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At least 541 records · Page 30
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DOE OSTI2021

Koopman wavefunctions and Clebsch variables in Vlasov–Maxwell kinetic theory

Motivated by recent discussions on the possible role of quantum computation in plasma simulations, here, we present different approaches to Koopman's Hilbert-space formulation of classical mechanics in the context of Vlasov–Maxwell kinetic theory. The celebrated Koopman–von Neumann construction is provided with two different Hamiltonian structures: one is canonical and recovers the usual Clebsch representation of the Vlasov density, the other is non-canonical and appears to overcome certain issues emerging in the canonical formalism. Furthermore, the canonical structure is restored for a variant of the Koopman–von Neumann construction that carries a different phase dynamics. Going back to van Hove's prequantum theory, the corresponding Koopman–van Hove equation provides an alternative Clebsch representation which is then coupled to the electromagnetic fields. Finally, the role of gauge transformations in the new context is discussed in detail.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Lifting at higher levels in the D1D 5 CFT

The D1D 5 P system has a large set of BPS states at its orbifold point. Perturbing away from this ‘free’ point leads to some states joining up into long supermultiplets and lifting, while other states remain BPS. We consider the simplest orbifold which exhibits this lift: that with N = 2 copies of the free c = 6 CFT. We write down the number of lifted and unlifted states implied by the index at all levels upto 6. We work to second order in the perturbation strength λ. For levels upto 4, we find the wavefunctions of the lifted states, their supermultiplet structure and the value of the lift. All states that are allowed to lift by the index are in fact lifted at order O(λ 2 ). We observe that the unlifted states in the untwisted sector have an antisymmetry between the copies in the right moving Ramond ground state sector, and extend this observation to find classes of states for arbitrary N that will remain unlifted to O(λ 2 )

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Fluctuation–dissipation relation for a quantum Brownian oscillator in a parametrically squeezed thermal field

In this paper we study the nonequilibrium evolution of a quantum Brownian oscillator, modeling the internal degree of freedom of a harmonic atom or an Unruh–DeWitt detector, coupled to a nonequilibrium and nonstationary quantum field bath and inquire whether a fluctuation–dissipation relation (FDR) can exist after/if it approaches equilibration. This is a nontrivial issue because a squeezed field bath cannot reach equilibration and yet, as this work shows, the system oscillator indeed can, which is a necessary condition for FDRs. We discuss three different settings: (A) The bath field essentially remains in a squeezed thermal state throughout, whose squeeze parameter is a mode- and time-independent constant. This situation is often encountered in quantum optics and quantum thermodynamics. (B) The bath field is initially in a thermal state, but is subjected to a parametric process leading to mode- and time-dependent squeezing. This scenario is encountered in cosmology and dynamical Casimir effects. The squeezing in the bath in both types of processes will affect the oscillator’s nonequilibrium evolution. We show that at late times it approaches equilibration and this stationarity condition warrants the existence of a FDR. The trait of squeezing is marked by the oscillator’s effective equilibrium temperature, and the proportionality factor in the FDR is only related to the stationary component of the noise kernel of the bath field. Setting (C) is more subtle: A finite system–bath coupling strength can set the oscillator in a squeezed state even though the bath field is stationary and does not engage in any parametric process. The squeezing of the system in this case is in general time-dependent but becomes constant when the internal dynamics is fully relaxed. We begin with comments on the broad range of physical processes involving squeezed thermal baths and end with some remarks on the significance of FDRs in capturing the essence of quantum backreaction in nonequilibrium and stochastic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Topology stabilized fluctuations in a magnetic nodal semimetal

Abstract The interplay between magnetism and electronic band topology enriches topological phases and has promising applications. However, the role of topology in magnetic fluctuations has been elusive. Here, we report evidence for topology stabilized magnetism above the magnetic transition temperature in magnetic Weyl semimetal candidate CeAlGe. Electrical transport, thermal transport, resonant elastic X-ray scattering, and dilatometry consistently indicate the presence of locally correlated magnetism within a narrow temperature window well above the thermodynamic magnetic transition temperature. The wavevector of this short-range order is consistent with the nesting condition of topological Weyl nodes, suggesting that it arises from the interaction between magnetic fluctuations and the emergent Weyl fermions. Effective field theory shows that this topology stabilized order is wavevector dependent and can be stabilized when the interband Weyl fermion scattering is dominant. Our work highlights the role of electronic band topology in stabilizing magnetic order even in the classically disordered regime.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Beyond AdS 2 /dCFT 1 : insertions in two Wilson loops

