# Publications

List of Papers, Presentations and Conferences Attended.

## Phonon Feedback Effects on Dynamics of Phase Slip Centers in Finite Gap Superconductors

July 2, 2020

The results on the behavior of phase-slip centers in thin superconducting wires based on finite-element modeling and time-dependent Ginzburg-Landau (TDGL) equations are discussed. For closer relationship with experiments, we used finite-gap formulation of the TDGL system. Both the dynamic equation for the Cooper-pair condensate wave-function and the expression for the electric current are more complex than in the gapless case. On this basis, the influence of nonequilibrium phonons is explored. These phonons can essentially change the location of geometrical points in which the phase slippage takes place. They also affect the frequency of phase-slip oscillations. The reported effects are experimentally detectable and can be used in practical devices.

## Visualization and Exploration of the Dynamics of Phase Slip Centers in Superconducting Wires

October 4th, 2019

The dynamics of phase slip centers in a 1D model of superconducting wire was created based on the set of time-dependent Ginzburg-Landau equations (TDGL). COMSOL Multiphysics®’ General Form PDE interface was used. TDGL has successfully applied to this problem decades ago and most recently, the visibility of solutions has been enhanced by engaging COMSOL's power. The feature which distinguishes the current report here is that, for the first time, the set of TDGL equations for superconductors with finite gap was used in full. The terms relevant to the presence of finite gap were included not only into the equation for the wave function of the condensate, but also into the equation for the current in the form of interference terms.

The performed thorough study of the solutions of these non-linear equations required extensive searches for multiple solutions at certain values of given parameters. We found it extremely helpful using the built-in capability of COMSOL which could be operated in tandem with MATLAB®. By developing the MATLAB code, we were able to automate findings of the relevant solutions. We obtained "branching" and "anti-branching" of these solutions at certain parameters of the problem. These properties are directly relevant to experimental results obtained with these objects.

Evolution of phase-slip centers takes place in picosecond time-scale, which can be very hard to visualize in practice. COMSOL's ability to generate animation provides unique opportunities to trace details of the microscopic evolution of various observables (such as the Cooper-pair density, superfluid and normal velocities, etc.).

## Conferences

New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative - Chapman University, November 2019

COMSOL Conference - Boston October 2019, Presenter

APS March Meeting - Boston 2019

PIMan Workshop - Chapman University, March 2019

APS Far West Fall Meeting - Cal State Fullerton, October 2018

7th International Workshop on Quantum Simulation and Quantum Walks - Chapman University, March 2018