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Articles 1 - 27 of 27
Full-Text Articles in Physical Sciences and Mathematics
Symplectically Integrated Symbolic Regression Of Hamiltonian Dynamical Systems, Daniel Dipietro
Symplectically Integrated Symbolic Regression Of Hamiltonian Dynamical Systems, Daniel Dipietro
Computer Science Senior Theses
Here we present Symplectically Integrated Symbolic Regression (SISR), a novel technique for learning physical governing equations from data. SISR employs a deep symbolic regression approach, using a multi-layer LSTMRNN with mutation to probabilistically sample Hamiltonian symbolic expressions. Using symplectic neural networks, we develop a model-agnostic approach for extracting meaningful physical priors from the data that can be imposed on-the-fly into the RNN output, limiting its search space. Hamiltonians generated by the RNN are optimized and assessed using a fourth-order symplectic integration scheme; prediction performance is used to train the LSTM-RNN to generate increasingly better functions via a risk-seeking policy gradients …
Long-Range Interactions Of Hydrogen Atoms In Excited States. Ii. Hyperfine-Resolved 2s-2s Systems, Ulrich D. Jentschura, Vincent Debierre, Chandra Mani Adhikari, Arthur N. Matveev, Nikolai N. Kolachevsky
Long-Range Interactions Of Hydrogen Atoms In Excited States. Ii. Hyperfine-Resolved 2s-2s Systems, Ulrich D. Jentschura, Vincent Debierre, Chandra Mani Adhikari, Arthur N. Matveev, Nikolai N. Kolachevsky
Physics Faculty Research & Creative Works
The interaction of two excited hydrogen atoms in metastable states constitutes a theoretically interesting problem because of the quasidegenerate 2P1/2 levels that are removed from the 2S states only by the Lamb shift. The total Hamiltonian of the system is composed of the van der Waals Hamiltonian, the Lamb shift, and the hyperfine effects. The van der Waals shift becomes commensurate with the 2S-2P3/2 fine-structure splitting only for close approach (R < 100a0, where a0 is the Bohr radius) and one may thus restrict the discussion to the levels with n = 2 and J = 1/2 …
Nonresonant Two-Photon Transitions In Length And Velocity Gauges, Ulrich D. Jentschura
Nonresonant Two-Photon Transitions In Length And Velocity Gauges, Ulrich D. Jentschura
Physics Faculty Research & Creative Works
We reexamine the invariance of two-photon transition matrix elements and corresponding two-photon Rabi frequencies under the "gauge" transformation from the length to the velocity gauge. It is shown that gauge invariance, in the most general sense, only holds at exact resonance, for both one-color as well as two-color absorption. The arguments leading to this conclusion are supported by analytic calculations which express the matrix elements in terms of hypergeometric functions, and ramified by a "master identity" which is fulfilled by off-diagonal matrix elements of the Schrödinger propagator under the transformation from the velocity to the length gauge. The study of …
Dirac Hamiltonian And Reissner-Nordström Metric: Coulomb Interaction In Curved Space-Time, J. H. Noble, Ulrich D. Jentschura
Dirac Hamiltonian And Reissner-Nordström Metric: Coulomb Interaction In Curved Space-Time, J. H. Noble, Ulrich D. Jentschura
Physics Faculty Research & Creative Works
We investigate the spin-1/2 relativistic quantum dynamics in the curved space-time generated by a central massive charged object (black hole). This necessitates a study of the coupling of a Dirac particle to the Reissner-Nordström space-time geometry and the simultaneous covariant coupling to the central electrostatic field. The relativistic Dirac Hamiltonian for the Reissner-Nordström geometry is derived. A Foldy-Wouthuysen transformation reveals the presence of gravitational and electrogravitational spin-orbit coupling terms which generalize the Fokker precession terms found for the Dirac-Schwarzschild Hamiltonian, and other electrogravitational correction terms to the potential proportional to αnG, where α is the fine-structure constant and …