We consider two-point correlators of local operator insertions in a system of two Wilson-Maldacena loops in $\mathcal{N}$ = 4 supersymmetric Yang-Mills theory on both sides of the AdS/CFT correspondence. On the holographic side the correlator of two Wilson-Maldacena loops is given by a classical string world-sheet which in one phase connects two asymptotically AdS 2 regions and in the other phase is given by two disconnected AdS 2 caps; this configuration breaks supersymmetry as well as conformal invariance. We present a complete systematic account of the string world-sheet fluctuations, including the fermionic sector, and study the behavior of the holographic two-point correlators. On the field theory side we compute certain two-point correlators of local operator insertions by resumming sets of ladder diagrams. Our results demonstrate the efficacy of previously developed methods in tackling this non-conformal, non-susy regime.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Denoising and Extension of Response Functions in the Time Domain

Response functions of quantum systems, such as electron Green’s functions, magnetic, or charge susceptibilities, describe the response of a system to an external perturbation. They are the central objects of interest in field theories and quantum computing and measured directly in experiment. Further, response functions are intrinsically causal. In equilibrium and steady-state systems, they correspond to a positive spectral function in the frequency domain. Since response functions define an inner product on a Hilbert space and thereby induce a positive definite function, the properties of this function can be used to reduce noise in measured data and, in equilibrium and steady state, to construct positive definite extensions for data known on finite time intervals, which are then guaranteed to correspond to positive spectra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Normal modes, rotational inertia, and thermal fluctuations of trapped ion crystals

The normal modes of a trapped ion crystal are derived using an approach based on the Hermitian properties of the system’s dynamical matrix. This method is equivalent to the standard Bogoliubov method, but for classical systems it is arguably simpler and more general in that canonical coordinates are not necessary. The theory is developed for stable, unstable, and neutrally-stable systems. The method is then applied to ion crystals in a Penning trap. Reduced eigenvalue problems for the case of large applied magnetic field are developed, for which the spectrum breaks into E x B drift modes, axial modes, and cyclotron modes. Thermal fluctuation levels in these modes are analyzed and shown to be consistent with the Bohr-van-Leeuwen theorem, provided that neutrally-stable modes associated with crystal rotations are included in the analysis. An expression for the rotational inertia of the crystal is derived, and a magnetic contribution to this inertia, which dominates in large magnetic fields, is described. An unusual limit is discovered for the special case of spherically-symmetric confinement, in which the rotational inertia does not exist and changes in angular momentum leave the rotation frequency unaffected.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

The holar wind

String theory in AdS 3 with purely NS-NS fluxes and vanishing RR moduli has a continuum of winding string excitations in radial plane wave states. BTZ black holes can emit such strings, which then flow out toward the AdS 3 boundary as a stream of massive quanta, and form a black hole analogue of the solar wind. The winding string sector thus provides a decay channel for the black hole to evaporate without having either to couple the system to an external reservoir or to match the AdS 3 throat onto an asymptotically flat region. We compute the emission amplitude of this “holar wind” in the semi-classical approximation, and consider the associated version of the black hole information paradox.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Entanglement structures in quantum field theories. II. Distortions of vacuum correlations through the lens of local observers

When observing a quantum field via detectors with access to only the mixed states of spatially separated, local regions—a ubiquitous experimental design—the capacity to access the full extent of distributed entanglement can be limited, shrouded by classical correlations. By performing projective measurements of the field external to two detection patches and classically communicating the results, underlying pure states may be identified for which entanglement quantification is clear. In the Gaussian continuous-variable states of the free scalar field vacuum, this protocol uncovers a disparity between the spacelike entanglement established within the field and that which is locally detectable. Further, this discrepancy is found to grow exponentially with the separation between observation regions. The protocol developed herein offers insight and practical guidance for clarifying the unavoidable distortion of quantum field correlations when viewed from the vantage of a pair of local observers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Report on the 35th Annual Workshop on Recent Developments in Electronic Structure Theory

