PotentialLibrary

About the PotentialLibrary class

The WaveBlocks Project

@author: R. Bourquin @copyright: Copyright (C) 2010, 2011, 2012 R. Bourquin @license: Modified BSD License

Class documentation

The WaveBlocks Project

This file contains some ready made potentials with up to five separate energy levels. This is a pure data file without any code. To load the potentials, use the PotentialFactory.

@author: R. Bourquin @copyright: Copyright (C) 2010, 2011 R. Bourquin @license: Modified BSD License

PotentialLibrary.cos_waves = {'potential': 'a * (1 - cos(b*x))', 'defaults': {'a': 0.07, 'b': 1.0}}

A potential consisting of a cosine wave

PotentialLibrary.delta_gap = {'potential': [['1/2 * tanh(x)', 'delta'], ['delta', '-1/2 * tanh(x)']]}

A potential with a single avoided crossing

PotentialLibrary.delta_gap_diag = {'potential': [['sqrt(delta**2 + tanh(x)**2/4)', '0'], ['0', '-sqrt(delta**2 + tanh(x)**2/4)']]}

Diagonalized single avoided crossing

PotentialLibrary.double_well = {'potential': 'sigma * (x**2 - 1)**2', 'defaults': {'sigma': 1.0}}

A double well potential

PotentialLibrary.eckart = {'potential': 'sigma * cosh(x/a)**(-2)', 'defaults': {'a': 0.9448580823160362, 'sigma': 0.038088000000000004}}

The Eckart potential

PotentialLibrary.five_quadratic = {'potential': [['1/2 * sigma * x**2', '0', '0', '0', '0'], ['0', '1/2 * sigma * x**2', '0', '0', '0'], ['0', '0', '1/2 * sigma * x**2', '0', '0'], ['0', '0', '0', '1/2 * sigma * x**2', '0'], ['0', '0', '0', '0', '1/2 * sigma * x**2']], 'defaults': {'sigma': 0.05}}

Decoupled harmonic potential for five components

PotentialLibrary.four_powers = {'potential': [['1/2 * sigma * x**2', '0', '0', '0'], ['0', '1/4 * sigma * x**4', '0', '0'], ['0', '0', '1/6 * sigma * x**6', '0'], ['0', '0', '0', '1/8 * sigma * x**8']], 'defaults': {'sigma': 0.05}}

Harmonic and higher order anharmonic potentials for four components

PotentialLibrary.four_quadratic = {'potential': [['1/2 * sigma * x**2', '0', '0', '0'], ['0', '1/2 * sigma * x**2', '0', '0'], ['0', '0', '1/2 * sigma * x**2', '0'], ['0', '0', '0', '1/2 * sigma * x**2']], 'defaults': {'sigma': 0.05}}

Decoupled harmonic potentials for four components

PotentialLibrary.free_particle = {'potential': 'c', 'defaults': {'c': '0'}}

Free particle

PotentialLibrary.morse = {'potential': 'D * (1 - exp(-a*(x-x0)))**2', 'defaults': {'a': 0.3, 'x0': 0.0, 'D': 3.0}}

The Morse potential

PotentialLibrary.pert_quadratic = {'potential': '1/2 * sigma * x**2 + 1/2 * delta**2 * x**2', 'defaults': {'sigma': 0.05, 'delta': 0.2}}

Perturbed harmonic potential

PotentialLibrary.quadratic = {'potential': '1/2 * sigma * x**2', 'defaults': {'sigma': '1/2'}}

Simple harmonic potential

PotentialLibrary.quartic = {'potential': '1/4 * sigma * x**4', 'defaults': {'sigma': 0.05}}

A simple fourth order anharmonic potential

PotentialLibrary.three_levels = {'potential': [['tanh(x+rho) + tanh(x-rho)', 'delta1', 'delta2'], ['delta1', '-tanh(x+rho)', '0'], ['delta2', '0', '1 - tanh(x-rho)']], 'defaults': {'rho': 3.0}}

A potential with three energy levels and multiple crossings

PotentialLibrary.three_quadratic = {'potential': [['1/2 * sigma * x**2', '0', '0'], ['0', '1/2 * sigma * x**2', '0'], ['0', '0', '1/2 * sigma * x**2']], 'defaults': {'sigma': 0.05}}

Decoupled harmonic potentials for three components

PotentialLibrary.two_crossings = {'potential': [['tanh(x-rho)*tanh(x+rho)/2', 'delta/2'], ['delta/2', '-tanh(x-rho)*tanh(x+rho)/2']], 'defaults': {'rho': 3.0}}

A potential with two avoided crossings in series

PotentialLibrary.two_quadratic = {'potential': [['1/2*sigma*x**2', '0'], ['0', '1/2*sigma*x**2']], 'defaults': {'sigma': 0.05}}

Double harmonic potential for two components

PotentialLibrary.two_quartic = {'potential': [['1/4*sigma*x**4', '0'], ['0', '1/8*sigma*x**4']], 'defaults': {'sigma': 1.0}}

Double quartic anharmonic potential for two components

PotentialLibrary.v_shape = {'potential': '1/2 * sqrt(tanh(x)**2+4*delta**2)', 'defaults': {'delta': 0.2}}

A narrow ‘V’-like potential

PotentialLibrary.wall = {'potential': 'atan(sigma*x) + pi/2', 'defaults': {'sigma': 10.0}}

A smooth unitstep like wall