Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering

We give a general overview of the high-frequency regime in periodically driven systems and identify three distinct classes of driving protocols in which the infinite-frequency Floquet Hamiltonian is not equal to the time-averaged Hamiltonian. These classes cover systems, such as the Kapitza pendulum, the Harper-Hofstadter model of neutral atoms in a magnetic field, the Haldane Floquet Chern insulator and others. In all setups considered, we discuss both the infinite-frequency limit and the leading finite-frequency corrections to the Floquet Hamiltonian. We provide a short overview of Floquet theory focusing on the gauge structure associated with the choice of stroboscopic frame and the differences between stroboscopic and non-stroboscopic dynamics. In the latter case one has to work with dressed operators representing observables and a dressed density matrix. We also comment on the application of Floquet Theory to systems described by static Hamiltonians with well-separated energy scales and, in particular, discuss parallels between the inverse-frequency expansion and the Schrieffer-Wolff transformation extending the latter to driven systems.Comment: 84 pages, 25 figures, 4 appendice

Dynamics of repeatedly driven closed systems

This thesis covers my work in the field of closed, repeatedly driven, Hamiltonian systems. These systems do not exchange particles with the surrounding environment and their time-evolution is described by Hamilton's equations of motion (in the classical framework) or the Schroedinger equation (in the quantum framework). Their interaction with the environment is encoded into the time-dependence of the system's Hamiltonian. Chapter 1 is an "Overview" in which the status of the field, my contributions and future prospective are outlined. Chapters 2 to 4 provide the theoretical background which is used in Chapters 5 to 7 to derive some original results. These results show that in Hamiltonian systems, after many driving events, universal properties emerge. In particular, using the framework of the linear Boltzmann equation, I have studied the dynamics of a mobile, light impurity in a gas of heavy particles. The impurity's kinetic energy increases and, in the long time limit, approaches a non-thermal asymptotic distribution. The significance of this work is to show explicitly the emergence of a non-thermal distribution in a closed, driven system. Moreover, using the work-fluctuation theorems, I have studied the character of the energy distribution of a generic isolated system driven according a generic protocol. Both thermal and non-thermal distributions can be realized for the same system by changing the characteristics of the driving protocol. These two different regimes are separated by a dynamical phase transition. Finally, I have used the Floquet Theory and the Magnus Expansion to analyze the behavior of a generic interacting system which is driven periodically in time. For fast driving the system is unable to absorb energy and remains localized in the low energy part of the Hilbert space while for slow driving the system absorbs energy and, in the long time limit, it is delocalized in the entire Hilbert space. These two qualitatively different behaviors are separated by a many-body localization transition which is related to the break down of the Magnus expansion at the critical value of the driving frequency

From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics

This review gives a pedagogical introduction to the eigenstate thermalization hypothesis (ETH), its basis, and its implications to statistical mechanics and thermodynamics. In the first part, ETH is introduced as a natural extension of ideas from quantum chaos and random matrix theory (RMT). To this end, we present a brief overview of classical and quantum chaos, as well as RMT and some of its most important predictions. The latter include the statistics of energy levels, eigenstate components, and matrix elements of observables. Building on these, we introduce the ETH and show that it allows one to describe thermalization in isolated chaotic systems without invoking the notion of an external bath. We examine numerical evidence of eigenstate thermalization from studies of many-body lattice systems. We also introduce the concept of a quench as a means of taking isolated systems out of equilibrium, and discuss results of numerical experiments on quantum quenches. The second part of the review explores the implications of quantum chaos and ETH to thermodynamics. Basic thermodynamic relations are derived, including the second law of thermodynamics, the fundamental thermodynamic relation, fluctuation theorems, the fluctuation–dissipation relation, and the Einstein and Onsager relations. In particular, it is shown that quantum chaos allows one to prove these relations for individual Hamiltonian eigenstates and thus extend them to arbitrary stationary statistical ensembles. In some cases, it is possible to extend their regimes of applicability beyond the standard thermal equilibrium domain. We then show how one can use these relations to obtain nontrivial universal energy distributions in continuously driven systems. At the end of the review, we briefly discuss the relaxation dynamics and description after relaxation of integrable quantum systems, for which ETH is violated. We present results from numerical experiments and analytical studies of quantum quenches at integrability. We introduce the concept of the generalized Gibbs ensemble and discuss its connection with ideas of prethermalization in weakly interacting systems.This work was supported by the Army Research Office [grant number W911NF1410540] (L.D., A.P, and M.R.), the U.S.-Israel Binational Science Foundation [grant number 2010318] (Y.K. and A.P.), the Israel Science Foundation [grant number 1156/13] (Y.K.), the National Science Foundation [grant numbers DMR-1506340 (A.P.)and PHY-1318303 (M.R.)], the Air Force Office of Scientific Research [grant number FA9550-13-1-0039] (A.P.), and the Office of Naval Research [grant number N000141410540] (M.R.). The computations were performed in the Institute for CyberScience at Penn State. (W911NF1410540 - Army Research Office; 2010318 - U.S.-Israel Binational Science Foundation; 1156/13 - Israel Science Foundation; DMR-1506340 - National Science Foundation; PHY-1318303 - National Science Foundation; FA9550-13-1-0039 - Air Force Office of Scientific Research; N000141410540 - Office of Naval Research)Accepted manuscrip

