The Phonon Network is a peer-to-peer network independent of the internet. It leverages the hardware security of smart cards to allow the secure storage and transfer of "phonons". Transactions occur without the need to broadcast it to an external ledger, and are fully contained between the two parties involved.
A phonon is a representation of a public/private key pair and some information (phonon descriptor) describing a digital asset encumbered to that key pair (e.g. a Bitcoin UTXO, or an Ethereum or ERC20 token). In this way, exchanging phonons is a secure mechanism of exchanging private keys, and consequently exchanging ownership of a digital asset without ever broadcasting a transaction to the asset's associated network/blockchain.
You can read more about Phonon on the Phonon website and forum: