Analysis technique for exceptional points in open quantum systems and QPT analogy for the appearance of irreversibility

Abstract

We propose an analysis technique for the exceptional points (EPs) occurring in the discrete spectrum of open quantum systems (OQS), using a semi-infinite chain coupled to an endpoint impurity as a prototype. We outline our method to locate the EPs in OQS, further obtaining an eigenvalue expansion in the vicinity of the EPs that gives rise to characteristic exponents. We also report the precise number of EPs occurring in an OQS with a continuum described by a quadratic dispersion curve. In particular, the number of EPs occurring in a bare discrete Hamiltonian of dimension $n_{\text{D}}$ is given by $n_{\text{D}}(n_{\text{D}}-1)$; if this discrete Hamiltonian is then coupled to continuum (or continua) to form an OQS, the interaction with the continuum generally produces an enlarged discrete solution space that includes a greater number of EPs, specifically $2^{n_{\text{C}}}(n_{\text{C}}+n_{\text{D}})[2^{n_{\text{C}}}(n_{\text{C}}+n_{\text{D}})-1]$, in which $n_{\text{C}}$ is the number of (non-degenerate) continua to which the discrete sector is attached. Finally, we offer a heuristic quantum phase transition analogy for the emergence of the resonance (giving rise to irreversibility via exponential decay) in which the decay width plays the role of the order parameter; the associated critical exponent is then determined by the above eigenvalue expansion.

16 pages, 7 figures

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• Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects
• Anomalous-order exceptional point and non-Markovian Purcell effect at threshold in one-dimensional continuum systems
• The arrow of time in open quantum systems and dynamical breaking of the resonance-antiresonance symmetry
• Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su-Schrieffer-Heeger model
• A new perspective on the Fano absorption spectrum in terms of complex spectral analysis
• Non-divergent representation of non-Hermitian operator near the exceptional point with application to a quantum Lorentz gas
• Spectral and transport properties of a $\mathcal{P}\mathcal{T}$-symmetric tight-binding chain with gain and loss
• Liouvillian exceptional points of an open driven two-level system
• Exceptional points treatment of cavity spectroscopies
• Phase Transitions and Virtual Exceptional Points in Quantum Emitters Coupled to Dissipative Baths
• Current-induced forces in single-resonance systems
• Long-time memory effects in a localizable central spin problem
• Characteristic influence of exceptional points in quantum dynamics
• Quantum/Relativistic Computation of Security and Efficiency of Electrical Power System for a Day-Ahead