# Faculty Publications and Research

Permanent link for this collectionhttps://hdl.handle.net/2022/17486

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Item Adiabatic theorem for quantum systems with spectral degeneracy(American Physical Society, 2012) Rigolin, G.; Ortiz, G.By stating the adiabatic theorem of quantum mechanics in a clear and rigorous way, we establish a necessary condition and a sufficient condition for its validity, where the latter is obtained employing our recently developed adiabatic perturbation theory. Also, we simplify further the sufficient condition into a useful and simple practical test at the expense of its mathematical rigor. We present results for the most general case of quantum systems, i.e. those with degenerate energy spectra. These conditions are of upmost importance for assessing the validity of practical implementations of non-Abelian braiding and adiabatic quantum computation. To illustrate the degenerate adiabatic approximation, and the necessary and sufficient conditions for its validity, we analyze in depth an exactly solvable time-dependent degenerate problem.Item Amplitudes for the analysis of the decay $J/ψ→K^+K^−π^0$(American Physical Society, 2012) Guo, P.; Mitchell, R.; Shepherd, M.; Szczepaniak, A.P.We construct an analytical model for two-channel, two-body scattering amplitudes, and then apply it in the description of the three-body $J/ψ→K^+K^−π^0$ decay. In the construction of the partial wave amplitudes, we combine the low-energy resonance region with the Regge asymptotic behavior determined from direct two-body production. We find that resonance production in the $Kπ$ channel in $J/ψ$ decays seems to differ from that observed in direct $Kπ$ production, while the mass distribution in the $K\overline{K}$ channel may be compatible.Item Analogue models for $T$ and $CPT$ violation in neutral-meson oscillations(American Physical Society, 2001) Kostelecký, V.A.; Roberts, A.Analogue models for $CP$ violation in neutral-meson systems are studied in a general framework. No-go results are obtained for models in classical mechanics that are nondissipative or that involve one-dimensional oscillators. A complete emulation is shown to be possible for a two-dimensional oscillator with rheonomic constraints, and an explicit example with spontaneous $T$ and $CPT$ violation is presented. The results have implications for analogue models with electrical circuits.Item Analytical construction of a nonperturbative vacuum for the open bosonic string(American Physical Society, 2001) Kostelecký, V.A.; Potting, R.Using analytical methods, a nonperturbative vacuum is constructed recursively in the field theory for the open bosonic string. Evidence suggests it corresponds to the Lorentz-invariant end point of tachyon condensation on a D25-brane. The corresponding string field is a twisted squeezed state.Item Analytical wave functions for atomic quantum-defect theory(American Physical Society, 1985) Kostelecký, V.A.; Nieto, M.M.We present an exactly solvable effective potential that reproduces atomic spectra in the limit of exact quantum-defect theory, i.e., the limit in which, for a fixed l, the principal quantum number is modified by a constant: $n^*=\text{n}-\delta (\text{l})$. Transition probabilities for alkali atoms are calculated using the analytical wave functions obtained and agree well with accepted values. This allows us to make phenomenological predictions for certain unknown transition probabilities. Our analytical wave functions might serve as useful trial wave functions for detailed calculations.Item Arbitrary dimensional Majorana dualities and architectures for topological matter(American Physical Society, 2012) Nussinov, Z.; Ortiz, G.; Cobanera, E.Motivated by the prospect of attaining Majorana modes at the ends of nanowires, we analyze interacting Majorana systems on general networks and lattices in an arbitrary number of dimensions, and derive universal spin duals. We prove that these interacting Majorana systems, quantum Ising gauge theories, and transverse-field Ising models with annealed bimodal disorder are all dual to one another on general planar graphs. This leads to an interesting connection between heavily disordered annealed Ising systemsand uniform Ising theories with nearest-neighbor interactions. As any Dirac fermion (including electronic) operator can be expressed as a linear combination of two Majorana fermion operators, our results further lead to dualities between interacting Dirac fermionic systems on rather general lattices and graphs and corresponding spin systems. Such general complex Majorana architectures (other than those of simple square or other crystalline arrangements) might be of empirical relevance. As these systems display low-dimensional symmetries, they are candidates for realizing topological quantum