We present a family of exact analytic solutions for non-linear quantum dynamics of a two-level system (TLS) subject to a periodic-in-time external field. In constructing the exactly solvable models, we use a "reverse engineering" approach where the form of external perturbation is chosen to preserve an integrability constraint, which yields a single non-linear differential equation for the ac-field. A solution to this equation is expressed in terms of Jacobi elliptic functions with three independent parameters that allows one to choose the frequency, average value, and amplitude of the time-dependent field at will. This form of the ac-drive is especially relevant to the problem of dynamics of TLS charge defects that cause dielectric losses in superconducting qubits. We apply our exact results to analyze non-linear dielectric response of such TLSs and show that the position of the resonance peak in the spectrum of the relevant correlation function is determined by the quantum-mechanical phase accumulated by the TLS wave-function over a time evolution cycle. It is shown that in the non-linear regime, this resonance frequency may be shifted strongly from the value predicted by the canonical TLS model. We also analyze the "spin" survival probability in the regime of strong external drive and recover a coherent destruction of tunneling phenomenon within our family of exact solutions, which manifests itself as a strong suppression of "spin-flip" processes and suggests that such non-linear dynamics in LC-resonators may lead to lower losses.
We study the magnetoresistance of two-dimensional bosonic Anderson insulators. We describe the change in spatial decay of localized excitations in response to a magnetic field, which is given by an interference sum over alternative tunnelling trajectories. The excitations become more localized with increasing field (in sharp contrast to generic fermionic excitations which get weakly delocalized): the localization length ξ(B) is found to change as ξ −1 (B) − ξ −1 (0) ∼ B 4/5 . The quantum interference problem maps onto the classical statistical mechanics of directed polymers in random media (DPRM). We explain the observed scaling using a simplified droplet model which incorporates the non-trivial DPRM exponents. Our results have implications for a variety of experiments on magnetic-field-tuned superconductor-to-insulator transitions observed in disordered films, granular superconductors, and Josephson junction arrays, as well as for cold atoms in artificial gauge fields.
Motivated by evidence of local electron-electron attraction in experiments on disordered insulating films, we propose a new two-component Coulomb glass model that combines strong disorder and long-range Coulomb repulsion with the additional possibility of local pockets of a short-range interelectron attraction. This model hosts a variety of interesting phenomena, in particular a crucial modification of the Coulomb gap previously believed to be universal. Tuning the short-range interaction to be repulsive, we find non-monotonic humps in the density of states within the Coulomb gap. We further study variable-range hopping transport in such systems by extending the standard resistor network approach to include the motion of both single electrons and local pairs. In certain parameter regimes the competition between these two types of carriers results in a distinct peak in resistance as a function of the local attraction strength, which can be tuned by a magnetic field.
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