The 35th Annual Workshop on Recent Developments in Electronic Structure Theory was held June 13 – 16, 2023 at the University of California, Merced, a minority-serving institution with R2 status. This workshop series travels to a different institution within the US each year, and this was the first time it was held in the underserved Central Valley of California. The Local Organizers collected suggestions from the international steering committee to put together a list of topics representing recent major developments in the field and speakers.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Role of generic scale invariance in a Mott transition from a U(1) spin-liquid insulator to a Landau Fermi-liquid metal

Highlights: • We look at the role played by generic scale invariance (GSI) in the phase transition between a U(1) spin liquid and a Fermi liquid. • We identify dangerously irrelevant operators in the renormalization group transformation, involved with the GSI. • We highlight novel mean-field dynamics of this Mott quantum criticality, resulting from the GSI. We investigate the role of generic scale invariance in a Mott transition from a U(1) spin-liquid insulator to a Landau Fermi-liquid metal, where there exist massless degrees of freedom in addition to quantum critical fluctuations. Here, the Mott quantum criticality is described by critical charge fluctuations, and additional gapless excitations are U(1) gauge-field fluctuations coupled to a spinon Fermi surface in the spin-liquid state, which turn out to play a central role in the Mott transition. An interesting feature of this problem is that the scaling dimension of effective leading local interactions between critical charge fluctuations differs from that of the coupling constant between U(1) gauge fields and matter-field fluctuations in the presence of a Fermi surface. As a result, there appear dangerously irrelevant operators, which can cause conceptual difficulty in the implementation of renormalization group (RG) transformations. Indeed, we find that the curvature term along the angular direction of the spinon Fermi surface is dangerously irrelevant at this spin-liquid Mott quantum criticality, responsible for divergence of the self-energy correction term in U(1) gauge-field fluctuations. Performing the RG analysis in the one-loop level based on the dimensional regularization method, we reveal that such extremely overdamped dynamics of U(1) gauge-field fluctuations, which originates from the emergent one-dimensional dynamics of spinons, does not cause any renormalization effects to the effective dynamics of both critical charge fluctuations and spinon excitations. However, it turns out that the coupling between U(1) gauge-field fluctuations and both matter-field excitations still persists at this Mott transition, which results in novel mean-field dynamics to explain the nature of the spin-liquid Mott quantum criticality. We discuss physical implications of effective one-dimensional spin dynamics and extremely overdamped gauge dynamics at the Mott quantum criticality.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Gauge-invariant perturbation expansion in powers of electric charge for the density-of-states of a network model for charged-particle motion in a uniform background magnetic flux density

An explicitly gauge-invariant expansion in powers of e/$\hbar$ times the magnetic flux density is formally obtained for the density of states [as characterized by the trace of the resolvent $\hat{G}$ = (ω-$\hat{ℎ}$)-1] of a charged particle moving on a Hermitian quantum network that is embedded in a Euclidean background that supports a uniform magnetic flux density. The explicit expressions, given here up to third order in the flux density, are also valid for the “local trace” (the trace of $\hat{P}_i\hat{G}$ , where $\hat{P}_i$ is the projector on a network node) and do not appear to have been previously given.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Variational quantum simulation of the critical Ising model with symmetry averaging

Here we investigate the use of deep multiscale entanglement renormalization ansatz (DMERA) circuits as a variational ansatz. We use the exactly solvable one-dimensional critical transverse-field Ising model as a test bed. Numerically exact simulation of the quantum circuit ansatz can in this case be carried out to hundreds of qubits by exploiting efficient classical algorithms for simulating matchgate circuits. We find that, for this system, the DMERA strongly outperforms a standard quantum approximate optimization algorithm (QAOA)–style ansatz, and that a major source of systematic error in correlation functions approximated using the DMERA is the breaking of the translational and Kramers-Wannier symmetries of the transverse-field Ising model. We are able to reduce this error by up to four orders of magnitude by symmetry averaging, without incurring additional cost in qubits or circuit depth. Here, we propose that this technique for mitigating systematic error could be applied to noisy intermediate-scale quantum (NISQ) simulations of physical systems with other symmetries.

