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DOE OSTI2021

The Markov gap for geometric reflected entropy

The reflected entropy S R (A : B) of a density matrix ρ AB is a bipartite correlation measure lower-bounded by the quantum mutual information I(A : B). In holographic states satisfying the quantum extremal surface formula, where the reflected entropy is related to the area of the entanglement wedge cross-section, there is often an order-N 2 gap between S R and I. We provide an information-theoretic interpretation of this gap by observing that S R - I is related to the fidelity of a particular Markov recovery problem that is impossible in any state whose entanglement wedge cross-section has a nonempty boundary; for this reason, we call the quantity S R - I the Markov gap. We then prove that for time-symmetric states in pure AdS 3 gravity, the Markov gap is universally lower bounded by log(2)ℓ AdS /2G N times the number of endpoints of the cross-section. We provide evidence that this lower bound continues to hold in the presence of bulk matter, and comment on how it might generalize above three bulk dimensions. Finally, we explore the Markov recovery problem controlling S R - I using fixed area states. This analysis involves deriving a formula for the quantum fidelity — in fact, for all the sandwiched Rényi relative entropies — between fixed area states with one versus two fixed areas, which may be of independent interest. We discuss, throughout the paper, connections to the general theory of multipartite entanglement in holography.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Radiative classical gravitational observables at $ \mathcal{O} $(G 3 ) from scattering amplitudes

We compute classical gravitational observables for the scattering of two spinless black holes in general relativity and N =8 supergravity in the formalism of Kosower, Maybee, and O’Connell (KMOC). We focus on the gravitational impulse with radiation reaction and the radiated momentum in black hole scattering at $ \mathcal{O} $(G 3 ) to all orders in the velocity. These classical observables require the construction and evaluation of certain loop-level quantities which are greatly simplified by harnessing recent advances from scattering amplitudes and collider physics. In particular, we make use of generalized unitarity to construct the relevant loop integrands, employ reverse unitarity, the method of regions, integration-by-parts (IBP), and (canonical) differential equations to simplify and evaluate all loop and phase-space integrals to obtain the classical gravitational observables of interest to two-loop order. The KMOC formalism naturally incorporates radiation effects which enables us to explore these classical quantities beyond the conservative two-body dynamics. From the impulse and the radiated momentum, we extract the scattering angle and the radiated energy. Finally, we discuss universality of the impulse in the high-energy limit and the relation to the eikonal phase.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs

We study two novel approaches to efficiently encoding universal constraints imposed by conformal symmetry, and describe applications to quantum chaos in higher dimensional CFTs. The first approach consists of a reformulation of the shadow operator formalism and kinematic space techniques. We observe that the shadow operator associated with the stress tensor (or other conserved currents) can be written as the descendant of a field ε with negative dimension. Computations of stress tensor contributions to conformal blocks can be systematically organized in terms of the “soft mode” ε, turning them into a simple diagrammatic perturbation theory at large central charge.Our second (equivalent) approach concerns a theory of reparametrization modes, generalizing previous studies in the context of the Schwarzian theory and two-dimensional CFTs. Due to the conformal anomaly in even dimensions, gauge modes of the conformal group acquire an action and are shown to exhibit the same dynamics as the soft mode ε that encodes the physics of the stress tensor shadow. We discuss the calculation of the conformal partial waves or the conformal blocks using our effective field theory. The separation of conformal blocks from shadow blocks is related to gauging of certain symmetries in our effective field theory of the soft mode. These connections explain and generalize various relations between conformal blocks, shadow operators, kinematic space, and reparametrization modes. As an application we study thermal physics in higher dimensions and argue that the theory of reparametrization modes captures the physics of quantum chaos in Rindler space. This is also supported by the observation of the pole skipping phenomenon in the conformal energy-energy two-point function on Rindler space.

1/N Expansion↗
DOE OSTI2019

Exact solutions of 2d supersymmetric gauge theories

We study dynamics of two-dimensional non-abelian gauge theories with N = (0, 2) supersymmetry that include N = (0, 2) supersymmetric QCD and its generalizations. In particular, we present the phase diagram of N = (0, 2) SQCD and determine its massive and low-energy spectrum. We find that the theory has no mass gap, a nearly constant distribution of massive states, and lots of massless states that in general flow to an interacting CFT. For a range of parameters where supersymmetry is not dynamically broken at low energies, we give a complete description of the low-energy physics in terms of 2d N = (0, 2) SCFTs using anomaly matching and modular invariance. Our construction provides a vast landscape of new N = (0, 2) SCFTs which, for small values of the central charge, could be used for building novel heterotic models with no moduli and, for large values of the central charge, could be dual to AdS3 string vacua.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Chern-Weil global symmetries and how quantum gravity avoids them

