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DOE OSTI2015

Emergent geometry experienced by fermions in graphene in the presence of dislocations

In graphene in the presence of strain the elasticity theory metric naturally appears. However, this is not the one experienced by fermionic quasiparticles. Fermions propagate in curved space, whose metric is defined by expansion of the effective Hamiltonian near the topologically protected Fermi point. We discuss relation between both types of metric for different parametrizations of graphene surface. Next, we extend our consideration to the case, when the dislocations are present. We consider the situation, when the deformation is described by elasticity theory and calculate both torsion and emergent magnetic field carried by the dislocation. The dislocation carries singular torsion in addition to the quantized flux of emergent magnetic field. Both may be observed in the scattering of quasiparticles on the dislocation. Emergent magnetic field flux manifests itself in the Aharonov–Bohm effect while the torsion singularity results in Stodolsky effect.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

The current density in quantum electrodynamics in external potentials

We review different definitions of the current density for quantized fermions in the presence of an external electromagnetic field. Several deficiencies in the popular prescription due to Schwinger and the mode sum formula for static external potentials are pointed out. We argue that Dirac’s method, which is the analog of the Hadamard point-splitting employed in quantum field theory in curved space–times, is conceptually the most satisfactory. As a concrete example, we discuss vacuum polarization and the stress–energy tensor for massless fermions in 1+1 dimension. Also a general formula for the vacuum polarization in static external potentials in 3+1 dimensions is derived.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Quantum dissipative Higgs model

By using a continuum of oscillators as a reservoir, we present a classical and a quantum-mechanical treatment for the Higgs model in the presence of dissipation. In this base, a fully canonical approach is used to quantize the damped particle on a spherical surface under the action of a conservative central force, the conjugate momentum is defined and the Hamiltonian is derived. The equations of motion for the canonical variables and in turn the Langevin equation are obtained. It is shown that the dynamics of the dissipative Higgs model is not only determined by a projected susceptibility tensor that obeys the Kramers–Kronig relations and a noise operator but also the curvature of the spherical space. Due to the gnomonic projection from the spherical space to the tangent plane, the projected susceptibility displays anisotropic character in the tangent plane. To illuminate the effect of dissipation on the Higgs model, the transition rate between energy levels of the particle on the sphere is calculated. It is seen that appreciable probabilities for transition are possible only if the transition and reservoir’s oscillators frequencies to be nearly on resonance.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Efficient quantum circuits for Szegedy quantum walks

A major advantage in using Szegedy’s formalism over discrete-time and continuous-time quantum walks lies in its ability to define a unitary quantum walk by quantizing a Markov chain on a directed or weighted graph. In this paper, we present a general scheme to construct efficient quantum circuits for Szegedy quantum walks that correspond to classical Markov chains possessing transformational symmetry in the columns of the transition matrix. In particular, the transformational symmetry criteria do not necessarily depend on the sparsity of the transition matrix, so this scheme can be applied to non-sparse Markov chains. Two classes of Markov chains that are amenable to this construction are cyclic permutations and complete bipartite graphs, for which we provide explicit efficient quantum circuit implementations. We also prove that our scheme can be applied to Markov chains formed by a tensor product. We also briefly discuss the implementation of Markov chains based on weighted interdependent networks. In addition, we apply this scheme to construct efficient quantum circuits simulating the Szegedy walks used in the quantum Pagerank algorithm for some classes of non-trivial graphs, providing a necessary tool for experimental demonstration of the quantum Pagerank algorithm. - Highlights: • A general theoretical framework for implementing Szegedy walks using quantum circuits. • Explicit efficient quantum circuit implementation of the Szegedy walk for several classes of graphs. • Efficient implementation of Szegedy walks for quantum page-ranking of a certain class of graphs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Quantum eye: Lattice plasmon effect on quantum fluctuations and photon detection

