uniform flow and still water. A physical account of its development is followed by the results of numerical calculations. These use finite-difference approximations to the partial differential equations of motion. The equations of motion are of the same order of approximation as is necessary to derive the solitary wave. The results are in general agreement with the available experimental measurements.

SEMICLASSICAL AND QUANTUM WORMHOLES

1992 ◽  
Vol 07 (05) ◽  
pp. 371-380 ◽  
Author(s):  
SUMIO WADA
Keyword(s):  
Equations Of Motion ◽  
Path Integrals ◽  
Saddle Points ◽  
Classical Solutions ◽  
Quantum Mechanical ◽  
The Creation ◽  
Baby Universes

Four-dimensional wormholes are classical solutions of Euclidean gravity which express the process for the creation of baby universes through the tunneling. But a problem is that they exist only in certain types of models. However, we should note that the semiclassical treatment of tunneling does not necessarily requires the existence of “physical” classical solutions. Solutions of classical equations of motion in unphysical regions sometimes represent relevant saddle points for the path integrals. We show that quantum mechanical wormholes proposed recently by Hawking and Page can be interpreted semiclassically in this way. We also discuss how the wormholes can be treated by the Wheeler-DeWitt equation. It is essential to choose an appropriate superspace for the wormholes.

THE AMPLITUDE SQUEEZING EFFECTS OF THE ELECTROMAGNETIC FIELD IN SIX-WAVE INTERACTION MODEL

2008 ◽  
Vol 22 (03) ◽  
pp. 219-230 ◽  
Author(s):  
DILIP-KUMAR GIRI ◽  
P. S. GUPTA
Keyword(s):  
Electromagnetic Field ◽  
Equations Of Motion ◽  
Interaction Model ◽  
Wave Interaction ◽  
Quantum Mechanical ◽  
Short Time Scale ◽  
Signal Photon ◽  
Signal Mode ◽  
Quantum Mechanical Approach ◽  
Short Time

The amplitude squeezing properties of the electromagnetic field is investigated in the fundamental, Stokes (probe) and signal mode in six-wave mixing process under short-time approximation based on a fully quantum mechanical approach. The interaction is looked upon as a process involving absorption of two pump photons and emission of three probe photons and one signal photon at different frequencies. The coupled Heisenberg quantum mechanical equations of motion involving real and imaginary parts of the quadrature operators are established and solved under short-time scale. The occurrence of amplitude squeezing effects in both the quadrature of the radiation field in the fundamental mode as well as in the Stokes (probe) mode is investigated using the required conditions of squeezing in each of the cases. It is also shown that the squeezing in the signal mode is found to be dependent on amplitude-squared squeezing of the initial pump field. This gives a method of converting higher-order (amplitude-squared) squeezing into normal squeezing.

nTH-ORDER AMPLITUDE SQUEEZING EFFECTS OF RADIATION IN MULTIPHOTON PROCESSES

2006 ◽  
Vol 20 (16) ◽  
pp. 2265-2281 ◽  
Author(s):  
DILIP KUMAR GIRI ◽  
P. S. GUPTA
Keyword(s):  
Radiation Field ◽  
Quantum Effect ◽  
Equations Of Motion ◽  
Photon Number ◽  
Zero Point ◽  
Optical Signal ◽  
Higher Order ◽  
Quantum Mechanical ◽  
Mixing Processes ◽  
Photon Process

Squeezing of the electromagnetic field is a purely quantum mechanical phenomenon and this quantum effect is expected to manifest itself in optical processes in which the nonlinear response of the system to the radiation field plays an important role. It has generated a great deal of interest in view of the possibility of reducing the noise of an optical signal below the vacuum limit i.e. zero-point oscillations. In this paper the concept of nth-order amplitude squeezing is introduced in the fundamental mode in four- and six-wave mixing processes as a generalization of the higher-order squeezing under short-time approximation based on a fully quantum mechanical approach. It established the coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators. The condition for occurrence of nth-order squeezing is obtained from which higher-order squeezing upto n=3 are studied. Dependence of squeezing on photon number is also established. The conditions for obtaining maximum and minimum squeezing are obtained. The method of present investigation can be applied to any higher-order non-linear optical processes and the technique can also be extended for studying squeezing in any N-photon process in general. Further, nth-order squeezing of radiation in N-photon process can also be investigated. The results obtained may help in selecting a suitable process to generate optimum squeezing in the radiation field.

scholarly journals SYMMETRIES OF THE NEAR HORIZON OF A BLACKHOLE BY GROUP THEORETIC METHODS

2007 ◽  
Vol 22 (08n09) ◽  
pp. 1717-1726
Author(s):  
K. MAHARANA
Keyword(s):  
Black Hole ◽  
Charged Particle ◽  
Magnetic Fields ◽  
Lie Algebras ◽  
Quantum Dynamics ◽  
Equations Of Motion ◽  
Scalar Particle ◽  
Lie Point Symmetries

We use group theoretic methods to obtain the extended Lie point symmetries of the quantum dynamics of a scalar particle probing the near horizon structure of a black hole. Symmetries of the classical equations of motion for a charged particle in the field of an inverse square potential and a monopole, in the presence of certain model magnetic fields and potentials are also studied. Our analysis gives the generators and Lie algebras generating the inherent symmetries.

Sign in / Sign up

Export Citation Format

Share Document