Skip to Content

Sponsors

No results

Tags

No results

Types

No results

Search Results

Events

No results
Search events using: keywords, sponsors, locations or event type
When / Where

Presented By: Leinweber Center for Theoretical Physics

HET Seminar | Quantum Complexity, Integrability, and Chaos

Vijay Balasubramanian (UPenn)

Seminar Link: http://myumi.ch/O4P7E

The states of quantum systems grow in complexity over time as entanglement spreads between degrees of freedom. Following ideas in computer science, we formulate the complexity of time evolution as the length of the shortest geodesic on the unitary group manifold between the identity and the time evolution operator, and use the SYK family of models with N fermions to study this quantity in free, integrable, and chaotic systems. In all cases, the complexity initially grows linearly in time, and the shortest path lies along the physical time evolution. This linear growth is eventually truncated by "shortcuts" on the unitary manifold that are shorter than the physical time evolution. We explicitly locate such shortcuts and hence show that in the free theory, shortcuts occur at a time of O(N^1/2), truncating complexity growth at this scale. We also find an explicit operator which "fast-forwards" time evolution with this complexity. In a class of integrable theories, we show that shortcuts appear in a time upper bounded by O(poly(N)), again truncating complexity growth. Finally, in chaotic theories we argue that shortcuts do not occur until exponential times, after which it becomes possible to find infinitesimally nearby fixed-complexity approximations to the time evolution operator. We relate these results to the Eigenstate Complexity Hypothesis, a new criterion on the spectrum of energy eigenstates that guarantees an exponential increase of complexity over time that is consistent with maximal chaos.

Explore Similar Events

  •  Loading Similar Events...
Report Event As Inappropriate
Back to Main Content