In this work, arrays of plasmonic nanoparticles coupled to a detector are designed and considered as a quantum eye. In the designed system, the plasmonic nanoparticles have a role like an ommatidium in the artificial compound eye; however, the quantum eye ommatidium acts with different functionality. To better understand this system, we analyze it with the full quantum theory, quantize lattice plasmon generated by the array of plasmonic nanoparticles, and finally derive bosonic operators using Heisenberg–Langevin equations. Moreover, we theoretically derive the radiative and non-radiative losses introduced by this system and examine lattice plasmon effect on spontaneous emission of the quantum dot (Purcell factor). The main goal of this article is to investigate the quantum eye’s quantum properties such as quantum fluctuations, which is modeled and analyzed by studying the second-order correlation function. This function exhibits a significant bunching as a function of lattice plasmon optical properties. We can easily manipulate and improve the lattice plasmon optical properties, which dramatically depend on the array geometry. Finally, we study the quantum eye photon detection by a quantum measuring approach and show that the lattice plasmon has a strong effect on quantum properties after the one-count process.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Analogue stochastic gravity in strongly-interacting Bose–Einstein condensates

Collective modes propagating in a moving superfluid are known to satisfy wave equations in a curved space–time, with a metric determined by the underlying superflow. We use the Keldysh technique in a curved space–time to develop a quantum geometric theory of fluctuations in superfluid hydrodynamics. This theory relies on a “quantized” generalization of the two-fluid description of Landau and Khalatnikov, where the superfluid component is viewed as a quasi-classical field coupled to a normal component — the collective modes/phonons representing a quantum bath. This relates the problem in the hydrodynamic limit to the “quantum friction” problem of Caldeira–Leggett type. By integrating out the phonons, we derive stochastic Langevin equations describing a coupling between the superfluid component and phonons. These equations have the form of Euler equations with additional source terms expressed through a fluctuating stress–energy tensor of phonons. Conceptually, this result is similar to stochastic Einstein equations that arise in the theory of stochastic gravity. We formulate the fluctuation–dissipation theorem in this geometric language and discuss possible physical consequences of this theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Magnonic Floquet Hofstadter butterfly

We introduce the magnonic Floquet Hofstadter butterfly in the two-dimensional (2D) insulating honeycomb ferromagnet using a combination of spin wave theory and quantum field theory. We show that hopping magnetic dipole moment (i.e. magnon quasiparticles) in the 2D insulating honeycomb ferromagnet accumulates the Aharonov–Casher phase when irradiated by an oscillating space- and time-dependent electric field. We study two different cases. In the first case, we consider the effects of only space-dependent electric field. In this case, we realize the magnonic Hofstadter spectrum with similar fractal structure as graphene subject to a perpendicular magnetic field, but with no spin degeneracy due to broken time-reversal symmetry by the ferromagnetic order. In addition, the magnonic Dirac points and Landau levels occur at finite energy as expected in a bosonic system. Remarkably, this discrepancy does not affect the topological invariant of the system. Consequently, the magnonic Chern number assumes odd values and the magnon Hall conductance gets quantized by odd integers. In the second case, we study the effects of both space- and time-dependent electric field. In this case, the theoretical framework is studied by the Floquet formalism. We show that the magnonic Floquet Hofstadter spectrum emerges entirely from the oscillating space- and time-dependent electric field, which is in stark contrast to electronic Floquet Hofstadter spectrum, where irradiation by circularly polarized light and a perpendicular magnetic field are applied independently. We study the deformation of the fractal structure at different laser frequencies and amplitudes, and analyze the topological phase transitions associated with gap openings in the magnonic Floquet Hofstadter butterfly.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Spontaneous mass generation due to phonons in a two-dimensional Dirac fermion system

Fermions with one and two Dirac nodes are coupled to in-plane phonons to study a spontaneous transition into the Hall insulating phase. At sufficiently strong electron–phonon interaction a gap appears in the spectrum of fermions, signaling a transition into a phase with spontaneously broken parity and time-reversal symmetry. The structure of elementary excitations above the gap in the corresponding phase reveals the presence of scale invariant parity breaking terms which resemble Chern–Simons excitations. Evaluating the Kubo formula for both models we find quantized Hall plateaux in each case, with conductance of binodal model exactly twice as large as of the mononodal model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2019

