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1. Characterizing the fundamental bending vibration of a linear polyatomic molecule for symmetry violation searches

   https://doi.org/10.1088/1367-2630/ace471  

   Jadbabaie, Arian ; Takahashi, Yuiki ; Pilgram, Nickolas H ; Conn, Chandler J ; Zeng, Yi ; Zhang, Chi ; Hutzler, Nicholas R ( July 2023 , New Journal of Physics)

   Polyatomic molecules have been identified as sensitive probes of charge-parity violating and parity violating physics beyond the Standard Model (BSM). For example, many linear triatomic molecules are both laser-coolable and have parity doublets in the ground electronic$\tilde{X}{}^2{\mathrm{\Sigma }}^{+}(010)$state arising from the bending vibration, both features that can greatly aid BSM searches. Understanding the$\tilde{X}{}^2{\mathrm{\Sigma }}^{+}(010)$state is a crucial prerequisite to precision measurements with linear polyatomic molecules. Here, we characterize the fundamental bending vibration of${}^{174}$YbOH using high-resolution optical spectroscopy on the nominally forbidden$\tilde{X}{}^2{\mathrm{\Sigma }}^{+}(010)$$\to \tilde{A}{}^2{\mathrm{\Pi }}_{1/2}(000)$transition at 588 nm. We assign 39 transitions originating from the lowest rotational levels of the$\tilde{X}{}^2{\mathrm{\Sigma }}^{+}(010)$state, and accurately model the state’s structure with an effective Hamiltonian using best-fit parameters. Additionally, we perform Stark and Zeeman spectroscopy on the$\tilde{X}{}^2{\mathrm{\Sigma }}^{+}(010)$state and fit the molecule-frame dipole moment to$D_{\mathrm{m}\mathrm{o}\mathrm{l}}=2.16(1)$Dand the effective electrong-factor to$g_S=2.07(2)$. Further, we use an empirical model to explain observed anomalous line intensities in terms of interference from spin–orbit and vibronic perturbations in the excited$\tilde{A}{}^2{\mathrm{\Pi }}_{1/2}(000)$state. Our work is an essential step toward searches for BSM physics in YbOH and other linear polyatomic molecules.

    

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2. Global existence and singularity formation for the generalized Constantin–Lax–Majda equation with dissipation: the real line vs. periodic domains

   https://doi.org/10.1088/1361-6544/ad140c  

   Ambrose, David M ; Lushnikov, Pavel M ; Siegel, Michael ; Silantyev, Denis A ( December 2023 , Nonlinearity)

   The question of global existence versus finite-time singularity formation is considered for the generalized Constantin–Lax–Majda equation with dissipation$-{\mathrm{\Lambda }}^{\sigma }$, where$\widehat{{\mathrm{\Lambda }}^{\sigma }}=|k{|}^{\sigma }$, both for the problem on the circle$x\in [-\pi ,\pi ]$and the real line. In the periodic geometry, two complementary approaches are used to prove global-in-time existence of solutions for$\sigma \text{⩾}1$and all real values of an advection parameterawhen the data is small. We also derive new analytical solutions in both geometries whena = 0, and on the real line when$a=1/2$, for various values ofσ. These solutions exhibit self-similar finite-time singularity formation, and the similarity exponents and conditions for singularity formation are fully characterized. We revisit an analytical solution on the real line due to Schochet fora = 0 andσ = 2, and reinterpret it terms of self-similar finite-time collapse. The analytical solutions on the real line allow finite-time singularity formation for arbitrarily small data, even for values ofσthat are greater than or equal to one, thereby illustrating a critical difference between the problems on the real line and the circle. The analysis is complemented by accurate numerical simulations, which are able to track the formation and motion of singularities in the complex plane. The computations validate and build upon the analytical theory.

    

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3. The metastable Q 3 Δ 2 state of ThO: a new resource for the ACME electron EDM search

   https://doi.org/10.1088/1367-2630/ab6a3a  

   Wu, X. ; Han, Z. ; Chow, J. ; Ang, D. G. ; Meisenhelder, C. ; Panda, C. D. ; West, E. P. ; Gabrielse, G. ; Doyle, J. M. ; DeMille, D. ( February 2020 , New Journal of Physics)