Vibrational Energy Levels Of The Simplest Criegee Intermediate (Ch₂Oo) From Full-Dimensional Lanczos, Mctdh, And Multimode Calculations, Hua-Gen Yu, Steve Alexandre Ndengué, Jun Li, Richard Dawes, Hua Guo
Vibrational Energy Levels Of The Simplest Criegee Intermediate (Ch₂Oo) From Full-Dimensional Lanczos, Mctdh, And Multimode Calculations, Hua-Gen Yu, Steve Alexandre Ndengué, Jun Li, Richard Dawes, Hua Guo
Chemistry Faculty Research & Creative Works
Accurate vibrational energy levels of the simplest Criegee intermediate (CH2OO) were determined on a recently developed ab initio based nine-dimensional potential energy surface using three quantum mechanical methods. the first is the iterative Lanczos method using a conventional basis expansion with an exact Hamiltonian. the second and more efficient method is the multi-configurational time-dependent Hartree (MCTDH) method in which the potential energy surface is refit to conform to the sums-of-products requirement of MCTDH. Finally, the energy levels were computed with a vibrational self-consistent field/virtual configuration interaction method in MULTIMODE. the low-lying levels obtained from the three methods are …
A Short Introduction To Numerical Linked-Cluster Expansions, Baoming Tang, Ehsan Khatami, Marcos Rigol
A Short Introduction To Numerical Linked-Cluster Expansions, Baoming Tang, Ehsan Khatami, Marcos Rigol
Faculty Publications
We provide a pedagogical introduction to numerical linked-cluster expansions (NLCEs). We sketch the algorithm for generic Hamiltonians that only connect nearest-neighbor sites in a finite cluster with open boundary conditions. We then compare results for a specific model, the Heisenberg model, in each order of the NLCE with the ones for the finite cluster calculated directly by means of full exact diagonalization. We discuss how to reduce the computational cost of the NLCE calculations by taking into account symmetries and topologies of the linked clusters. Finally, we generalize the algorithm to the thermodynamic limit, and discuss several numerical resummation techniques …
Poincare Recurrence And Spectral Cascades In Three-Dimensional Quantum Turbulence, George Vahala, Jeffrey Yepez, Linda L. Vahala, Min Soe, Bo Zhang, Sean Ziegeler
Poincare Recurrence And Spectral Cascades In Three-Dimensional Quantum Turbulence, George Vahala, Jeffrey Yepez, Linda L. Vahala, Min Soe, Bo Zhang, Sean Ziegeler
Electrical & Computer Engineering Faculty Publications
The time evolution of the ground state wave function of a zero-temperature Bose-Einstein condensate (BEC) gas is well described by the Hamiltonian Gross-Pitaevskii (GP) equation. Using a set of appropriately interleaved unitary collision-stream operators, a qubit lattice gas algorithm is devised, which on taking moments, recovers the Gross-Pitaevskii (GP) equation under diffusion ordering (time scales as length2). Unexpectedly, there is a class of initial states whose Poincaré recurrence time is extremely short and which, as the grid resolution is increased, scales with diffusion ordering (and not as length3). The spectral results of J. Yepez et al. …
Cluster Solver For Dynamical Mean-Field Theory With Linear Scaling In Inverse Temperature, Ehsan Khatami, C. Lee, Z. Bai, R. Scalettar, M. Jarrell
Cluster Solver For Dynamical Mean-Field Theory With Linear Scaling In Inverse Temperature, Ehsan Khatami, C. Lee, Z. Bai, R. Scalettar, M. Jarrell
Faculty Publications
Dynamical mean-field theory and its cluster extensions provide a very useful approach for examining phase transitions in model Hamiltonians and, in combination with electronic structure theory, constitute powerful methods to treat strongly correlated materials. The key advantage to the technique is that, unlike competing real-space methods, the sign problem is well controlled in the Hirsch-Fye (HF) quantum Monte Carlo used as an exact cluster solver. However, an important computational bottleneck remains; the HF method scales as the cube of the inverse temperature, β. This often makes simulations at low temperatures extremely challenging. We present here a method based on determinant …