We draw attention to a class of generalized global symmetries, which we call “Chern-Weil global symmetries,” that arise ubiquitously in gauge theories. The Noether currents of these Chern-Weil global symmetries are given by wedge products of gauge field strengths, such as F 2 $\wedge$ H 3 and tr(F$^2_2$), and their conservation follows from Bianchi identities. As a result, they are not easy to break. However, it is widely believed that exact global symmetries are not allowed in a consistent theory of quantum gravity. As a result, any Chern-Weil global symmetry in a low-energy effective field theory must be either broken or gauged when the theory is coupled to gravity. In this paper, we explore the processes by which Chern-Weil symmetries may be broken or gauged in effective field theory and string theory. We will see that many familiar phenomena in string theory, such as axions, Chern-Simons terms, worldvolume degrees of freedom, and branes ending on or dissolving in other branes, can be interpreted as consequences of the absence of Chern-Weil symmetries in quantum gravity, suggesting that they might be general features of quantum gravity. We further discuss implications of breaking and gauging Chern-Weil symmetries for particle phenomenology and for boundary CFTs of AdS bulk theories. Chern-Weil global symmetries thus offer a unified framework for understanding many familiar aspects of quantum field theory and quantum gravity.

Brane dynamics in gauge theories↗
DOE OSTI2021

Scattering amplitudes for all masses and spins

We introduce a formalism for describing four-dimensional scattering amplitudes for particles of any mass and spin. This naturally extends the familiar spinor-helicity formalism for massless particles to one where these variables carry an extra SU(2) little group index for massive particles, with the amplitudes for spin Sparticles transforming as symmetric rank 2S tensors. We systematically characterise all possible three particle amplitudes compatible with Poincare symmetry. Unitarity, in the form of consistent factorization, imposes algebraic conditions that can be used to construct all possible four-particle tree amplitudes. This also gives us a convenient basis in which to expand all possible four-particle amplitudes in terms of what can be called “spinning polynomials”. Many general results of quantum field theory follow the analysis of four-particle scattering, ranging from the set of all possible consistent theories for massless particles, to spin-statistics, and the Weinberg-Witten theorem. We also find a transparent understanding for why massive particles of sufficiently high spin cannot be “elementary”. The Higgs and Super-Higgs mechanisms are naturally discovered as an infrared unification of many disparate helicity amplitudes into a smaller number of massive amplitudes, with a simple understanding for why this can’t be extended to Higgsing for gravitons. We illustrate a number of applications of the formalism at one-loop, giving few-line computations of the electron (g - 2) as well as the beta function and rational terms in QCD. “Off-shell” observables like correlation functions and form-factors can be thought of as scattering amplitudes with external “probe” particles of general mass and spin, so all these objects — amplitudes, form factors and correlators, can be studied from a common on-shell perspective.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Holographic entanglement from the UV to the IR

In AdS/CFT, observables on the boundary are invariant under renormalization group (RG) flow in the bulk. In this paper, we study holographic entanglement entropy under bulk RG flow and find that it is indeed invariant. We focus on tree-level RG flow, where massive fields in a UV theory are integrated out to give the IR theory. We explicitly show that in several simple examples, holographic entanglement entropy calculated in the UV theory agrees with that calculated in the IR theory. Moreover, we give an argument for this agreement to hold for general tree-level RG flow. Along the way, we generalize the replica method of calculating holographic entanglement entropy to bulk theories that include matter fields with nonzero spin.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Unitarization from geometry

We study the perturbative unitarity of scattering amplitudes in general dimensional reductions of Yang–Mills theories and general relativity on closed internal manifolds. For the tree amplitudes of the dimensionally reduced theory to have the expected high-energy behavior of the higher-dimensional theory, the masses and cubic couplings of the Kaluza–Klein states must satisfy certain sum rules that ensure there are nontrivial cancellations between Feynman diagrams. These sum rules give constraints on the spectra and triple overlap integrals of eigenfunctions of Laplacian operators on the internal manifold and can be proven directly using Hodge and eigenfunction decompositions. One consequence of these constraints is that there is an upper bound on the ratio of consecutive eigenvalues of the scalar Laplacian on closed Ricci-flat manifolds with special holonomy. This gives a sharp bound on the allowed gaps between Kaluza–Klein excitations of the graviton that also applies to Calabi–Yau compactifications of string theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Characterizing Topological Order with Matrix Product Operators

