Quantum exploration of high-dimensional canyon landscapes

Understand

Canyon landscapes in high dimension can be described as manifolds of small, but extensive dimension, immersed in a higher dimensional ambient space and characterized by a zero potential energy on the manifold.

• Here we consider the problem of a quantum particle exploring a prototype of a high-dimensional random canyon landscape.
• We characterize the thermal partition function and show that around the point where the classical phase space has a satisfiability transition so that zero potential energy canyons disappear, moderate quantum fluctuations have a deleterious effect and induce glassy phases at temperature where classical thermal fluctuations alone would thermalize the system.
• Surprisingly we show that even when, classically, diffusion is expected to be unbounded in space, the interplay between quantum fluctuations and the randomness of the canyon landscape conspire to have a confining effect.