Long-Time Electron Spin Storage Via Dynamical Suppression Of Hyperfine-Induced Decoherence In A Quantum Dot, Wenxian Zhang, N. P. Konstantinidis, V. V. Dobrovitski, B. N. Harmon, Lea F. Santos, Lorenza Viola
Long-Time Electron Spin Storage Via Dynamical Suppression Of Hyperfine-Induced Decoherence In A Quantum Dot, Wenxian Zhang, N. P. Konstantinidis, V. V. Dobrovitski, B. N. Harmon, Lea F. Santos, Lorenza Viola
Dartmouth Scholarship
The coherence time of an electron spin decohered by the nuclear spin environment in a quantum dot can be substantially increased by subjecting the electron to suitable dynamical decoupling sequences. We analyze the performance of high-level decoupling protocols by using a combination of analytical and exact numerical methods, and by paying special attention to the regimes of large interpulse delays and long-time dynamics, which are outside the reach of standard average Hamiltonian theory descriptions. We demonstrate that dynamical decoupling can remain efficient far beyond its formal domain of applicability, and find that a protocol exploiting concatenated design provides best performance …
A Mössbauer Spectral Study Of The Gdco₄₋ₓfeₓb Compounds, Fernande Grandjean, Raphäel P. Hermann, Eustachy S. Popiel, Gary J. Long
A Mössbauer Spectral Study Of The Gdco₄₋ₓfeₓb Compounds, Fernande Grandjean, Raphäel P. Hermann, Eustachy S. Popiel, Gary J. Long
Chemistry Faculty Research & Creative Works
The iron-57 Mössbauer spectra of the GdCo4-xFexB compounds, where x is 0.10, 0.15, 0.20, 0.25, 1, 2, 2.5, and 2.6, have been measured at room temperature and reveal relatively small iron hyperfine fields of approximately 12-18 T, relatively large quadrupole interactions of approximately +0.9 and -1 mm/s, and three very different types of spectra for x=0.10 and 0.15, x=0.25, 1, and 2, and x=2.5 and 2.6. The differences result from both the different easy magnetization directions in these compounds and the different cobalt and/or iron occupancies of the crystallographic 2c and 6i sites. The spectra have …
Using Genetic Algorithms To Map First-Principles Results To Model Hamiltonians: Application To The Generalized Ising Model For Alloys, Gus L. W. Hart, Volker Blum, Michael J. Walorski, Alex Zunger
Using Genetic Algorithms To Map First-Principles Results To Model Hamiltonians: Application To The Generalized Ising Model For Alloys, Gus L. W. Hart, Volker Blum, Michael J. Walorski, Alex Zunger
Faculty Publications
The cluster expansion method provides a standard framework to map first-principles generated energies for a few selected configurations of a binary alloy onto a finite set of pair and many-body interactions between the alloyed elements. These interactions describe the energetics of all possible configurations of the same alloy, which can hence be readily used to identify ground state structures and, through statistical mechanics solutions, find finite-temperature properties. In practice, the biggest challenge is to identify the types of interactions which are most important for a given alloy out of the many possibilities. We describe a genetic algorithm which automates this …
How To Choose One-Dimensional Basis Functions So That A Very Efficient Multidimensional Basis May Be Extracted From A Direct Product Of The One-Dimensional Functions: Energy Levels Of Coupled Systems With As Many As 16 Coordinates, Richard Dawes, Tucker Carrington Jr.
How To Choose One-Dimensional Basis Functions So That A Very Efficient Multidimensional Basis May Be Extracted From A Direct Product Of The One-Dimensional Functions: Energy Levels Of Coupled Systems With As Many As 16 Coordinates, Richard Dawes, Tucker Carrington Jr.
