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Calculations of Electric Potential II

Calculations of Electric Potential II

An electric dipole is a system of two equal but opposite charges, separated by a fixed distance. This system is used to model many real-world systems, including atomic and molecular interactions. One of these systems is the water molecule, but only under certain circumstances. These circumstances are met inside a microwave oven, where electric fields with alternating directions make the water molecules change orientation. This vibration is equivalent to heat at the molecular level.
Consider a...

Poisson's And Laplace's Equation

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The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.

Electric Dipoles and Dipole Moment

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Consider two charges of equal magnitude but opposite signs. If they cannot be separated by an external electric field, the system is called a permanent dipole. For example, the water molecule is a dipole, making it a good solvent.
Theoretically, studying electric dipoles leads to understanding why the resultant electric forces around us are weak. Since electric forces are strong, remnant net charges are rare. Hence, the interaction between dipoles helps us understand electrical interactions in...

Potential Due to a Polarized Object

Potential Due to a Polarized Object

A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...

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Induced Electric Dipoles

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A permanent electric dipole orients itself along an external electric field. This rotation can be quantified by defining the potential energy because the external torque does work in rotating it. Then, the potential energy is minimum at the parallel configuration and maximum at the antiparallel configuration. While the former is a stable equilibrium, the latter is an unstable equilibrium.
Since the absolute value of potential energy holds no physical meaning, its zero value can be chosen as per...

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Numerical method for evolving the dipolar projected Gross-Pitaevskii equation.

P B Blakie¹, C Ticknor, A S Bradley

¹Department of Physics, Jack Dodd Centre for Quantum Technology, University of Otago, Dunedin 9016, New Zealand.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|August 8, 2009

Summary

We developed an efficient method to solve the projected Gross-Pitaevskii equation (PGPE) for Bose gases with dipolar interactions. This approach accurately models the low-energy behavior of these quantum systems.

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Area of Science:

Quantum physics
Condensed matter physics
Atomic physics

Background:

The projected Gross-Pitaevskii equation (PGPE) models interacting Bose gases.
Incorporating long-range dipolar interactions complicates PGPE solutions.
Restricting the field to low-energy modes is computationally challenging.

Purpose of the Study:

To develop an efficient and accurate method for solving the dipolar PGPE.
To enable the study of Bose gases with long-range interactions.
To accurately represent the low-energy c-field region.

Main Methods:

Utilized a Hermite-polynomial-based spectral representation for mode restriction.
Employed auxiliary oscillator states for reciprocal space Fourier transforms.
Derived Ehrenfest equations to track angular momentum evolution.

Main Results:

Successfully implemented an efficient and accurate scheme for the dipolar PGPE.
Demonstrated precise mode restriction for low-energy physics.
Characterized the accuracy of the developed method extensively.

Conclusions:

The Hermite-polynomial spectral method provides an effective solution for the dipolar PGPE.
This method accurately captures the dynamics of Bose gases with dipolar interactions.
The approach facilitates the study of angular momentum in such systems.