Signaling through Ras is essential for ret oncogene-induced cell differentiation in PC12 cells.

Specific germline mutations of the receptor tyrosine kinase, Ret, predispose to multiple endocrine neoplasia types 2A and 2B and familial medullary thyroid carcinoma. The mechanisms by which different Ret isoforms (Ret-2A and Ret-2B) cause distinct neoplastic diseases remain largely unknown. On the other hand, forced expression of these mutated versions of Ret induces the rat pheochromocytoma cell line, PC12, to differentiate. Here we used an inducible vector encoding a dominant-negative Ras (Ras p21(N17)) to investigate the contributions of the Ras pathway to the phenotype induced in PC12 cells by the expression of either Ret-2A or Ret-2B mutants. We show that the Ret-induced molecular and morphological changes are both mediated by Ras-dependent pathways. However, even though inhibition of Ras activity was sufficient to revert Ret-induced differentiation, the kinetics of morphological reversion of the Ret-2B- was more rapid than the Ret-2A- transfected cells. Further, we show that in Ret-transfected cells the suc1- associated neurotrophic factor-induced tyrosine phosphorylation target, SNT, is chronically phosphorylated in tyrosine residues, and associates with the Sos substrate. These results indicate the activation of the Ras cascade as an essential pathway triggered by the chronic active Ret mutants in PC12 cells. Moreover, our data indicate SNT as a substrate for both Ret mutants, which might mediate the activation of this cascade

Pre-Main Sequence variables in the VMR-D : identification of T Tauri-like accreting protostars through Spitzer-IRAC variability

We present a study of the infrared variability of young stellar objects by means of two Spitzer-IRAC images of the Vela Molecular Cloud D (VMR-D) obtained in observations separated in time by about six months. By using the same space-born IR instrumentation, this study eliminates all the unwanted effects usually unavoidable when comparing catalogs obtained from different instruments. The VMR-D map covers about 1.5 square deg. of a site where star formation is actively ongoing. We are interested in accreting pre-main sequence variables whose luminosity variations are due to intermittent events of disk accretion (i.e. active T Tauri stars and EXor type objects). The variable objects have been selected from a catalog of more than 170,000 sources detected at a S/N ratio > 5. We searched the sample of variables for ones whose photometric properties are close to those of known EXor's. These latter are monitored in a more systematic way than T Tauri stars and the mechanisms that regulate the observed phenomenology are exactly the same. Hence the modalities of the EXor behavior is adopted as driving criterium for selecting variables in general. We selected 19 bona fide candidates that constitute a well-defined sample of new variable targets for further investigation. Out of these, 10 sources present a Spitzer MIPS 24 micron counterpart, and have been classified as 3 Class I, 5 flat spectrum and 2 Class II objects, while the other 9 sources have spectral energy distribution compatible with phases older than Class I. This is consistent with what is known about the small sample of known EXor's, and suggests that the accretion flaring or EXor stage might come as a Class I/II transition. We present also new prescriptions that can be useful in future searches for accretion variables in large IR databases.Comment: 35 pages, 12 figures To appear in Ap