Heralded magnetism in non-Hermitian atomic systems

Quantum phase transitions are usually studied in terms of Hermitian Hamiltonians. However, cold-atom experiments are intrinsically non-Hermitian due to spontaneous decay. Here, we show that non-Hermitian systems exhibit quantum phase transitions that are beyond the paradigm of Hermitian physics. We consider the non-Hermitian XY model, which can be implemented using three-level atoms with spontaneous decay. We exactly solve the model in one dimension and show that there is a quantum phase transition from short-range order to quasi-long-range order despite the absence of a continuous symmetry in the Hamiltonian. The ordered phase has a frustrated spin pattern. The critical exponent $\nu$ can be 1 or 1/2. Our results can be seen experimentally with trapped ions, cavity QED, and atoms in optical lattices.Comment: 7 pages + appendi

Statistically Preserved Structures and Anomalous Scaling in Turbulent Active Scalar Advection

The anomalous scaling of correlation functions in the turbulent statistics of active scalars (like temperature in turbulent convection) is understood in terms of an auxiliary passive scalar which is advected by the same turbulent velocity field. While the odd-order correlation functions of the active and passive fields differ, we propose that the even-order correlation functions are the same to leading order (up to a trivial multiplicative factor). The leading correlation functions are statistically preserved structures of the passive scalar decaying problem, and therefore universality of the scaling exponents of the even-order correlations of the active scalar is demonstrated.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let

Entanglement tongue and quantum synchronization of disordered oscillators

We study the synchronization of dissipatively-coupled van der Pol oscillators in the quantum limit, when each oscillator is near its quantum ground state. Two quantum oscillators with different frequencies exhibit an entanglement tongue, which is the quantum analogue of an Arnold tongue. It means that the oscillators are entangled in steady state when the coupling strength is greater than a critical value, and the critical coupling increases with detuning. An ensemble of many oscillators with random frequencies still exhibits a synchronization phase transition in the quantum limit, and we analytically calculate how the critical coupling depends on the frequency disorder. Our results can be experimentally observed with trapped ions or neutral atoms.Comment: 11 pages, 5 figure

SIMULATED EFFECTS OF USE VALUE ASSESSMENT ON PROPERTY TAX RATES

Public Economics,