Can I use a Thunderbolt cable to connect an iPad to a MacBook Air as second display? Is it possible to use a Thunderbolt to Thunderbolt cable to connect a new-generation iPad with a new-generation MacBook Air so that the iPad can be used as a 2nd monitor?
No, the iPad doesn't have thunderbolt, nor the capacity to function as a screen for another device by any cable.

You could use your iPad as an external display over the network though (remember your Macbook can create a network if you don't have one), there are quite a few apps that do this,