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Register a new userDegeneracies in a nonintegrable pairing model
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The evolution pattern of exceptional points is studied in a non-integrable limit of the complex-extended 3-level Richardson-Gaudin model. The appearance of a pseudo-diabolic point from the fusion of two exceptional points is demonstrated in the anti-hermitian limit of the model and studied in some details.
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Using the fact that the nonintegrable phase factor can reformulate the gauge theory in terms of path dependent vector potentials, the quantization condition for the nonintegrable phase is investigated. It is shown that the path-dependent formalism can provide compact description of the flux quantization and the charge quantization at the existence of a magnetic monopole. Moreover, the path-dependent formalism gives suggestions for searching of the quantized flux in different configurations and for other possible reasons of the charge quantization. As an example, the developed formalism is employed for a (1+1) dimensional world, showing the relationship between the fundamental unit of the charge and the fine structure constant for this world.
We show how, upon heating the spin degrees of freedom of the Hubbard model to infinite temperature, the symmetries of the system allow the creation of steady-states with long-range correlations between $eta$-pairs. With induce this heating with either dissipation or periodic driving and evolve the system towards a nonequilibrium steady state, a process which melts all spin order in the system. The steady state is identical in both cases and displays distance-invariant off-diagonal $eta$-correlations. These correlations were first recognised in the superconducting eigenstates in Yangs seminal paper [Phys. Rev. Lett 63, 2144 (1989)], which are a subset of our steady states. We show that our results are a consequence of symmetry properties and entirely independent of the microscopic details of the model and the heating mechanism.
Resonating valence bond (RVB) states are a class of entangled quantum many body wavefunctions with great significance in condensed matter physics. We propose a scheme to synthesize a family of RVB states using a cavity QED setup with two-level atoms (with states $vert 0 rangle$ and $vert 1 rangle$) coupled to a common photon mode. In the lossy cavity limit, starting with an initial state of $M$ atoms excited and $N$ atoms in the ground state, we show that this setup can be configured as a Stern Gerlach experiment. A measurement of photon emission collapses the wavefunction of atoms onto an RVB state composed of resonating long-ranged singlets of the form $frac{1}{sqrt{2}}[vert 0 1 rangle - vert 1 0 rangle]$. Each emitted photon reduces the number of singlets by unity, replacing it with a pair of lone spins or `spinons. As spinons are formed coherently in pairs, they are analogous to Cooper pairs in a superconductor. To simulate pair fluctuations, we propose a protocol in which photons are allowed to escape the cavity undetected. This leads to a mixed quantum state with a fluctuating number of spinon pairs -- an inchoate superconductor. Remarkably, in the limit of large system sizes, this protocol reveals an underlying quantum phase transition. Upon tuning the initial spin polarization ($M-N$), the emission exhibits a continuous transition from a dark state to a bright state. This is reflected in the spinon pair number distribution which can be tuned from sub-poissonian to super-poissonian regimes. This opens an exciting route to simulate RVB states and superconductivity.
The combined analysis of $ u_mu$ disappearance and $ u_e$ appearance data of NO$ u$A experiment leads to three nearly degenerate solutions. This degeneracy can be understood in terms of deviations in $ u_e$ appearance signal, caused by unknown effects, with respect to the signal expected for a reference set of oscillations parameters. We define the reference set to be vacuum oscillations in the limit of maximal $theta_{23}$ and no CP-violation. We then calculate the deviations induced in the $ u_e$ appearance signal event rate by three unknown effects: (a) matter effects, due to normal or inverted hierarchy (b) octant effects, due to $theta_{23}$ being in higher or lower octant and (c) CP-violation, whether $delta_{CP} sim - pi/2$ or $delta_{CP} sim pi/2$. We find that the deviation caused by each of these effects is the same for NO$ u$A. The observed number of $ u_e$ events in NO$ u$A is equivalent to the increase caused by one of the effects. Therefore, the observed number of $ u_e$ appearance events of NO$ u$A is the net result of the increase caused by two of the unknown effects and the decrease caused by the third. Thus we get the three degenerate solutions. We also find that further data by NO$ u$A can not distinguish between these degenerate solutions but addition of one year of neutrino run of DUNE can make a distinction between all three solutions. The distinction between the two NH solutions and the IH solution becomes possible because of the larger matter effect in DUNE. The distinction between the two NH solutions with different octants is a result of the synergy between the anti-neutrino data of NO$ u$A and the neutrino data of DUNE.
Many real-world networks exhibit a high degeneracy at few eigenvalues. We show that a simple transformation of the networks adjacency matrix provides an understanding of the origins of occurrence of high multiplicities in the networks spectra. We find that the eigenvectors associated with the degenerate eigenvalues shed light on the structures contributing to the degeneracy. Since these degeneracies are rarely observed in model graphs, we present results for various cancer networks. This approach gives an opportunity to search for structures contributing to degeneracy which might have an important role in a network.
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