Stern College for Women -- Faculty Publicationshttps://hdl.handle.net/20.500.12202/422020-10-25T03:03:59Z2020-10-25T03:03:59ZInterview with Prof. Jill Katz at Tel es Safi. [video]Katz, Jill C.Selavan, Nachlielhttps://hdl.handle.net/20.500.12202/61272020-09-16T17:59:23Z2016-07-01T00:00:00ZInterview with Prof. Jill Katz at Tel es Safi. [video]
Katz, Jill C.; Selavan, Nachliel
Interview with Prof. Dr. Jill C. Katz, Stern College for Women, Yeshiva University and Nachliel Selavan about Tel es Safi, Goliath's hometown).
Video / 12:48
2016-07-01T00:00:00ZLevel Repulsion and Dynamics in the Finite One-Dimensional Anderson Model.Torres-Herrera, E. JonathanMéndez-Bermúdez, J. A.Santos, Lea F.https://hdl.handle.net/20.500.12202/48462020-01-07T20:57:58Z2019-09-12T00:00:00ZLevel Repulsion and Dynamics in the Finite One-Dimensional Anderson Model.
Torres-Herrera, E. Jonathan; Méndez-Bermúdez, J. A.; Santos, Lea F.
This work shows that dynamical features typical of full random matrices can be observed also in the simple finite one-dimensional (1D) noninteracting Anderson model with nearest neighbor couplings. In the thermodynamic limit, all eigenstates of this model are exponentially localized in configuration space for any infinitesimal onsite disorder strength W. But this is not the case when the model is finite and the localization length is larger than the system size L, which is a picture that can be experimentally investigated. We analyze the degree of energy-level repulsion, the structure of the eigenstates, and the time evolution of the finite 1D Anderson model as a function of the parameter ξ∝(W2L)−1. As ξ increases, all energy-level statistics typical of random matrix theory are observed. The statistics are reflected in the corresponding eigenstates and also in the dynamics. We show that the probability in time to find a particle initially placed on the first site of an open chain decays as fast as in full random matrices and much faster that when the particle is initially placed far from the edges. We also see that at long times, the presence of energy-level repulsion manifests in the form of the correlation hole. In addition, our results demonstrate that the hole is not exclusive to random matrix statistics, but emerges also for W=0, when it is in fact deeper.
Scholarly article (pre-print)
2019-09-12T00:00:00ZDynamical signatures of quantum chaos and relaxation timescales in a spin-boson system.Lerma-Hernández, S.Villaseñor, D.Bastarrachea-Magnani, M. A.Torres-Herrera, E.J.Santos, L.F.Hirsch, J.G.https://hdl.handle.net/20.500.12202/48452020-01-07T20:59:00Z2019-05-10T00:00:00ZDynamical signatures of quantum chaos and relaxation timescales in a spin-boson system.
Lerma-Hernández, S.; Villaseñor, D.; Bastarrachea-Magnani, M. A.; Torres-Herrera, E.J.; Santos, L.F.; Hirsch, J.G.
Quantum systems whose classical counterparts are chaotic typically have highly correlated eigenvalues and level statistics that coincide with those from ensembles of full random matrices. A dynamical manifestation of these correlations comes in the form of the so-called correlation hole, which is a dip below the saturation point of the survival probability's time evolution. In this work, we study the correlation hole in the spin-boson (Dicke) model, which presents a chaotic regime and can be realized in experiments with ultracold atoms and ion traps. We derive an analytical expression that describes the entire evolution of the survival probability and allows us to determine the timescales of its relaxation to equilibrium. This expression shows remarkable agreement with our numerical results. While the initial decay and the time to reach the minimum of the correlation hole depend on the initial state, the dynamics beyond the hole up to equilibration is universal. We find that the relaxation time of the survival probability for the Dicke model increases linearly with system size.
Scholarly article
2019-05-10T00:00:00ZSelf-averaging in many-body quantum systems out of equilibrium.Schiulaz, MauroTorres-Herrera, E. JonathanPérez-Bernal, FranciscoSantos, Lea F.https://hdl.handle.net/20.500.12202/48442020-01-07T20:35:14Z2019-06-27T00:00:00ZSelf-averaging in many-body quantum systems out of equilibrium.
Schiulaz, Mauro; Torres-Herrera, E. Jonathan; Pérez-Bernal, Francisco; Santos, Lea F.
Despite its importance to experiments, numerical simulations, and the development of theoretical models, self-averaging in many-body quantum systems out of equilibrium remains underinvestigated. Usually, in the chaotic regime, self-averaging is just taken for granted. The numerical and analytical results presented here force us to rethink these expectations. They demonstrate that self-averaging properties depend on the quantity and also on the time scale considered. We show analytically that the survival probability in chaotic systems is not self-averaging at any time scale, even when evolved under full random matrices. We also analyze the participation ratio, Rényi entropies, the spin autocorrelation function from experiments with cold atoms, and the connected spin-spin correlation function from experiments with ion traps. We find that self-averaging holds at short times for the quantities that are local in space, while at long times, self-averaging applies for quantities that are local in time. Various behaviors are revealed at intermediate time scales.
Scholarly article (pre-print)
2019-06-27T00:00:00Z