Width bifurcation and dynamical phase transitions in open quantum systems

Abstract

The states of an open quantum system are coupled via the environment of scattering wavefunctions. The complex coupling coefficients $\omega$ between system and environment arise from the principal value integral and the residuum. At high level density where the resonance states overlap, the dynamics of the system is determined by exceptional points. At these points, the eigenvalues of two states are equal and the corresponding eigenfunctions are linearly dependent. It is shown in the present paper that Im$(\omega )$ and Re$(\omega )$ influence the system properties differently in the surrounding of exceptional points. Controlling the system by a parameter, the eigenvalues avoid crossing in energy near an exceptional point under the influence of Re$(\omega )$ in a similar manner as it is well known from discrete states. Im$(\omega )$ however leads to width bifurcation and finally (when the system is coupled to one channel, i.e. to a common continuum of scattering wavefunctions), to a splitting of the system into two parts with different characteristic time scales. Physically, the system is stabilized by this splitting since the lifetimes of most ($N-1$) states are longer than before while that of only one state is shorter. In the cross section the short-lived state appears as a background term in high-resolution experiments. The wavefunctions of the long-lived states are mixed in those of the original ones in a comparably large parameter range. Numerical results for the eigenvalues and eigenfunctions are shown for $N=2,4$ and 10 states coupled mostly to 1 channel.

31 pages, 11 figures

References in corpus (10)

• Controlled Dicke Subradiance from a Large Cloud of Two-Level Systems
• Environmentally induced Quantum Dynamical Phase Transition in the spin swapping operation
• Revisiting the Fermi Golden Rule: Quantum Dynamical Phase Transition as a Paradigm Shift
• Probing the microscopic structure of bound states in quantum point contacts
• Detector Backaction on the Self-Consistent Bound State in Quantum Point Contacts
• Transmission phase lapses in quantum dots: the role of dot-lead coupling asymmetry
• Avoided level crossings in open quantum systems
• Dynamical stabilization and time in open quantum systems
• Level-occupation switching of the Quantum Dot, and phase anomalies in mesoscopic interferometry
• Decoherence under many-body system-environment interactions: a stroboscopic representation based on a fictitiously homogenized interaction rate

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