COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > CQIF Seminar > A system equilibrates if diagonalizing its hamiltonian is difficult

## A system equilibrates if diagonalizing its hamiltonian is difficultAdd to your list(s) Download to your calendar using vCal - Lluis Masanes (ICFO)
- Thursday 09 June 2011, 14:15-15:15
- MR2, Centre for Mathematical Sciences.
If you have a question about this talk, please contact Ashley Montanaro. In classical mechanics there is a relation between integrability and equilibration, but this is not well understood in the quantum case. Closed quantum systems never equilibrate to a stationary state. However, in some circumstances, the system equilibrates locally (the reduced density matrix of a subsystem evolves to a stationary state). All finite-dimensional quantum systems are integrable, in the sense that solving its dynamics reduces to diagonalizing its hamiltonian. This procedure may need a large computational effort, which differs from system to system. In some sense, the lack of integrability of a quantum system can be quantified by the computational complexity of diagonalizing its hamiltonian. We show that, if this complexity is at least quadratic with the size of the system then local equilibration holds (for almost all hamiltonians); and if this complexity is sub-quadratic then local equilibration does not hold. This talk is part of the CQIF Seminar series. ## This talk is included in these lists:Note that ex-directory lists are not shown. |
## Other listsCombinatorics Seminar Individual in the Labour Market Research Group Computer Science Research Students mini-conference## Other talksRandom Feature Expansions for Deep Gaussian Processes High-Dimensional Collocation for Lognormal Diffusion Problems Localization estimates for hypoelliptic equations The Warsaw Uprising in Polish Popular Culture after 1989 It takes two to tango:platelet collagen receptor GPVI-dimer in thrombosis and clinical implications All-resolutions inference for brain imaging |