1-dimensional spin chains↗
DOE OSTI2020

Coexistence of antiferromagnetism and topological superconductivity on the honeycomb lattice Hubbard model

In this report, motivated by the recent numerical simulations for doped t-J model on the honeycomb lattice, we study superconductivity of singlet and triplet pairing on the honeycomb lattice Hubbard model. We show that a superconducting state with coexisting spin-singlet and spin-triplet pairings is induced by the antiferromagnetic order near half filling. The superconducting state we obtain has a topological phase transition that separates a topologically trivial state and a nontrivial state with Chern number two. Possible experimental realization of such a topological superconductivity is also discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Robust analytic continuation of Green's functions via projection, pole estimation, and semidefinite relaxation

Green's functions of fermions are described by matrix-valued Herglotz-Nevanlinna functions. Since analytic continuation is fundamentally an ill-posed problem, the causal space described by the matrix-valued Herglotz-Nevanlinna structure can be instrumental in improving the accuracy and in enhancing the robustness with respect to noise. We demonstrate a three-pronged procedure for robust analytic continuation called PES: (1) projection of data to the causal space; (2) estimation of pole locations; and (3) semidefinite relaxation within the causal space. We compare the performance of PES with the recently developed Nevanlinna and Carathéodory continuation methods and find that PES is more robust in the presence of noise and does not require the usage of extended precision arithmetics. We also demonstrate that a causal projection improves the performance of the Nevanlinna and Carathéodory methods. The PES method is generalized to bosonic response functions, for which the Nevanlinna and Carathéodory continuation methods have not yet been developed. Furthermore, it is particularly useful for studying spectra with sharp features, as they occur in the study of molecules and band structures in solids.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Cascading from $\mathscr{N}$ = 2 supersymmetric Yang–Mills theory to confinement and chiral symmetry breaking in adjoint QCD

We argue that adjoint QCD in 3 + 1 dimensions, with any SU(N) gauge group and two Weyl fermion flavors (i.e. one adjoint Dirac fermion), confines and spontaneously breaks its chiral symmetries via the condensation of a fermion bilinear. We flow to this theory from pure $\mathscr{N}$ = 2 SUSY Yang–Mills theory with the same gauge group, by giving a SUSY-breaking mass M to the scalars in the $\mathscr{N}$ = 2 vector multiplet. This flow can be analyzed rigorously at small M, where it leads to a deconfined vacuum at the origin of the $\mathscr{N}$ = 2 Coulomb branch. The analysis can be extended to all M using an Abelian dual description that arises from the N multi-monopole points of the $\mathscr{N}$ = 2 theory. At each such point, there are N −1 hypermultiplet Higgs fields h$^{i=1,2}_m$, which are SU(2) R doublets. We provide a detailed study of the phase diagram as a function of M, by analyzing the semi-classical phases of the dual using a combination of analytic and numerical techniques. The result is a cascade of first-order phase transitions, along which the Higgs fields h i m successively turn on, and which interpolates between the Coulomb branch at small M, where all h$^{i}_m$ = 0, and a maximal Higgs branch, where all h$^{i}_m$ ≠ 0, at sufficiently large M. We show that this maximal Higgs branch precisely matches the confining and chiral symmetry breaking phase of two-flavor adjoint QCD, including its broken and unbroken symmetries, its massless spectrum, and the expected large-N scaling of various observables. The spontaneous breaking pattern SU(2) R → U(1) R , consistent with the Vafa–Witten theorem, is ensured by an intricate alignment mechanism for the h$^{i}_m$ in the dual, and leads to a CP 1 sigma model of increasing radius along the cascade.

D’Hoker, Eric [Univ. of California, Los Angeles, C↗