   The best upper limit for the electron electric dipole moment was recently set by the ACME collaboration. This experiment measures an electron spin-precession in a cold beam of ThO molecules in their metastable$H{(}^3{\mathrm{\Delta }}_1)$state. Improvement in the statistical and systematic uncertainties is possible with more efficient use of molecules from the source and better magnetometry in the experiment, respectively. Here, we report measurements of several relevant properties of the long-lived$Q{(}^3{\mathrm{\Delta }}_2)$state of ThO, and show that this state is a very useful resource for both these purposes. TheQstate lifetime is long enough that its decay during the time of flight in the ACME beam experiment is negligible. The large electric dipole moment measured for theQstate, giving rise to a large linear Stark shift, is ideal for an electrostatic lens that increases the fraction of molecules detected downstream. The measured magnetic moment of theQstate is also large enough to be used as a sensitive co-magnetometer in ACME. Finally, we show that theQstate has a large transition dipole moment to the$C{(}^1{\mathrm{\Pi }}_1)$state, which allows for efficient population transfer between the ground state$X{(}^1{\mathrm{\Sigma }}^{+})$and theQstate via$X-C-Q$Stimulated Raman Adiabatic Passage (STIRAP). We demonstrate 90 % STIRAP transfer efficiency. In the course of these measurements, we also determine the magnetic moment ofCstate, the$X\to C$transition dipole moment, and branching ratios of decays from theCstate.

    

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4. Asymptotics of noncolliding q-exchangeable random walks

   https://doi.org/10.1088/1751-8121/acedda  

   Petrov, Leonid ; Tikhonov, Mikhail ( August 2023 , Journal of Physics A: Mathematical and Theoretical)

   We consider a process of noncollidingq-exchangeable random walks on$\mathbb{Z}$making steps 0 (‘straight’) and −1 (‘down’). A single random walk is calledq-exchangeable if under an elementary transposition of the neighboring steps$(\text{down},\text{straight})\to (\text{straight},\text{down})$the probability of the trajectory is multiplied by a parameter$q\in (0,1)$. Our process ofmnoncollidingq-exchangeable random walks is obtained from the independentq-exchangeable walks via the Doob’sh-transform for a nonnegative eigenfunctionh(expressed via theq-Vandermonde product) with the eigenvalue less than 1. The system ofmwalks evolves in the presence of an absorbing wall at 0. The repulsion mechanism is theq-analogue of the Coulomb repulsion of random matrix eigenvalues undergoing Dyson Brownian motion. However, in our model, the particles are confined to the positive half-line and do not spread as Brownian motions or simple random walks. We show that the trajectory of the noncollidingq-exchangeable walks started from an arbitrary initial configuration forms a determinantal point process, and express its kernel in a double contour integral form. This kernel is obtained as a limit from the correlation kernel ofq-distributed random lozenge tilings of sawtooth polygons. In the limit as$m\to \mathrm{\infty }$,$q=e^{-\gamma /m}$withγ > 0 fixed, and under a suitable scaling of the initial data, we obtain a limit shape of our noncolliding walks and also show that their local statistics are governed by the incomplete beta kernel. The latter is a distinguished translation invariant ergodic extension of the two-dimensional discrete sine kernel.

    

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5. Weyl Fermions and broken symmetry phases of laterally confined 3 He films

   https://doi.org/10.1088/1361-648X/acf42b  

   Wu, Hao ; Sauls, J. A. ( September 2023 , Journal of Physics: Condensed Matter)

   Broken symmetries in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. The Fermionic spectrum of confined (quasi-2D)³He-A consists of branches of chiral edge states. The negative energy states are related to the ground-state angular momentum,$L_z=(N/2)\hslash$, for$N/2$Cooper pairs. The power law suppression of the angular momentum,$L_z(T)\simeq (N/2)\hslash [1-\frac{2}{3}(\pi T/\mathrm{\Delta }{)}^2]$for$0⩽T\ll T_c$, in the fully gapped 2D chiral A-phase reflects the thermal excitation of the chiral edge Fermions. We discuss the effects of wave function overlap, and hybridization between edge states confined near opposing edge boundaries on the edge currents, ground-state angular momentum and ground-state order parameter of superfluid³He thin films. Under strong lateral confinement, the chiral A phase undergoes a sequence of phase transitions, first to a pair density wave (PDW) phase with broken translational symmetry at$D_{c2}\sim 16{\xi }_0$. The PDW phase is described by a periodic array of chiral domains with alternating chirality, separated by domain walls. The period of PDW phase diverges as the confinement length$D\to D_{c_2}$. The PDW phase breaks time-reversal symmetry, translation invariance, but is invariant under the combination of time-reversal and translation by a one-half period of the PDW. The mass current distribution of the PDW phase reflects this combined symmetry, and originates from the spectra of edge Fermions and the chiral branches bound to the domain walls. Under sufficiently strong confinement a second-order transition occurs to the non-chiral ‘polar phase’ at$D_{c1}\sim 9{\xi }_0$, in which a single p-wave orbital state of Cooper pairs is aligned along the channel.

    

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