The purpose of this study is to determine whether long-term treatment with an approved blood thinner reduces the risk of stroke in patients who develop short-term atrial fibrillation after non-heart surgery, versus taking no blood thinner. Participants will be randomly assigned to either the “no oral anti-coagulant group” or the “non-vitamin K oral anticoagulation (blood thinner) group.” Patients who are assigned to the non-vitamin K oral anticoagulant group will receive either rivaroxaban or apixaban, as determined by their physician. These anticoagulants are approved by the U.S. Food and Drug Administration (FDA) for use in people with nonvalvular atrial fibrillation to reduce the risk of stroke and blood clots. It is currently unclear whether the drugs are also effective and safe in patients with short-term atrial fibrillation after surgery. Researchers will collect information about how often stroke, bleeding, and other blood vessel-related complications occur in patients who take these medications. The results of the study may be used to help create guidance for the use of blood thinners.