Hamiltonian deformations in quantum mechanics, $Tbar T$, and SYK

Kavli Affiliate: David J. Gross

| First 5 Authors: David J. Gross, Jorrit Kruthoff, Andrew Rolph, Edgar Shaghoulian,

| Summary:

Motivated by $Tbar T$, we introduce and study a wide class of solvable
deformations of quantum-mechanical theories. These deformations map the
Hamiltonian to a function of itself. We solve these theories by computing all
finite-temperature correlation functions of the deformed theory in terms of the
correlators of the undeformed theory. Applications to AdS/CFT, SYK, and the
Schwarzian theory are considered. We write down the deformed Schwarzian action
for an arbitrary Hamiltonian deformation and find that the maximal Lyapunov
exponent is unchanged.

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