order. The spin duals allow us to predict the feasibility of various standard transitions as well as spin-glass-type behavior in interacting Majorana fermion or electronic systems. Several systems that can be simulated by arrays of Majorana wires are further introduced and investigated: (1) the XXZ honeycomb compass model (intermediate between the classical Ising model on the honeycomb lattice and Kitaev's honeycomb model), (2) a checkerboard lattice realization of the model of Xu and Moore for superconducting (p+ip) arrays, and a (3) compass-type two-flavor Hubbard model with both pairing and hopping terms. By the use of our dualities (tantamount to high-dimensional fermionization), we show that all of these systems lie in the three-dimensional Ising universality class. We further discuss how the existence of topological orders and bounds on autocorrelation times can be inferred by the use of symmetries and also propose to engineer quantum simulators via such Majorana wire networks.Item Astrophysical Tests of Lorentz and CPT Violation with Photons(IOP Publishing, 2008) Kostelecký, V.A.; Mewes, M.A general framework for tests of Lorentz invariance with electromagnetic waves is presented, allowing for operators of arbitrary mass dimension. Signatures of Lorentz violations include vacuum birefringence, vacuum dispersion, and anisotropies. Sensitive searches for violations using sources such as active galaxies, gamma-ray bursts, and the cosmic microwave background are discussed. Direction-dependent dispersion constraints are obtained on operators of dimension 6 and 8 using gamma-ray bursts and the blazar Markarian 501. Stringent constraints on operators of dimension 3 are found using 5 year data from the Wilkinson Microwave Anisotropy Probe. No evidence appears for isotropic Lorentz violation, while some support at 1 σ is found for anisotropic violation.Item Atomic supersymmetry and the Stark effect(American Physical Society, 1993) Bluhm, R.; Kostelecký, V.A.A search is conducted for physical quantum-mechanical supersymmetries involving the hydrogen atom. In all coordinate systems admitting a direct separation of the Schrödinger equation, the structure of the separated equations is examined for possible supersymmetric extensions. In addition to the known supersymmetry involving the radial equation for spherical coordinates, we uncover a related supersymmetry involving the radial equation for conical coordinates and a pair of supersymmetries involving parabolic coordinates. The associated spectra and possible physical import of the latter are discussed. They connect certain eigenfunctions of the hydrogen and lithium atoms in the unbroken-symmetry limit. Following the established procedure for the case of spherical coordinates, the breaking of these parabolic supersymmetries is incorporated in a model constructed using notions of quantum-defect theory. The model yields analytical wave functions in parabolic coordinates for the valence electron of alkali-metal atoms, while correctly reproducing the eigenvalue spectra. These ideas are applied to the study of the Stark effect in alkali-metal atoms. Using supersymmetry-based quantum-defect eigenfunctions, we obtain Stark maps for lithium and sodium. The spherical case shows striking agreement with experiment.Item Atomic supersymmetry, Rydberg wave packets, and radial squeezed states(American Physical Society, 1994) Bluhm, R.; Kostelecký, V.A.We study radial wave packets produced by short-pulsed laser fields acting on Rydberg atoms, using analytical tools from supersymmetry-based quantum-defect theory. We begin with a time-dependent perturbative calculation for alkali-metal atoms, incorporating the atomic-excitation process. This provides insight into the general wave-packet behavior and demonstrates agreement with conventional theory. We then obtain an alternative analytical description of a radial wave packet as a member of a particular family of squeezed states, which we call radial squeezed states. By construction, these have close to minimum uncertainty in the radial coordinates during the first pass through the outer apsidal point. The properties of radial squeezed states are investigated, and they are shown to provide a description of certain aspects of Rydberg atoms excited by short-pulsed laser fields. We derive expressions for the time evolution and the autocorrelation of the radial squeezed states, and we study numerically and analytically their behavior in several alkali-metal atoms. Full and fractional revivals are observed. Comparisons show agreement with other theoretical results and with experiment.Item $B$- and $D$-meson decay constants from three-flavor lattice QCD(American Physical Society, 2012) Bazavov, A.; Bernard, C.; Bouchard, C.M.; DeTar, C.; Di