Two body relativistic wave equations

The relativistic quantum mechanics of two interacting particles is considered. We first present a covariant formulation of kinematics and of reduced phase space, giving a short outline of the classical results. We then quantize the systems for the scalar–scalar, fermion–scalar and fermion–fermion cases. We study the spectrum and the spherical waves solutions of the free case. The interaction with central scalar and vector potentials is introduced and the explicit equations are deduced. The one particle and the non relativistic limits are recovered and the general lines for the solution of the boundary value problems are given. We make a numerical analysis of the first two cases with Coulomb interaction. For the two fermions we largely revisit the model we had previously derived in order to uniformize the description for all the three cases. In order to give a complete review we report in the Appendix some of the most interesting results obtained for atomic and mesonic systems with Coulomb and Cornell potential interactions respectively.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Gauge-potential-induced vortices in spin-1 Bose–Einstein condensates with spin–orbit coupling

Highlights: •Effectively rotate the so-coupled condensate by an external magnetic field. •New effects of the Aharonov–Bohm geometric phase in ultracold atomic gases. •Many novel vortex structures have been studied. •A new stabilization mechanism for multiquantum vortices in spinor BECs. -- Abstract: We investigate the vortex states generated by the gauge-potential-induced rotation in spin-1 Bose–Einstein condensates with spin–orbit coupling. An external magnetic field coupling with spin equivalently imprints a non-zero gauge angular momentum, which induces an equivalent canonical angular momentum in the opposite direction, accompanied by the generation of quantized vortices. The competition between interatomic interactions, spin–orbit coupling and magnetic field leads to a variety of vortex structures. In the weakly interatomic interacting regime, as the increase of SO coupling strength, the condensate with a weak magnetic field gradient experiences the transition from polar-core vortex to Mermin–Ho vortex then to vortex cluster , and the three-vortex structures are found in the vortex cluster. As the SO coupling increases further, the condensate presents symmetrical density domains separated by radial vortex arrays. With the increase of magnetic field gradient, the number of density domains increases, and the condensate eventually turns into a giant vortex. In the relatively strong interatomic interacting regime, vortex sheets are formed when the magnetic field gradient is weak, and the increasing of magnetic field gradient makes the vortex arrangement orderly. Compared with the cases of weak interatomic interacting regime, density domain structures are broken because of the strong interatomic interactions, and the vortices are arranged in coaxial annular arrays.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Physics of the Inverted Harmonic Oscillator: From the lowest Landau level to event horizons

In this work, we present the inverted harmonic oscillator (IHO) Hamiltonian as a paradigm to understand the quantum mechanics of scattering and time-decay in a diverse set of physical systems. As one of the generators of area preserving transformations, the IHO Hamiltonian can be studied as a dilatation generator, squeeze generator, a Lorentz boost generator, or a scattering potential. In establishing these different forms, we demonstrate the physics of the IHO that underlies phenomena as disparate as the Hawking–Unruh effect and scattering in the lowest Landau level (LLL) in quantum Hall systems. We derive the emergence of the IHO Hamiltonian in the LLL in a gauge invariant way and show its exact parallels with the Rindler Hamiltonian that describes quantum mechanics near event horizons. This approach of studying distinct physical systems with symmetries described by isomorphic Lie algebras through the emergent IHO Hamiltonian enables us to reinterpret geometric response in the lowest Landau level in terms of relativistic effects such as Wigner rotation. Further, the analytic scattering matrix of the IHO points to the existence of quasinormal modes (QNMs) in the spectrum, which have quantized time-decay rates. We present a way to access these QNMs through wave packet scattering, thus proposing a novel effect in quantum Hall point contact geometries that parallels those found in black holes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Topological approach to electron correlations at fractional quantum Hall effect