Chemistry Faculty Research & Creative Works
In this paper we propose a scheme for choosing basis functions for quantum dynamics calculations. Direct product bases are frequently used. The number of direct product functions required to converge a spectrum, compute a rate constant, etc., is so large that direct product calculations are impossible for molecules or reacting systems with more than four atoms. It is common to extract a smaller working basis from a huge direct product basis by removing some of the product functions. We advocate a build and prune strategy of this type. the one-dimensional (1D) functions from which we build the direct product basis …
Nonrelativistic Qed Approach To The Bound-Electron G Factor, Krzysztof Pachucki, Ulrich D. Jentschura, Vladimir A. Yerokhin
Nonrelativistic Qed Approach To The Bound-Electron G Factor, Krzysztof Pachucki, Ulrich D. Jentschura, Vladimir A. Yerokhin
Physics Faculty Research & Creative Works
Within a systematic approach based on nonrelativistic quantum electrodynamics, we derive the one-loop self-energy correction of order α ( Z α )4 to the bound-electron g factor. In combination with numerical data, this analytic result improves theoretical predictions for the self-energy correction for carbon and oxygen by an order of magnitude. Basing on one-loop calculations, we obtain the logarithmic two-loop contribution of order α2 ( Z α )4 ln [ ( Z α )- 2 ] and the dominant part of the corresponding constant term. The results obtained improve the accuracy of the theoretical predictions for …
Exotic Versus Conventional Scaling And Universality In A Disordered Bilayer Quantum Heisenberg Antiferromagnet, Rastko Sknepnek, Thomas Vojta, Matthias Vojta
Exotic Versus Conventional Scaling And Universality In A Disordered Bilayer Quantum Heisenberg Antiferromagnet, Rastko Sknepnek, Thomas Vojta, Matthias Vojta
Physics Faculty Research & Creative Works
We present Monte Carlo simulations of a two-dimensional bilayer quantum Heisenberg antiferromagnet with random dimer dilution. In contrast with exotic scaling scenarios found in other random quantum systems, the quantum phase transition in this system is characterized by a finite-disorder fixed point with power-law scaling. After accounting for corrections to scaling, with a leading irrelevant exponent of ω ≈ 0.48, we find universal critical exponents z = 1.310(6) and ν = 1.16(3). We discuss the consequences of these findings and suggest new experiments.
Broadening Of A Nonequilibrium Phase Transition By Extended Structural Defects, Thomas Vojta
Broadening Of A Nonequilibrium Phase Transition By Extended Structural Defects, Thomas Vojta
Physics Faculty Research & Creative Works
We study the effects of quenched extended impurities on nonequilibrium phase transitions in the directed percolation universality class. We show that these impurities have a dramatic effect: they completely destroy the sharp phase transition by smearing. This is caused by rare strongly coupled spatial regions which can undergo the phase transition independently from the bulk system. We use extremal statistics to determine the stationary state as well as the dynamics in the tail of the smeared transition, and we illustrate the results by computer simulations.
Protonium Formation In The P̅-H Collision At Low Energies By A Diabatic Approach, M. Hesse, Anh-Thu Le, C. D. Lin
Protonium Formation In The P̅-H Collision At Low Energies By A Diabatic Approach, M. Hesse, Anh-Thu Le, C. D. Lin
Physics Faculty Research & Creative Works
We present a diabatization technique in combination with the recently developed hyperspherical close coupling (HSCC) method. In contrast to the strict diabatization, our simple diabatization procedure transforms only sharp avoided crossings in the adiabatic hyperspherical potential curves into real crossings. With this approach, the weak collision channels can be removed from the close-coupling calculations. This method is used to study the antiproton-hydrogen collision at low energies. In the case of a scaled down (anti)proton mass, we show that a 10-channel calculation is enough to obtain converged cross sections at low energies. The results also indicate that protonium formation occurs mostly …
Self-Energy Correction To The Two-Photon Decay Width In Hydrogenlike Atoms, Ulrich D. Jentschura
Self-Energy Correction To The Two-Photon Decay Width In Hydrogenlike Atoms, Ulrich D. Jentschura
Physics Faculty Research & Creative Works
We investigate the guage invariance of the leading logarithmic radiative correction to the two-photon decay width in hydrogenlike atoms, was investigated. The effective treatment of the correction using a Lamb-shift led to the equivalent results in both the length and velocity gages. The relevant radiative corrections were found to be related to the energies that entered into the propagator denominators, to the Hamiltonian, to the wave functions, and to the energy conservation condition, that holds between two photons. The results show that the dominant radiative correction to the 2S two-photon decay width is about -2.020 536(α/π)(Zα)2 1n[(Zα)-2] …
Lamb Shift Of Laser-Dressed Atomic States, Ulrich D. Jentschura, Jorg Evers, Martin K. Haas, Christoph H. Keitel
Lamb Shift Of Laser-Dressed Atomic States, Ulrich D. Jentschura, Jorg Evers, Martin K. Haas, Christoph H. Keitel
Physics Faculty Research & Creative Works
We discuss radiative corrections to an atomic two-level system subject to an intense driving laser field. It is shown that the Lamb shift of the laser-dressed states, which are the natural state basis of the combined atom-laser system, cannot be explained in terms of the Lamb shift received by the atomic bare states which is usually observed in spectroscopic experiments. In the final part, we propose an experimental scheme to measure these corrections based on the incoherent resonance fluorescence spectrum of the driven atom.