One of the most striking features of gapped quantum phases that exhibit topological order is the presence of long-range entanglement that cannot be detected by any local order parameter. The formalism of projected entangled-pair states is a natural framework for the parameterization of gapped ground state wavefunctions which allows one to characterize topological order in terms of the virtual symmetries of the local tensors that encode the wavefunction. In their most general form, these symmetries are represented by matrix product operators acting on the virtual level, which leads to a set of algebraic rules characterizing states with topological quantum order. This construction generalizes the concepts of $\mathsf G$- and twisted injectivity; the corresponding matrix product operators encode all topological features of the theory and provide a complete picture of the ground state manifold on the torus. We show how the string-net models of Levin and Wen fit within this formalism and in doing so provide a particularly intuitive interpretation of the pentagon equation for F-symbols as the pulling of matrix product operators through the string-net tensor network. Our approach paves the way to finding novel topological phases beyond string nets and elucidates the description of topological phases in terms of entanglement Hamiltonians and edge theories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Quantifying Microstructure Variability in Laser Powder Bed Fusion 316 L Stainless Steel Microstructures with Spatial Statistics

Here, we have explored data-driven methods for material microstructure quantification that improve sensitivity to microstructural changes compared to traditional approaches. The methods integrate multiple microstructural properties, including grain morphology, crystallographic orientation, and material phase information. The simpler method employs maps of the Euclidean distance transformation metric to evaluate the morphology of grain boundary networks. The more intensive approach employs generalized spherical harmonic mapping for crystallographic orientations, per-pixel phase information, and a variational auto-encoder for dimensionality reduction and results in a multidimensional clustering of by microstructure similarity. Applied to an experimental dataset of additively manufactured steel, both methods detected slight variations in samples produced under nominally identical processing conditions. Both methods were able to distinguish between samples from multiple (nominally identical) builds, while the generalized spherical harmonics-based method could additionally cluster data samples rotated at two orientations on the build plate. The improved sensitivity of the methods, demonstrated through comparison with traditional microstructure characterization techniques, offers advantages for microstructure quantification and comparisons in advanced manufacturing applications.

SS316L↗
DOE OSTI2019

Integrable nonlinear evolution of the qubit

Highlights: •We study the nonlinear generalization of the von Neumann equation. •We discuss the nonlinear von Neumann equation for the qubit states. •We analyze solutions to the Riccati system corresponding to evolution of a qubit. -- Abstract: The nonlinear generalization of the von Neumann equation is studied. The global version of this equation preserves convexity of the space of states. The particular case of the evolution of pure states refers to the nonlinear Schrödinger equation discovered by Gisin. The concrete realization of the nonlinear von Neumann equation is investigated in detail for the density matrix representing the qubit states. Such equation reduces to the integrable classical Riccati system of nonlinear ordinary differential equations. An interesting property of the nonlinear dynamics described by this system is the global asymptotical stability of stationary solutions related to evolution from mixed states to pure states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Nonlinear dynamics from linear quantum evolutions

Linear dynamics restricted to invariant submanifolds generally gives rise to nonlinear dynamics. Submanifolds in the quantum framework may emerge for several reasons: one could be interested in specific properties possessed by a given family of states, either as a consequence of experimental constraints or inside an approximation scheme. In this work we investigate such issues in connection with a one parameter group ϕ{sub t} of transformations on a Hilbert space, H, defining the unitary evolutions of a chosen quantum system. Two procedures will be presented: the first one consists in the restriction of the vector field associated with the Schrödinger equation to a submanifold invariant under the flow ϕ{sub t}. The second one makes use of the Lagrangian formalism and can be extended also to non-invariant submanifolds, even if in such a case the resulting dynamics is only an approximation of the flow ϕ{sub t}. Such a result, therefore, should be conceived as a generalization of the variational method already employed for stationary problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

A covariant simultaneous action for branes

Highlights: • A novel variational approach is presented. • It provides a shortcut towards the second variation of geometrical models. • This should be of interest, for its generality, to various areas of theoretical physics. - Abstract: A covariant simultaneous action for branes in an arbitrary curved background spacetime is considered. The term ‘simultaneous’ is imported from variational calculus and refers to the fact that extremization of the action produces at once both the first and second variations of a given geometrical action for the brane. The action depends on a pair of independent field variables, the brane embedding functions, through the canonical momentum of a reparametrization invariant geometric model for the brane, and an auxiliary vector field. The form of the action is analogous to a symplectic potential. Extremization of the simultaneous action produces at once the equations of motion and the Jacobi equations for the brane geometric model, and it also provides a convenient shortcut towards its second variation. In this note, we consider geometric models depending only on the intrinsic geometry of the brane worldvolume, and discuss briefly the generalization to extrinsic geometry dependent models. The approach is illustrated for Dirac–Nambu–Goto [DNG] branes. For a relativistic particle, a simultaneous action was introduced by Ba z-dot ański, that served as an inspiration for the present work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Entanglement Enabled Intensity Interferometry of different wavelengths of light

