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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Width bifurcation and dynamical phase transitions in open quantum systems.

Hichem Eleuch¹, Ingrid Rotter

¹École Polytechnique, C.P. 6079, Succ. Centre-Ville, Montréal (QC), H3C 3A7 Canada. eleuchh@iro.umontreal.ca

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|June 18, 2013

Summary

This summary is machine-generated.

Complex coupling coefficients in open quantum systems influence system dynamics near exceptional points. Imaginary parts cause splitting into distinct time scales, enhancing stability and altering state lifetimes.

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Area of Science:

Quantum Mechanics
Quantum Dynamics
Scattering Theory

Background:

Open quantum systems interact with their environment via scattering wave functions.
Complex coupling coefficients (ω) arise from principal value integrals and residua.
System dynamics are governed by exceptional points at high state density where resonances overlap.

Purpose of the Study:

To investigate the distinct influences of the imaginary (Im(ω)) and real (Re(ω)) parts of coupling coefficients on open quantum system dynamics near exceptional points.
To analyze the phenomenon of width bifurcation and system splitting induced by Im(ω).
To explore the stabilization effects and altered state lifetimes resulting from this splitting.

Main Methods:

Analysis of complex coupling coefficients (ω) derived from principal value integrals and residua.
Theoretical investigation of system behavior near exceptional points where eigenvalues coincide and eigenfunctions become linearly dependent.
Numerical simulations for systems with N=2, 4, and 10 coupled states, primarily to a single channel.

Main Results:

Re(ω) influences eigenvalues near exceptional points, causing avoidance of energy level crossings similar to discrete systems.
Im(ω) induces width bifurcation and, in single-channel systems, splits the system into two parts with different characteristic time scales.
This splitting stabilizes the system, leading to longer lifetimes for some states and a shorter lifetime for one state, which appears as a background term in cross-sections.

Conclusions:

The real and imaginary components of coupling coefficients have differential effects on open quantum system dynamics near exceptional points.
Width bifurcation and system splitting driven by Im(ω) offer a mechanism for stabilizing quantum systems by creating states with extended lifetimes.
The observed phenomena have implications for interpreting high-resolution experimental data and understanding the behavior of complex quantum systems.