Two-Loop Bethe-Logarithm Correction In Hydrogenlike Atoms, Krzysztof Pachucki, Ulrich D. Jentschura
Two-Loop Bethe-Logarithm Correction In Hydrogenlike Atoms, Krzysztof Pachucki, Ulrich D. Jentschura
Physics Faculty Research & Creative Works
We calculate the two-loop Bethe logarithm correction to atomic energy levels in hydrogenlike systems. The two-loop Bethe logarithm is a low-energy quantum electrodynamic (QED) effect involving multiple summations over virtual excited atomic states. Although much smaller in absolute magnitude than the well-known one-loop Bethe logarithm, the two-loop analog is quite significant when compared to the current experimental accuracy of the 1 S – 2 S transition: It contributes - 8.19 and - 0.84 k H z for the 1 S and the 2 S state, respectively. The two-loop Bethe logarithm has been the largest unknown correction to the hydrogen Lamb …
Role Of The Ground State In Electron-Atom Double Ionization, Stephenie J. Jones, Don H. Madison
Role Of The Ground State In Electron-Atom Double Ionization, Stephenie J. Jones, Don H. Madison
Physics Faculty Research & Creative Works
Recently, absolute measurements have been reported for double ionization of helium by 5.6 keV electron-impact. At this high energy, one would think that the first Born approximation for the interaction of the projectile with the atom would be valid. However, on the basis of a lowest-order implementation of a Faddeev-type approach, Berakdar concluded that the approximation was not valid. Here we argue that (i) it is valid at this energy and (ii) the previous discrepancy between calculations in the first Born approximation and the overall magnitude of the measurements was due to a poor description of the ground state.
Disorder-Induced Rounding Of Certain Quantum Phase Transitions, Thomas Vojta
Disorder-Induced Rounding Of Certain Quantum Phase Transitions, Thomas Vojta
Physics Faculty Research & Creative Works
We study the influence of quenched disorder on quantum phase transitions in systems with overdamped dynamics. For Ising order-parameter symmetry disorder destroys the sharp phase transition by rounding because a static order parameter can develop on rare spatial regions. This leads to an exponential dependence of the order parameter on the coupling constant. At finite temperatures the static order on the rare regions is destroyed. This restores the phase transition and leads to a double exponential relation between critical temperature and coupling strength. We discuss the behavior based on Lifshitz-tail arguments and illustrate the results by simulations of a model …
Doubly Differential Electron-Emission Spectra In Single And Multiple Ionization Of Noble-Gas Atoms By Fast Highly-Charged-Ion Impact, Tom Kirchner, Laszlo Gulyas, Robert Moshammer, Michael Schulz, Joachim Hermann Ullrich
Doubly Differential Electron-Emission Spectra In Single And Multiple Ionization Of Noble-Gas Atoms By Fast Highly-Charged-Ion Impact, Tom Kirchner, Laszlo Gulyas, Robert Moshammer, Michael Schulz, Joachim Hermann Ullrich
Physics Faculty Research & Creative Works
Low-energy electron emission spectra are studied in collisions of 3.6 MeV/amu Au53+ ions with neon and argon atoms for well-defined degrees of target ionization. We calculate doubly differential cross sections as functions of the recoil-ion charge state in the continuum-distorted-wave with eikonal initial-state approximation using a binomial analysis of the total and differential ionization probabilities, and compare them with the present and with previously published experimental data. Very good agreement is found for the single-ionization spectra and for double ionization of neon, while some discrepancies are observed in the spectra for double and triple ionization of argon.