Pierro, M.; El-Khadra, A.X.; Evans, R.T.; Freeland, E.D.; Gámiz, E.; Gottlieb, S.; Heller, U.M.; Hetrick, J.E.; Jain, R.; Kronfeld, A.S.; Laiho, J.; Levkova, L.; Mackenzie, P.B.; Neil, E.T.; Oktay, M.B.; Simone, J.N.; Sugar, R.; Toussaint, D.; Van de Water, R.S.We calculate the leptonic decay constants of $B_{(s)}$ and $D_{(s)}$ mesons in lattice QCD using staggered light quarks and Fermilab bottom and charm quarks. We compute the heavy-light-meson correlation functions on the MILC Asqtad-improved staggered gauge configurations, which include the effects of three light dynamical sea quarks. We simulate with several values of the light valence- and sea-quark masses (down to $∼m_{s}$/10) and at three lattice spacings ($\alpha \approx$ 0.15, 0.12, and 0.09 fm) and extrapolate to the physical up and down quark masses and the continuum using expressions derived in heavy-light-meson staggered chiral perturbation theory. We renormalize the heavy-light axial current using a mostly nonperturbative method such that only a small correction to unity must be computed in lattice perturbation theory, and higher-order terms are expected to be small. We use the two finer lattice spacings for our central analysis, and we use the third to help estimate discretization errors. We obtain $f_{B^{+}}$=196.9(9.1) MeV, $f_{B_{s}}$=242.0(10.0) MeV, $f_{D^{+}}$=218.9(11.3) MeV, $f_{D_{s}}$=260.1(10.8) MeV, and the SU(3) flavor-breaking ratios $f_{B_{s}}$/$f_{B}$=1.229(26) and $f_{D_{s}}$/$f_{D}$=1.188(25), where the numbers in parentheses are the total statistical and systematic uncertainties added in quadrature.Item $B_{s} \rightarrow D_{s}/B \rightarrow D$ semileptonic form-factor ratios and their application to $\text{BR}(B_{s}^{0} \rightarrow \mu + \mu-)$(American Physical Society, 2012) Bailey, J.A.; Bazavov, A.; Bernard, C.; Bouchard, C.M.; DeTar, C.; Du, D.; El-Khadra, A.X.; Foley, J.; Freeland, E.D.; Gámiz, E.; Gottlieb, S.; Heller, U.M.; Kim, J.; Kronfeld, A.S.; Laiho, J.; Levkova, L.; Mackenzie, P.B.; Meurice, Y.; Neil, E.; Oktay, M.B.; Qiu, S.-W.; Simone, J.N.; Sugar, R.; Toussaint, D.; Van de Water, R.S.; Zhou, RanWe calculate form-factor ratios between the semileptonic decays $\overline{B}^{0} \rightarrow D^{+}\ell^{-}\overline{\nu}$ and $\overline{B}^{0}_{s} \rightarrow D^{+}_{s}\ell^{-}\overline{\nu}$ with lattice QCD. These ratios are a key theoretical input in a new strategy to determine the fragmentation fractions of neutral $B$ decays, which are needed for measurements of $\text{BR}(B_{s}^{0} \rightarrow \mu + \mu-)$. We use the MILC ensembles of gauge configurations with $2 + 1$ flavors of sea-quarks at two s of approximately 0.12 fm and 0.09 fm. We use the model-independent z parametrization to extrapolate our simulation results at small recoil toward maximum recoil. Our results for the form-factor ratios are $f^{(s)}_{0}(M^{2}_{π})/f^{(d)}_{0}(M^{2}_{K})=1.046(44)_{\text{stat}}(15)_{\text{syst}}$ and $f^{(s)}_{0}(M^{2}_{π})/f^{(d)}_{0}(M^{2}_{\pi})=1.054(47)_{\text{stat}}(17)_{\text{syst}}$. In contrast to a QCD sum-rule calculation, no significant departure from $U$-spin $(d \leftrightarrow s)$ symmetry is observed.Item Background enhancement of $\text{CPT}$ reach at an asymmetric $\phi$ factory(Physics Letters B, 2001) Isgur, Nathan; Kostelecký, V.A.; Szczepaniak, Adam P.Photoproduction of neutral-kaon pairs is studied from the perspective of $\text{CP}$ and $\text{CPT}$ studies. Interference of the $\text{P}$- and $\text{S}$-waves, with the former due to diffractive $\phi$ production and the latter to $f_{0}/a_{0}$ production, is shown to enhance the $\text{CPT}$ reach. Results are presented of Monte Carlo studies based on rates expected in future experiments.Item Being critical of criticality in the brain(Frontiers Media S.A., 2012) Beggs, J.M.; Timme, N.Relatively recent work has reported that networks of neurons can produce avalanches of activity whose sizes follow a power law distribution. This suggests that these networks may be operating near a critical point, poised between a phase where activity rapidly dies out and a phase where activity is amplified over time. The hypothesis that the electrical activity of neural networks in the brain is critical is potentially important, as many simulations suggest that information processing functions would be optimized at the critical point. This hypothesis, however, is still controversial. Here we will explain the concept of criticality and review the substantial objections to the criticality hypothesis raised by skeptics. Points and counter points are presented in dialog form.Item Bipartite Riemann–Finsler geometry and Lorentz violation(Elsevier, 2012) Kostelecký, V.A.; Russell, N.; Tso, R.Bipartite Riemann–Finsler geometries with complementary Finsler structures are constructed. Calculable examples are presented based on a bilinear-form coefficient for explicit Lorentz violation.Item Bound on Lorentz and $CPT$ violating