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DOE OSTI2021

A three-step model of high harmonic generation using complex classical trajectories

Highlights: • Rigorous trajectory formulation of strong field physics and high harmonic generation. • The Coulomb ground state is represented by an ensemble of complex trajectories. • Trajectories transition seamlessly from the ground state to ionization or recollision. • The ionized wavepacket is reproduced well from the complex trajectories. • Classically allowed and forbidden processes are treated in a single framework. We present a new trajectory formulation of high harmonic generation that treats classically allowed and classically forbidden processes within a single dynamical framework. Complex trajectories orbit the nucleus, producing the stationary Coulomb ground state. When the field is turned on, these complex trajectories continue their motion in the field-dressed Coulomb potential and therefore tunnel ionization, unbound evolution and recollision are described within a single, seamless framework. The new formulation can bring mechanistic understanding to a broad range of strong field physics effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Nonequilibrium steady state and heat transport in nonlinear open quantum systems: Stochastic influence action and functional perturbative analysis

In this paper, we show that a nonequilibrium steady state (NESS) exists at late times in open quantum systems with weak nonlinearity by following its nonequilibrium dynamics with a perturbative analysis. We consider an oscillator chain containing three-types of anharmonicity: cubic α- and quartic β-type Fermi–Pasta–Ulam–Tsingou (FPUT) nearest-oscillator interactions and the on-site (pinned) Klein–Gordon (KG) quartic self-interaction. Assuming weak nonlinearity, we introduce a stochastic influence action approach to the problem and obtain the energy flows in different junctures across the chain. The formal results obtained here can be used for quantum transport problems in weakly nonlinear quantum systems. For α-type anharmonicity, we observe that the first-order corrections do not play any role in the thermal transport in the NESS of the configuration we considered. For KG and β-types anharmonicity, we work out explicitly the case of two weakly nonlinearly coupled oscillators, with results scalable to any number of oscillators. We examine the late-time energy flows from one thermal bath to the other via the coupled oscillators, and show that both the zeroth- and the first-order contributions of the energy flows become constant in time at late times, signaling the existence of a late-time NESS to first order in nonlinearity. Our perturbative calculations provide a measure of the strength of nonlinearity for nonlinear open quantum systems, which may help control the mesoscopic heat transport distinct from or close to linear transport. Furthermore, our results also give a benchmark for the numerical challenge of simulating heat transport. Our setup and predictions can be implemented and verified by investigating heat flow in an array of Josephson junctions in the limit of large Josephson energy with the platform of circuit QED.

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

Quantum field theory with the generalized uncertainty principle II: Quantum Electrodynamics

Highlights: • Relativistic Generalized Uncertainty Principle gives Frame independent minimum length. • Quantum Gravity modified Dirac equation from Modified Klein–Gordon Equations. • There exists a Quantum Gravity modified Lagrangian for a spinor field theory. • Feynman vertices contain 2 fermions & up to 5 gauge bosons are allowed. • Minimum length modifies the amplitude of Electrodynamic electron–muon scattering. Continuing our earlier work on the application of the Relativistic Generalized Uncertainty Principle (RGUP) to quantum field theories, in this paper we study Quantum Electrodynamics (QED) with minimum length. We obtain expressions for the Lagrangian, Feynman rules and scattering amplitudes of the theory, and discuss their consequences for current and future high energy physics experiments. We hope this will provide an improved window for testing Quantum Gravity effects in the laboratory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A unified system for Coleman–De Luccia transitions

Highlights: • Monotonicity controls whether radius of CDL bounce is negative mode direction. • Decays from de Sitter and Anti-de Sitter analyzed in single geometric framework. • de Sitter to Anti-de Sitter instantons come in two types, similar to type-A vs type-B. We show that the presence or absence of negative modes associated with the expansion or contraction of Coleman–De Luccia instantons is controlled by the monotonicity properties of a single function parameterized by the tension and two vacuum energies. This approach simplifies and unifies certain aspects of phase transitions between two de Sitter vacua, between two Anti-de Sitter, and between one of each. This strategy may serve as a guide for identifying negative modes in more complicated gravitational theories, for instance supergravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Higher-rank tensor field theory of non-abelian fracton and embeddon