Electron-Impact Excitation From The (4p⁵5s) Metastable States Of Krypton, Arati K. Dasgupta, Klaus Bartschat, D. Vaid, Alexei N. Grum-Grzhimailo, Don H. Madison, Milan Blaha, John L. Giuliani
Electron-Impact Excitation From The (4p⁵5s) Metastable States Of Krypton, Arati K. Dasgupta, Klaus Bartschat, D. Vaid, Alexei N. Grum-Grzhimailo, Don H. Madison, Milan Blaha, John L. Giuliani
Physics Faculty Research & Creative Works
Theoretical results from multistate semirelativistic Breit-Pauli R-matrix calculations and two first-order distorted-wave calculations are presented for electron-impact excitation of krypton from the (4p55s) J = 0,2 metastable states to the (4p55s) and (4p55p) manifolds. Except for a few cases, in which the method to account for relativistic effects becomes surprisingly critical, fair overall agreement between the predictions from the various theoretical models is achieved for intermediate and high energies. However, significant discrepancies remain with the few available experimental data.
Electron-Impact Excitation To The 4p⁵5s And 4p⁵5p Levels Of Kr | Using Different Distorted-Wave And Close-Coupling Methods, Arati K. Dasgupta, Klaus Bartschat, D. Vaid, Alexei N. Grum-Grzhimailo, Don H. Madison, Milan Blaha, John L. Giuliani
Electron-Impact Excitation To The 4p⁵5s And 4p⁵5p Levels Of Kr | Using Different Distorted-Wave And Close-Coupling Methods, Arati K. Dasgupta, Klaus Bartschat, D. Vaid, Alexei N. Grum-Grzhimailo, Don H. Madison, Milan Blaha, John L. Giuliani
Physics Faculty Research & Creative Works
Electron-impact excitation of the 4p55s and 4p55p levels of Kr I has been investigated in detail by calculating cross sections using distorted-wave and close-coupling approaches. The results are presented from the excitation thresholds up to 50 eV incident energy. They are contrasted among the different calculations and compared with other theoretical predictions and experimental data. Significant disagreement is found with many of the recent experimental data of Chilton et al. [Phys. Rev. A 62, 032714 (2000)].
Exact Solutions Of The Schroedinger Equation: Connection Between Supersymmetric Quantum Mechanics And Spectrum Generating Algebras, Asim Gangopadhyaya, Jeffrey Mallow, C. Rasinariu, Uday P. Sukhatne
Exact Solutions Of The Schroedinger Equation: Connection Between Supersymmetric Quantum Mechanics And Spectrum Generating Algebras, Asim Gangopadhyaya, Jeffrey Mallow, C. Rasinariu, Uday P. Sukhatne
Physics: Faculty Publications and Other Works
Using supersymmetric quantum mechanics, one can obtain analytic expressions for the eigenvalues and eigenfunctions for all nonrelativistic shape invariant Hamiltonians. These Hamiltonians also possess spectrum generating algebras and are hence solvable by an independent, group theoretical method. In this paper, we demonstrate the equivalence of the two methods of solution, and review related progress in this field.
Algebraic Shape Invariant Models, S Chaturvedi, Ranabir Dutt, Asim Gangopadhyaya, Prasanta K. Panigrahi, C. Rasinariu, Uday P. Sukhatme
Algebraic Shape Invariant Models, S Chaturvedi, Ranabir Dutt, Asim Gangopadhyaya, Prasanta K. Panigrahi, C. Rasinariu, Uday P. Sukhatme
Physics: Faculty Publications and Other Works
Motivated by the shape invariance condition in supersymmetric quantum mechanics, we develop an algebraic framework for shape invariant Hamiltonians with a general change of parameters. This approach involves nonlinear generalizations of Lie algebras. Our work extends previous results showing the equivalence of shape invariant potentials involving translational change of parameters with standard SO (2,1) potential algebra for Natanzon type potentials.
The Vacuum In Light Cone Field Theory, David G. Robertson
The Vacuum In Light Cone Field Theory, David G. Robertson
Physics Faculty Scholarship
This is an overview of the problem of the vacuum in light-cone field theory, stressing its close connection to other puzzles regarding light-cone quantization. I explain the sense in which the light-cone vacuum is ``trivial,'' and describe a way of setting up a quantum field theory on null planes so that it is equivalent to the usual equal-time formulation. This construction is quite helpful in resolving the puzzling aspects of the light-cone formalism. It furthermore allows the extraction of effective Hamiltonians that incorporate vacuum physics, but that act in a Hilbert space in which the vacuum state is simple. The …