Highlights: • Braids in 2D electron systems in magnetic field acquire a cyclotron metrics. • Commensurability of 2D braids with Wigner crystal of electrons leads to FQHE. • Homotopy invariants define the hierarchy of FQHE universal in all 2D Hall systems. • Composite fermions illustrate multiloop braids in the simplest homotopy case. • Correlations in FQHE reveal long-range quantum entanglement of all electrons. The classification of homotopy invariants in interacting multi-electron 2D systems at quantizing magnetic fields is presented, explaining the topologically protected correlations occurring at integer and fractional quantum Hall effects. The long-range quantum entanglement is essential for homotopy correlated phases in contrast to the binary entanglement for conventional phases with local order parameters. The classification of homotopy long-range correlated phases induced by the Coulomb interaction of electrons has been derived in terms of homotopy invariants, which are universal and robust against local disorder and single-particle crystal field, as illustrated by experimental observations in various materials with different microscopic structure, like GaAs 2DES, graphene monolayer and bilayer and in Chern topological insulators. The homotopy phases are demonstrated to be topologically protected and immune to single-particle perturbations, temperature chaos and variation of the electron interaction strength. The nonzero repulsive interaction between electrons is shown, however, to be essential for the definition of the homotopy invariants, which disappear in gaseous systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Restricting loop expansions in gauge theories coupled to matter

Highlights: • Lagrange multiplier fields are used to restrict radiative effects to one-loop order. • This approach is exemplified in the Yang-Mills theory coupled to a scalar matter field. • We showed that it can be used with the Einstein–Hilbert action coupled to matter. • The resulting quantum gravity theory is both renormalizable and unitary. Quantizing any model in which a Lagrange multiplier (LM) field is used to restrict field configurations to those that satisfy the classical equations of motion, leads to at most one-loop radiative corrections. This approach can be used with both the Yang–Mills (YM) and Einstein–Hilbert (EH) action; the resulting theory is both renormalizable and unitary, has a positive energy spectrum and has no negative norm states contributing to physical processes. Although this approach cannot be consistently used with scalar fields alone, scalar fields can be coupled to gauge fields so that loop effects in the gauge sector are restricted to one-loop order in a way that satisfies the usual criterion for a consistent quantum field theory. The tree-level diagrams are those of the classical theory in which the metric couples to the energy–momentum tensor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Entanglement between valence and sea quarks in hadrons of 1+1 dimensional QCD

The conceptual interpretation of valence- and sea-quark separation, which is a key aspect of the parton model and of an intuitive picture of hadron structure, becomes obscured by quantum effects in QCD. This suggests that there may be measures of entanglement between quark degrees of freedom that are present in QCD, but absent in the intuitive picture with a clear valence-sea (VS) separation. In this paper, we define the first rigorous measure of VS entanglement in QCD in an attempt to bring conceptual clarity to this issue, and, potentially, to find a measure of the applicability of the parton model to QCD bound states. This VS entanglement vanishes in the large-N c limit, and it remains low when finite-N c states resemble their large-N c counterparts. We perform a numerical study of VS entanglement in 1 + 1 dimensional discrete light-cone quantized QCD, and in the process develop a method for building the color-singlet basis of 1 + 1d QCD that is manifestly complete and orthogonal by construction. We calculate this VS entanglement entropy for the first time and find that it is relatively low for the first few excited states of both mesons and baryons compared to all other states in the spectrum, with the VS entropy of ground state hadrons providing a minimum. We also see that for ground state mesons the entropy is well described in the 1/N c approximation. These results suggest that low energy hadrons may be the only QCD bound states for which the large-N c expansion, and perhaps the parton model, provide an accurate description. This work also provides the first evidence that the VS entanglement entropy of QCD in 3 + 1d, which would likely serve as an order parameter for the transition between quark and hadron degrees of freedom, may be perturbatively accessible through a large-N c expansion.

