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Transmon qubits are the predominant element in circuit-based quantum information processing, such as existing quantum computers, due to their controllability and ease of engineering implementation. But more than qubits, transmons are multilevel nonlinear oscillators that can be used to investigate fundamental physics questions. Here, they are explored as simulators of excited state quantum phase transitions (ESQPTs), which are generalizations of quantum phase transitions to excited states. We show that the spectral kissing (coalescence of pairs of energy levels) experimentally observed in the effective Hamiltonian of a driven SNAIL-transmon is an ESQPT precursor. We explore the dynamical consequences of the ESQPT, which include the exponential growth of out-of-time-ordered correlators, followed by periodic revivals, and the slow evolution of the survival probability due to localization. These signatures of ESQPT are within reach for current superconducting circuits platforms and are of interest to experiments with cold atoms and ion traps. [ABSTRACT FROM AUTHOR]

This work is concerned with the excited state quantum phase transitions (ESQPTs) defined in Ann. Phys. 323, 1106 (2008). In many-body models that exhibit such transitions, the ground state quantum phase transition (QPT) occurs in parallel with a singularity in the energy spectrum that propagates to higher energies as the control parameter increases beyond the QPT critical point. The analysis of the spectrum has been a main tool for the detection of these ESQPTs. Studies of the effects of this transition on the system dynamics are more limited. Here, we extend our previous works and show that the evolution of an initial state with energy close to the ESQPT critical point may be extremely slow. This result is surprising, because it may take place in systems with long-range interactions, where the dynamics is usually expected to be very fast. A timely example is the one-dimensional spin-1/2 model with infinite-range Ising interaction studied in experiments with ion traps. Its Hamiltonian has a U(2) algebraic structure. More generally, the slow dynamics described here occurs in two-level bosonic or fermionic models with pairing interactions and a [ABSTRACT FROM AUTHOR]

• Modeling of the experimental bending rovibrational spectra data of a set of molecular species which encompasses the full gamut of structures: semirigid linear (HNC), semirigid bent (H2S) and nonrigid (Si2C and NCNCS). • Most general Hamiltonian of the two dimensional limit of the vibron model including all possible interactions up to four-body. • Predictions of the higher excited rovibrational energies are provided. • Analysis of the molecular dynamical structure using the quantum monodromy diagram, the Birge-Sponer plot and the participation ratio. We present an extension of the Hamiltonian of the two dimensional limit of the vibron model to encompass all possible interactions up to four-body operators. We apply this Hamiltonian to the modeling of the bending spectrum of four molecules: HNC, H 2 S, Si 2 C, and NCNCS. The selected molecular species include linear, bent, and nonrigid equilibrium structures, proving the versatility of the algebraic approach which allows for the consideration of utterly different physical cases within a single Hamiltonian and a general formalism. For each case we compute predicted bending energies and wave functions, that we use to depict the associated quantum monodromy diagram, Birge-Sponer plot, and participation ratio. In nonrigid cases, we also show the bending energy functional obtained using the coherent –or intrinsic– state formalism. [ABSTRACT FROM AUTHOR]