Donnerstag, 06.02.2025: Stability of slow Hamiltonian dynamics and Dynamical generation of alpha-Rényi entropies
Dr. Daniele Toniolo (UCL London)
In this talk I will present two results. The first regards the stability of the slow dynamics for spin systems from the point of view of Lieb-Robinson (L-R) bounds. L-R bounds quantify the speed at which a generic local operator spreads across the system due to Heisenberg evolution. A slow dynamics happens when to spread across a region the operator takes a time proportional to the exponential of such region. This is relevant in particular for so called many-body localized systems. In this case when the system is perturbed, for example with the insertion of perturbations that would lead to regions of fast dynamics, I will show that the dynamics remains locally slow. With this theory I can also consider the non perturbative scenario of the junction among systems with fast and slow dynamics. This is based upon [1].
The second result that I will discuss is the dynamical generation of entanglement as quantified by alpha-Rényi entropies, with 0<alpha<1, including the case alpha=1 of the von Neuman entropy, starting from a generic product state. I will show that this follows from the Lieb-Robinson bound of the dynamics. For a generic local spin system in one dimension then the entanglement grows at most linearly in time. On the other hand when a slow dynamics is considered, like in the first part of the talk, I will obtain the log t-law of entanglement that has been shown before for MBL systems mostly by numerics or by assuming the existence of local integrals of motions. The second part of the talk is based upon [2], and [3].
[1] D. Toniolo, S. Bose, https://arxiv.org/abs/2405.05958
[2] D. Toniolo, S. Bose, https://arxiv.org/abs/2408.00743
[3] D. Toniolo, S. Bose, https://arxiv.org/abs/2408.02016
| Uhrzeit: |
14:30 |
| Ort: |
C4H33 |
| Gruppe: |
Oberseminar Mathematical Physics |
| Einladender: |
Keppeler, Lemm, Pickl, Teufel, Tumulka |
Donnerstag, 06.02.2025: Electrons, Photons, and Darwin's Dream
Prof. Dr. Shadi Tahvildar-Zadeh (Rutgers)
In this report on several joint works with M. Kiessling, M. Lienert, and L. Frolov, I will present a quantum-mechanical treatment of Compton scattering, in one space dimension, in which photons are treated as particles on equal footing with electrons. This is achieved through a certain relativistic extension of the framework proposed in 1927 by de Broglie and 25 years later again by Bohm, and relies on our ability to describe (in any number of space dimensions) not just the electron, but also the photon, as a point particle whose motion is guided by a relativistic quantum mechanical wave function, one that possesses a conserved time-like future-directed probability current. The interaction between the two particles is implemented via a Lorentz-invariant no-crossing-of-paths boundary condition for the multi-body, multi-time wave function of the system. Boundary conditions are imposed on the submanifold of coincident events in this configuration space and are shown to be compatible with particle current conservation. The corresponding initial-boundary-value problem is proved to be well-posed, and particle trajectories are shown to exist globally in a Hypersurface Bohm-Dirac setting, for typical initial configurations. I will then report on our recent extension of this work to a quantum-mechanical three-body system, still in one space dimension, comprised of one photon situated between two electrons. The electrons do not interact directly, but only via the photon bouncing between them. The corresponding initial-boundary value problem is shown to be well-posed, and it is shown that the unique solution can be represented by a convergent infinite sum of Feynman-like diagrams, each one corresponding to the photon bouncing between the two electrons a fixed number of times.
| Uhrzeit: |
16:15 |
| Ort: |
C3N14 |
| Gruppe: |
Oberseminar Mathematical Physics |
| Einladender: |
Keppeler, Lemm, Pickl, Teufel, Tumulka |
