We investigate precursors of critical behavior in the quasienergy spectrum due to the dynamical instability in the kicked top. Using a semiclassical approach, we analytically obtain a logarithmic divergence in the density of states, which is analogous to a continuous excited state quantum phase transition in undriven systems. We propose a protocol to observe the cusp behavior of the magnetization close to the critical quasienergy.PACS numbers: 05.30. Rt, 64.70.Tg, 05.45.Mt, 05.70.Fh The emerging field of excited state quantum phase transitions (ESQPTs) describes the nonanalytical behavior of excited states upon changes of parameters in the Hamiltonian [1][2][3]. This is in direct correspondence to quantum phase transitions (QPTs) [4], but takes place at critical energies above the ground state energy [5]. They entail dramatic dynamic consequences, e.g., environments with ESQPTs lead to enhanced decoherence, which could be a major drawback for building a quantum computer [6]. They appear in models of nuclear physics, such as the interacting Boson model [7,8] and the Lipkin-Meshkov-Glick model (LMG) [9]. In molecular physics, singularities of the density of states (DOS) arise in the vibron model [10], which are closely related to the monodromy in molecular bending degrees of freedom [11]. ESQPTs have been predicted to occur in prominent models of quantum optics such as the Dicke and Jaynes-Cummings models [12,13], too.Despite the striking observation of the QPT in the Dicke and the LMG model [14,15], ESQPTs have so far not been found experimentally for systems different to molecular ones, as the energies at which they occur are difficult to reach with standard techniques. Recently, however, the observation of low-energy singularities of the DOS in twisted graphene layers [16], and monodromy in diverse molecules [11], has opened an increasing interest in the experimental investigation of spectral singularities.Quantum critical behavior is usually defined with respect to system energies [4]. Under the effect of a nonadiabatic external control the energy is not conserved and it is not possible to uniquely define a ground state and the corresponding excited states. In this paper we make use of Floquet theory to introduce the concept of critical quasienergy states (CQS), which are a direct generalization of ESQPTs to driven quantum systems. Our model of choice is a paradigmatic model in the quantum chaos community: the kicked top. Quantum kicked systems play a prominent role in the investigation of quantum signatures of chaos and have intriguing relations to condensed matter systems [17]. Examples of these relations are the metal-supermetal [18] and metaltopological-insulator [19] QPTs in the kicked rotator, which can be thought of as a limiting case of the kicked top. Such a limit is established when the top is restricted to evolve along a small equatorial band, which is topologically equivalent to a cylinder [17].We are motivated by a recent experimental realization of the kicked top with driven ultra-cold Cesiuma...

We theoretically study cooperative effects in the steady-state transmission of photons through a medium of $N$ radiators. Using methods from quantum transport, we find a cross-over in scaling from $N$ to $N^2$ in the current and even higher powers of $N$ in the higher cumulants of the photon counting statistics as a function of the tunable source occupation. The effect should be observable for atoms confined within a nano-cell with a pumped optical cavity as photon source.Comment: extended results, 9 pages, 2 figures, to appear in Annals of Physic

We consider thermal transport between two reservoirs coupled by a quantum Ising chain as a model for nonequilibrium physics induced in quantum-critical many-body systems. By deriving rate equations based on exact expressions for the quasiparticle pairs generated during the transport, we observe signatures of the underlying quantum phase transition in the steady-state energy current already at finite and different reservoir temperatures.

We investigated the evolution and transformation of scientific knowledge in the early modern period, analyzing more than 350 different editions of textbooks used for teaching astronomy in European universities from the late fifteenth century to mid-seventeenth century. These historical sources constitute the Sphaera Corpus. By examining different semantic relations among individual parts of each edition on record, we built a multiplex network consisting of six layers, as well as the aggregated network built from the superposition of all the layers. The network analysis reveals the emergence of five different communities. The contribution of each layer in shaping the communities and the properties of each community are studied. The most influential books in the corpus are found by calculating the average age of all the out-going and in-coming links for each book. A small group of editions is identified as a transmitter of knowledge as they bridge past knowledge to the future through a long temporal interval. Our analysis, moreover, identifies the most impactful editions. These books introduce new knowledge that is then adopted by almost all the books published afterwards until the end of the whole period of study. The historical research on the content of the identified books, as an empirical test, finally corroborates the results of all our analyses.

We discuss singularities in the spectrum of driven many-body spin systems. In contrast to undriven models, the driving allows us to control the geometry of the quasienergy landscape. As a consequence, one can engineer singularities in the density of quasienergy states by tuning an external control. We show that the density of levels exhibits logarithmic divergences at the saddle points, while jumps are due to local minima of the quasienergy landscape. We discuss the characteristic signatures of these divergences in observables like the magnetization, which should be measurable with current technology.Comment: 10 pages, 4 figures, comments welcom