boost effects for the neutron(American Physical Society, 2004) Canè, F.; Bear, D.; Phillips, D.F.; Rosen, M.S.; Smallwood, C.L.; Stoner, R.E.; Walsworth, R.L.; Kostelecký, V.A.A search for an annual variation of a daily sidereal modulation of the frequency difference between colocated $^{129}\text{Xe}$ and $^{3}\text{He}$ Zeeman masers sets a stringent limit on boost-dependent Lorentz and $CPT$ violation involving the neutron, consistent with no effect at the level of 150 nHz. In the framework of the general standard-model extension, the present result provides the first clean test for the fermion sector of the symmetry of spacetime under boost transformations at a level of $10^{−27}$ GeV.Item Bounding $CPT$ violation in the neutral $B$ system(American Physical Society, 1996) Kostelecký, V.A.; Van Kooten, R.The feasibility of placing bounds on $CPT$ violation from experiments with neutral $B$ mesons is examined. We consider situations with uncorrelated mesons and ones with either unboosted or boosted correlated mesons. Analytical expressions valid for small $T$- and $CPT$-violating parameters are presented for time-dependent and time-integrated decay rates, and various relevant asymmetries are derived. We use Monte Carlo simulations to model experimental conditions for a plausible range of $CPT$-violating parameters. The treatment uses realistic data incorporating background effects, resolutions, and acceptances for typical detectors at CERN LEP, CESR, and the future $B$ factories. Presently, there are no bounds on $CPT$ violation in the $B$ system. We demonstrate that limits of order 10% on $CPT$ violation can be obtained from data already extant, and we determine the $CPT$ reach attainable within the next few years.Item Charged-current neutrino interactions in core-collapse supernovae in a virial expansion(American Physical Society, 2012) Horowitz, C.J.; Shen, G.; O'Connor, Evan; Ott, Christian D.Core-collapse supernovae may depend sensitively on charged-current neutrino interactions in warm, low-density, neutron-rich matter. A proton in neutron-rich matter is more tightly bound than is a neutron. This energy shift $\Delta{U}$ increases the electron energy in $\nu_{e}+{n}\rightarrow{p}+{e}$, increasing the available phase space and absorption cross section. Likewise $\Delta{U}$ decreases the positron energy in $\bar\nu_{e}+{n}\rightarrow{p}+{e}^+$, decreasing the phase space and cross section. We have calculated $\Delta{U}$ using a model-independent virial expansion and we find that $\Delta{U}$ is much larger, at low densities, than the predictions of many mean-field models. Therefore $\Delta{U}$ could have a significant impact on charged-current neutrino interactions in supernovae. Preliminary simulations of the accretion phase of core-collapse supernovae find that $\Delta{U}$ increases $\bar\nu_{e}$ energies and decreases the $\nu_{e}$ luminosity.Item Chiral and deconfinement aspects of the QCD transition(American Physical Society, 2012) Bazavov, A.; Bhattacharya, T.; Cheng, M.; DeTar, C.E.; Ding, H.-T.; Gottlieb, S.; Gupta, R.; Hedge, P.; Heller, U.M.; Karsch, F.; Laermann, E.; Levkova, L.; Mukherjee, S.; Petreczky, P.; Schmidt, C.; Soltz, R.A.; Soeldner, W.; Sugar, R.; Toussaint, D.; Unger, W.; Vranas, P.We present results on the chiral and deconfinement properties of the QCD transition at finite temperature. Calculations are performed with 2+1 flavors of quarks using the p4, asqtad, and HISQ/tree actions. Lattices with temporal extent $N_{T}=$6, 8, and 12 are used to understand and control discretization errors and to reliably extrapolate estimates obtained at finite lattice spacings to the continuum limit. The chiral transition temperature is defined in terms of the phase transition in a theory with two massless flavors and analyzed using $O(N)$ scaling fits to the chiral condensate and susceptibility. We find consistent estimates from the HISQ/tree and asqtad actions and our main result is $T_{c}=154 \pm 9 MeV$.Item Classical kinematics for Lorentz violation(Elsevier, 2010) Kostelecký, V.A.; Russell, N.Classical point-particle relativistic lagrangians are constructed that generate the momentum–velocity and dispersion relations for quantum wave packets in Lorentz-violating effective field theory.Item Clock-comparison tests of Lorentz and CPT symmetry in space(American Physical Society, 2002) Bluhm, R.; Kostelecký, V.A.; Lane, C.D.; Russell, N.Clock-comparision experiments on satellite and other spacecarft were used to determine unmeasured coefficients for Lorentz and CPT violation. The presence of Lorentz and CPT violation caused frequency shifts in certain Zeeman hyperfine transitions. A broad range of tests with Planck-scale sensitivity were permitted by the orbital configuration of a satellite platform and the relatively large velocities attainable in a deep-space mission.