Highlights: • We use quantum entanglement to erase the color of photons for a new imaging method. • Can achieve higher resolution imaging by accessing hidden phase information. • We detail practical experimental designs to implement our theoretical protocols. We propose methods to perform intensity interferometry of photons having two different wavelengths. Distinguishable particles typically cannot interfere with each other, but we overcome that obstacle by processing the particles via entanglement and projection so that they lead to the same final state at the detection apparatus. Specifically, we discuss how quasi-phase-matched nonlinear crystals can be used to convert a quantum superposition of light of different wavelengths onto a common wavelength, while preserving the phase information essential for their meaningful interference. We thereby gain access to a host of new observables, which can probe subtle frequency correlations and entanglement. Further, we generalize the van Cittert–Zernike formula for the intensity interferometry of extended sources, demonstrate how our proposal supports enhanced resolution of sources with different spectral character, and suggest potential applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

The oscillatory anisotropy in the spatially flat cosmological models

Highlights: • Relations among asymptotic anisotropy and matter content. • A new scheme for obtaining physically motivated exact solutions. • The process of isotropization/anisotropization in cosmology. • The conversion among the anisotropy and the energy density into one another. In this manuscript, we investigate the oscillatory behaviour of the anisotropy in the diagonal Bianchi-I spacetimes. Our starting point is a simplification of Einstein’s equations using only observable or physical variables. As a consequence, we are able to: (a) Prove general results concerning the existence of oscillations of the anisotropy in the primordial and the late-time universe. For instance, in the expanding scenario, we show that a past weakly mixmaster behaviour (oscillations as we approach the Kasner solutions) might appear even with no violation of the usual energy conditions, while in the future, the pulsation (oscillations around isotropic solutions) seems to be most favoured; (b) Determine a large scheme for deriving classes of physically motivated exact solutions, and we give some (including the general barotropic perfect fluid and the magnetic one); (c) Understand the physical conditions for the occurrence of the isotropization or anisotropization during the cosmological evolution; (d) Understand how anisotropy and energy density are converted one into another. In particular, we call attention to the presence of a residue in the energy density in a late-time isotropic universe coming from its past anisotropic behaviour.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Some aspects of the five-dimensional Lovelock black hole spacetime: Strong homotopy retract, perihelion precession and quasistationary levels

Highlights: • Some topological aspects are explored. • The perihelion precession is calculated. • The general Heun functions are applied to obtain analytical solutions. • The quasibound states and the radial wave eigenfunctions are obtained. In this work we explore some mathematical physics aspects of the spherically symmetric Lovelock black hole in high dimensions. Intended for this aim, we thoroughly consider the metric corresponding to the five-dimensional Lovelock black hole spacetime. We construct the strong retractions by the geodesic equations on the background under consideration. As a result, from the topological point of view, we construct the theory of strong homotopy retract, which will allow us, in principle, to better understand some of its suitable applications on astrophysics and cosmology, in particular, in the analysis of the spacetime singularities. We find the solutions of the equation of motion for both radial and angular coordinates, and then we describe the outer (“exterior”) and lower (“interior”) apparent horizons. Indeed, the outer apparent horizon is the last surface from which the light waves could still escape from the black hole. Thus, it is meaningful to analyze some physical phenomena related to quantum particles propagating outside the exterior apparent horizon, in particular, we discuss the quasistationary levels of scalar fields and their radial wave functions, which are given in terms of the general Heun functions. We also calculate the perihelion precession in this background.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Ground state properties of a spin-3/2 Fermi gas

Highlights: • A generalized spin-3/2 Fermi liquid is studied via diagram technique and Green’s function • The spin-mixing term strengthens ground state energy and effective mass Diagram technique is employed to study ground state properties of a generalized spin-3/2 Fermi gas which consists of more spin components and interacting channels than the spin-1/2 system. The interaction parameters are supposed to be spin-dependent, including a spin-mixing parameter which is absent in the spin-1/2 Fermi gas. The chemical potential, ground state energy and effective mass are calculated after elaborately dealing with the effective interaction and the self-energy. Contributions of each interaction term are derived within the second-order perturbation. It is found that the spin-mixing term always strengthens the ground state energy and effective mass.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Non-Markovian dynamics of open quantum system with memory

Highlights: • Non-Markovian master equation for open quantum system with power-law memory is proposed. • Non-Markovian dynamics of two-level quantum system with memory is described. • Solutions of non-Markovian quantum master equations are derived. • Complete positivity and bi-positivity in non-Markovian quantum dynamics with memory are described. • Exact solution of non-Markovian equations of system with memory is proposed. In this paper, non-Markovian generalization of master equation for open quantum system is proposed. Non-Markovian dynamics of two-level quantum system with memory and interaction with environment is described. To describe this system, the Gorini–Kossakowski–Sudarshan equation for open quantum states is generalized by taking into account power-law fading memory. The non-Markovian quantum processes with power-law memory are described by using integration and differentiation of non-integer orders. Complete positivity and bi-positivity in non-Markovian quantum dynamics with memory are described. An example of two-level quantum systems with power-law memory is suggested. Exact solution of the non-Markovian master equations of two-level open quantum systems with memory is derived.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