1+1 dimensional QCD↗

DOE OSTI2023

NeRVI: Compressive neural representation of visualization images for communicating volume visualization results

We present NeRVI, a new deep-learning approach that compresses a large collection of visualization images generated from time-varying data for communicating volume visualization results. Based on an image-based implicit neural representation, our approach represents tens of thousands of high-resolution rendering images parametrized by different parameters via a hybrid model of multilayer perceptrons and convolutional neural networks. Here, our model predicts images and corresponding masks, and the masks are utilized for loss computation and network training to capture fine structural details and small components. In conjunction with model quantization and weight encoding, NeRVI yields highly compact compressive neural representations while preserving the image fidelity well. We demonstrate the effectiveness of NeRVI with isosurface rendering and direct volume rendering images generated from multiple data sets and compare NeRVI with other state-of-the-art deep learning-based (InSituNet, SIREN, NeRF, and NeRV) methods. Quantitative and qualitative results show that NeRVI provides an alternative solution that augments domain scientists' ability to manage, represent, and communicate scientific visualization output.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

A multilayer multiconfiguration time-dependent Hartree study of the nonequilibrium Anderson impurity model at zero temperature

Quantum transport is studied for the nonequilibrium Anderson impurity model at zero temperature employing the multilayer multiconfiguration time-dependent Hartree theory within the second quantization representation (ML-MCTDH-SQR) of Fock space. To address both linear and nonlinear conductance in the Kondo regime, two new techniques of the ML-MCTDH-SQR simulation methodology are introduced: (i) the use of correlated initial states, which is achieved by imaginary time propagation of the overall Hamiltonian at zero voltage and (ii) the adoption of the logarithmic discretization of the electronic continuum. Employing the improved methodology, the signature of the Kondo effect is analyzed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Quantum microgrid state estimation

This paper investigates the feasibility and efficiency of quantum-circuit-based algorithms for microgrid state estimation. Here, our new contributions include: (1) a general quantum state estimation (GQSE) formulation is devised for swing-bus-contained microgrids through the quantized Gaussian–Newton iteration, (2) a preconditioned quantum linear solver (PQLS) is developed for tackling the ill-conditioned GQSE with limited quantum resources, and (3) an enhanced quantum state estimation (EQSE) algorithm is further established for hierarchical-control-based microgrids with exogenous disturbances. Extensive case studies demonstrate the correctness of GQSE, PQLS and EQSE in two typical microgrids. The robustness and convergence performance of EQSE are also verified.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2017

One possible source of mass-independent fractionation of sulfur isotopes in the Archean atmosphere of Earth

Energy transfer mechanism for recombination of two sulfur atoms into a diatomic molecule, S 2 , is studied theoretically and computationally to determine whether the rate coefficient of this process can be significantly affected by isotopic substitutions, and whether the resultant isotope effect is expected to be mass-dependent or mass-independent. This is one of sulfur polymerization processes thought to be important in the anoxic atmosphere of the Archean Earth and, potentially, relevant to mass-independent fractionation of sulfur isotopes. A simplified theoretical approach is employed, in which all properties of S 2 molecule are characterized rather accurately, whereas the process of stabilization of metastable S 2 * by bath gas collisions is described approximately. Properties of individual scattering resonances in S 2 are studied in detail, and it is found that most important contributions to the recombination process come from ro-vibrational states formed near the top of centrifugal barrier, and that the number of such states is about 50 (in 32 S 32 S). Absolute value of recombination rate coefficient is computed to be 1.22 x 10 -33 cm 6 /s (for 32 S 32 S at room temperature and atmospheric pressure), close to experimental result. Two distinct isotope effects are identified. One is a classical mass-dependent effect due to translational partition function, which leads to a weak, smooth, and negative mass-dependence of rate coefficient (4% decrease when the mass is raised from 32 S 32 S to 34 S 34 S). Second effect, due to quantized resonances, is two orders of magnitude stronger, but is local. In practice, due to presence of multiple individual resonances, this phenomenon leads to irregular mass-independent variations of rate coefficients in the ranges ±5%. It is also demonstrated that in real molecules this irregular behavior is expected to be somewhat smoother, and the isotope effect is somewhat smaller, due to dependence of stabilization cross section on properties of individual resonances (not described by present model). So additional calculations of stabilization cross sections are needed in order to give quantitative prediction of this mass-independent isotope effect, and to determine its relevance to mass-independent fractionation of sulfur isotopes in the Archean rock record.

58 GEOSCIENCES↗