Response and Propagator Methods

Shaul Mukamel, Jeremy B. Maddox

We propose a quantum trajectory algorithm for computing nonlinear response functions of condensed phase molecular systems based on a time-ordered expansion of the density matrix. The nth-order response function is expressed as a sum of 2(n) impulsive response pathways representing trajectories involving zero, one, and up to n interactions with short external pulses. These are evaluated using a forward propagation algorithm based upon a Liouville space extension of the Bohmian propagation method.

A. O. Caldeira

C Benoit

The moments method was shown to be very useful for determining the linear response of very large harmonic systems. In the presence of anharmonicity or electron-phonon coupling, the phonon self-energy appears in the one-phonon propagator. The phonon frequency is then renormalized and the system is damped. In this paper, we show that it is possible to extend the moments method to compute the response of these damped systems. The method involves introducing a two-dimensional density functional that can be calculated by the moments techniques and which allows the computation of the response function. We illustrate these results via applications to several models: systems with constant damping, systems of coupled relaxation modes and oscillators, and systems with electron-phonon coupling.

Jean‐Philippe Bouchaud, Julius Bonart, Jonathan Donier +1 more

A. A. Kalenyuk, S. I. Futimsky, Andrii P. Shapovalov

In this work, we experimentally investigated the nonlinear microwave response of YBa2Cu3O7–x Hilbert fractal superconducting microstrip resonators with sharp and rounded corners. We developed a resonator model that incorporates a distributed current-dependent nonlinear propagation parameter, γ(I), and used the ABCD matrix method for numerical simulations. Our findings demonstrated that the nonlinear response of the resonators can be effectively modeled with a current-proportional propagation parameter, γ∼I. In addition, we observed a significant reduction in the nonlinear response when transitioning from sharp to rounded corners in the resonator design. This work provides valuable insights into improving the design of superconducting resonators by minimizing their nonlinearities, which is crucial for advancing applications in microwave and quantum technologies.