There could be a number of variations of this basic concept, but I hope this will do to explain the basics.
Start with adding a styrofoam sheet to the bottom of your rafters on the south side and a baffle to trap the hot air at the peak of the roof, as shown in red. This increases the temperature of the air at the peak and helps create a draft effect to move the air upwards. Then, again shown in red, add a chimney which has a warm section on the south side and a cool section on the north. Again, this adds to the temperature and draft effect of the hot air exiting the attic. A downward draft effect is also created in the north half of the chimney for cool air.
Cool the air in the north half of the chimney by blowing through an exchanger with a swamp cooler. Alternatively, it could be cooled by circulating water through the ground or rerouting the cool air outlet from the bottom of the cool half of the chimney. For arid regions, more temperate climates or for the shoulder season, this would likely create all the air conditioning required. Unfortunately, most air conditioning demand is in more humid climates and in the peak season, and that is where your solar heat comes in.
By adding a slowly rotating desiccant wheel at the top of the chimney, you can remove humidity from the air entering the cool side. This will warm the air, but this heat can easily be removed by your swamp cooler exhanger. So, below the desiccant wheel and swamp cooler you will have dry, cool (approximately 80 degrees) air. By misting at this point, you can reduce the air and water temperature further, to approximately 55-65 degrees depending on the condition and characteristics of the desiccant. The desiccant is then regenerated (ie, the moisture is removed) by the hot air on the warm side of the chimney.
The cool air and water generated in this way can be circulated through exchangers to cool the house. Alternatively, the cool air from the chimney could be introduced directly to the house, although this would require opening the windows slightly and might result in too much humidity in the house as with a traditional swamp cooler.
Side benefits include a cooler attic since the drafting effect and baffles remove the heat from the main part of the attic. Air conditioning by this method should reduce power usage by 75-90%. At the same time, I believe this system could be installed for less than the cost of a traditional central heating system.