We formulate a new class of tensor gauge field theories in any dimension that is a hybrid class between symmetric higher-rank tensor gauge theory (i.e., higher-spin gauge theory) and anti-symmetric tensor topological field theory. Our theory describes a mixed unitary phase interplaying between gapless and gapped topological order phases (which can live with or without Euclidean, Poincaré, or anisotropic symmetry, at least in ultraviolet high or intermediate energy field theory, but not yet to a lattice cutoff scale). The “gauge structure” can be compact, continuous, abelian or non-abelian. Our theory sits outside the paradigm of Maxwell electromagnetic theory in 1865 and Yang–Mills isospin/color theory in 1954. We discuss its local gauge transformation in terms of the ungauged vector-like or tensor-like higher-moment global symmetry. The non-abelian gauge structure is caused by gauging the non-commutative symmetries: a higher-moment symmetry and a charge conjugation (particle–hole) symmetry. Vector global symmetries along time direction may exhibit time crystals. We explore the relation of these long-range entangled matters to a non-abelian generalization of Fracton order in condensed matter, a field theory formulation of foliation, the spacetime embedding and Embeddon that we newly introduce, and possible fundamental physics applications to dark matter or dark energy.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Information-theoretic aspects of Werner states

Highlights: • The rich structures of Werner states are reviewed. • Werner states are characterized in terms of quantum uncertainty. • Information-theoretic aspects of Werner states are revealed. In a seminal study of quantum states with Einstein–Podolsky–Rosen correlations (entanglement) admitting a hidden-variable model (Werner, 1989), Werner introduced the dichotomy of entanglement/separability and devised a family of highly symmetric states, now termed the Werner states, some of which exhibit entanglement but no Bell nonlocality. It turns out that the Werner states have a rich structure of correlations and constitute a paradigm which has played an innovative role in both theoretical and experimental explorations of quantum information. Given the theoretical significance and wide applications of the Werner states, here we first give a concise review of information contents of the Werner states, and then present an information-theoretic characterization of them in terms of the Wigner–Yanase skew information: The Werner states are identified as the states with the minimum quantum uncertainty with respect to a natural family of observables (i.e., the generators of the diagonal unitary group). For this purpose, we introduce a measure of quantum uncertainty which is of independent interest in studying asymmetry, coherence, and uncertainty, and reveal its fundamental properties. We further identify the Bell triplet states as the opposite states of the Werner states in the sense that they have the maximal amount of quantum uncertainty. Analogously, we provide a similar characterization of the isotropic states as the minimum quantum uncertainty states with respect to a closely related family of operators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Kinklike structures in an arcsin real scalar dynamics

Highlights: • Kinklike analyses in a real scalar theory with an arcsin dynamic. • First-order formalism implementation and deformation procedure in an arcsin scalar dynamics. In this paper, we analyze kink-like analytical solutions in a real scalar theory with an arcsin dynamics inspired by the arcsin electrodynamics presented in Kruglov (2015). This analysis is done by means of the first-order formalism. This formalism provides a framework where the equations of motion can be simplified by preserving the linear stability of the theory. In this work, the deformation procedure is implemented with the aim of finding exact solutions in systems with generalized dynamics. Along the paper, we explore how the first-order formalism is implemented in the arcsin kinetics and how such a term influences the kink-like solutions. As a part of the result of our paper, we show that the kink-like solutions are similar to the ones obtained in the standard scalar kinetic theory. We also show that the extra parameter, that controls the non-linearities of the model, plays an essential role in the energy densities and stability potentials. These quantities vary according to this parameter. The goals here are to show how the first-order framework is implemented in this arcsin scenario and to present the analytical kink-like solutions that can be found by means of the first-order framework and deformation method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Power spectrum and form factor in random diagonal matrices and integrable billiards

Triggered by a controversy surrounding a universal behavior of the power spectrum in quantum systems exhibiting regular classical dynamics, we focus on a model of random diagonal matrices (RDM), often associated with the Poisson spectral universality class, and examine how the power spectrum and the form factor get affected by two-sided truncations of RDM spectra. Having developed a nonperturbative description of both statistics, we perform their detailed asymptotic analysis to demonstrate explicitly how a traditional assumption (lying at the heart of the controversy) – that the power spectrum is merely determined by the spectral form factor – breaks down for truncated spectra. This observation has important consequences as we further argue that bounded quantum systems with integrable classical dynamics are described by heavily truncated rather than complete RDM spectra. High-precision numerical simulations of semicircular and irrational rectangular billiards lend independent support to these conclusions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Algebraic Structures in the Coupling of Gravity to Gauge Theories

