Exceptional phonon point versus free phonon coupling in Zn1−xBexTe under pressure: an experimental and ab initio Raman study

Raman scattering and ab initio Raman/phonon calculations, supported by X-ray diffraction, are combined to study the vibrational properties of Zn1−xBexTe under pressure. The dependence of the Be–Te (distinct) and Zn–Te (compact) Raman doublets that distinguish between Be- and Zn-like environments is examined within the percolation model with special attention to x ~ (0,1). The Be-like environment hardens faster than the Zn-like one under pressure, resulting in the two sub-modes per doublet getting closer and mechanically coupled. When a bond is so dominant that it forms a matrix-like continuum, its two submodes freely couple on crossing at the resonance, with an effective transfer of oscillator strength. Post resonance the two submodes stabilize into an inverted doublet shifted in block under pressure. When a bond achieves lower content and merely self-connects via (finite/infinite) treelike chains, the coupling is undermined by overdamping of the in-chain stretching until a «phonon exceptional point» is reached at the resonance. Only the out-of-chain vibrations «survive» the resonance, the in-chain ones are «killed». This picture is not bond-related, and hence presumably generic to mixed crystals of the closing-type under pressure (dominant over the opening-type), indicating a key role of the mesostructure in the pressure dependence of phonons in mixed crystals.

Non-Hermitian topology in rock–paper–scissors games

Non-Hermitian topology is a recent hot topic in condensed matters. In this paper, we propose a novel platform drawing interdisciplinary attention: rock–paper–scissors (RPS) cycles described by the evolutionary game theory. Specifically, we demonstrate the emergence of an exceptional point and a skin effect by analyzing topological properties of their payoff matrix. Furthermore, we discover striking dynamical properties in an RPS chain: the directive propagation of the population density in the bulk and the enhancement of the population density only around the right edge. Our results open new avenues of the non-Hermitian topology and the evolutionary game theory.

Non-linear coherent perfect absorption in the proximity of exceptional points

Coherent perfect absorption is one of the possibilities to get high absorption but typically suffers from being a resonant phenomena, i.e., efficient absorption only in a local frequency range. Additionally, if applied in high power applications, the understanding of the interplay of non-linearities and coherent perfect absorption is crucial. Here we show experimentally and theoretically the formation of non-linear coherent perfect absorption in the proximity of exceptional point degeneracies of the zeros of the scattering function. Using a microwave platform, consisting of a lossy nonlinear resonator coupled to two interrogating antennas, we show that a coherent incident excitation can trigger a self-induced perfect absorption once its intensity exceeds a critical value. Note, that a (near) perfect absorption persists for a broad-band frequency range around the nonlinear coherent perfect absorption condition. Its origin is traced to a quartic behavior that the absorbance spectrum acquires in the proximity of the exceptional points of the nonlinear scattering operator.

Correlations and commuting transfer matrices in integrable unitary circuits

We consider a unitary circuit where the underlying gates are chosen to be \check{R}Ř-matrices satisfying the Yang-Baxter equation and correlation functions can be expressed through a transfer matrix formalism. These transfer matrices are no longer Hermitian and differ from the ones guaranteeing local conservation laws, but remain mutually commuting at different values of the spectral parameter defining the circuit. Exact eigenstates can still be constructed as a Bethe ansatz, but while these transfer matrices are diagonalizable in the inhomogeneous case, the homogeneous limit corresponds to an exceptional point where multiple eigenstates coalesce and Jordan blocks appear. Remarkably, the complete set of (generalized) eigenstates is only obtained when taking into account a combinatorial number of nontrivial vacuum states. In all cases, the Bethe equations reduce to those of the integrable spin-1 chain and exhibit a global SU(2) symmetry, significantly reducing the total number of eigenstates required in the calculation of correlation functions. A similar construction is shown to hold for the calculation of out-of-time-order correlations.

Detecting deformed commutators with exceptional points in optomechanical sensors

Models of quantum gravity imply a modification of the canonical position-momentum commutation relations. In this manuscript, working with a binary mechanical system, we examine the effect of quantum gravity on the exceptional points of the system. On the one side, we find that the exceedingly weak effect of quantum gravity can be sensed via pushing the system towards a second-order exceptional point, where the spectra of the non-Hermitian system exhibits non-analytic and even discontinuous behavior. On the other side, the gravity perturbation will affect the sensitivity of the system to deposition mass. In order to further enhance the sensitivity of the system to quantum gravity, we extend the system to the other one which has a third-order exceptional point. Our work provides a feasible way to use exceptional points as a new tool to explore the effect of quantum gravity.

A new type of non-Hermitian phase transition in open systems far from thermal equilibrium

We demonstrate a new type of non-Hermitian phase transition in open systems far from thermal equilibrium, which can have place in the absence of an exceptional point. This transition takes place in coupled systems interacting with reservoirs at different temperatures. We show that the spectrum of energy flow through the system caused by the temperature gradient is determined by the $$\varphi^{4}$$ φ 4 -potential. Meanwhile, the frequency of the maximum in the spectrum plays the role of the order parameter. The phase transition manifests itself in the frequency splitting of the spectrum of energy flow at a critical point, the value of which is determined by the relaxation rates and the coupling strength. Near the critical point, fluctuations of the order parameter diverge according to a power law with the critical exponent that depends only on the ratio of reservoirs temperatures. The phase transition at the critical point has the non-equilibrium nature and leads to the change in the energy flow between the reservoirs. Our results pave the way to manipulate the heat energy transfer in the coupled out-of-equilibrium systems.

Chiral mode transfer of symmetry-broken states in anti-parity-time-symmetric mechanical system

Non-Hermitian systems with parity-time (PT) symmetry reveal rich physics beyond the Hermitian regime. As the counterpart of conventional PT symmetry, anti-parity-time (APT) symmetry may lead to new insights and applications. Complementary to PT-symmetric systems, non-reciprocal and chiral mode switching for symmetry-broken modes have been reported in optics with an exceptional point dynamically encircled in the parameter space of an APT-symmetric system. However, it has remained an open question whether and how the APT-symmetry-induced chiral mode transfer could be realized in mechanical systems. This paper investigates the implementation of APT symmetry in a three-element mass–spring system. The dynamic encircling of an APT-symmetric exceptional point has been implemented using dynamic-modulation mechanisms with time-driven stiffness. It is found that the dynamic encircling of an exceptional point in an APT-symmetric system with the starting point near the symmetry-broken phase leads to chiral mode switching. These findings may provide new opportunities for unprecedented wave manipulation in mechanical systems.