Highlights: • Geometric foundation for Quantum General Relativity coupled to Quantum Electrodynamics. • Rigorous introduction to Hopf algebraic renormalization. • Appropriate modifications in case renormalization Hopf algebra is ill-defined. • Generalization of Furry’s Theorem to include gravitons and ghosts. • Discussion of obstructions to multiplicative renormalization. This article is an extension of the author’s second master thesis, Prinz (2017). It aims to introduce to the theory of perturbatively quantized General Relativity coupled to Spinor Electrodynamics, provide the results thereof and set the notation to serve as a starting point for further research in this direction. It includes the differential geometric and Hopf algebraic background, as well as the corresponding Lagrange density and some renormalization theory. Then, a particular problem in the renormalization of Quantum General Relativity coupled to Quantum Electrodynamics is addressed and solved by a generalization of Furry’s Theorem. Next, the restricted combinatorial Green’s functions for all two-loop propagators and all one-loop divergent subgraphs thereof are presented. Finally, relations between these one-loop restricted combinatorial Green’s functions necessary for multiplicative renormalization are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Complexity and near extremal charged black branes

Highlights: • Trying to explore a remedy to overcome the puzzle in holographic complexity by assuming a cutoff behind the horizon and the corresponding boundary term. • Holographic complexity growth obtained by the WDW patch on shell action is insensitive to the UV cutoff at the late time. Therefore one may conclude that either on shell action does not compute complexity, or the late time is not given by the physical charges, or in our computations we have missed something! • We find that one needs to carefully compute on shell action taking into account the behind the horizon and the corresponding boundary term. Doing so, one arrives at a consistent picture. • We check this consistency by evaluating the late time complexity growth for near horizon limit of the near extremal black hole using two different methods. We would have obtained non-consistent picture, if we had not considered the behind the horizon cutoff as well as the corresponding boundary term. We compute holographic complexity of charged black brane solutions in arbitrary dimensions for the near horizon limit of near extremal case using two different methods. The corresponding complexity may be obtained either by taking the limit from the complexity of the charged black brane, or by computing the complexity for near horizon limit of near extremal solution. One observes that these results coincide if one assumes to have a cutoff behind horizon whose value is fixed by UV cutoff and also taking into account a proper counterterm evaluated on this cutoff. We also consider the situation for Vaidya charged black branes too.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Post-Newtonian kinetic theory

A kinetic theory for relativistic gases in the presence of gravitational fields is developed in the second post-Newtonian approximation. The corresponding Boltzmann equation is determined from the evolution of the one-particle distribution function with respect to the proper time along the world line of the particle. From the knowledge of the equilibrium Maxwell–Jüttner distribution function in the second post-Newtonian approximation the components of the particle four-flow and energy–momentum tensor are obtained. The Eulerian hydrodynamic equations for the mass density, mass-energy density and momentum density in the second post-Newtonian approximation are determined from the Boltzmann equation. It is shown that the combination of the hydrodynamic equations of mass and mass-energy densities leads to the hydrodynamic equation for the internal energy density in the first post-Newtonian approximation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Non-local entanglement and fast scrambling in de-Sitter holography

We study holographic entanglement and information scrambling in de-Sitter (dS) space in the context of the DS/dS correspondence. We find that our previously identified non-local entanglement structure of dS vacua can be extended out of the time-reflection symmetric slice. We extend the geometry to a two-sided configuration and calculate the zero-time mutual information between two intervals on different sides when there is a localized shock wave in the bulk. Interestingly, we find that the information scrambling time saturates the fast scrambler bound proposed by Sekino and Susskind and that the shock wave renders a wormhole to be traversable. Furthermore, we calculate a two-sided out-of-time-ordered correlator (OTOC) in the late time regime and we see that, before scrambling, it exponentially grows with an exponent whose value saturates the maximal bound of chaos proposed by Maldacena, Shenker and Stanford. At the end, we provide an explanation why the exponential growing of the late-time OTOC with the maximal bound of chaos saturated and the traversability of the wormhole are simple results of the non-local entanglement structure and we point out that this is a realization of the ER=EPR proposal.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Distinguishing localization from chaos: Challenges in finite-size systems

Highlights: • Provides an overview of the current understanding of the many-body localization phase transition. • Discusses the subtleties of finite-size scaling near this transition • Assesses the implications of these subtleties for numerical studies of spin chains. • Explores scaling of diagnostics in models with known localization transitions. • Presents suggestions for future numerical work. We re-examine attempts to study the many-body localization transition using measures that are physically natural on the ergodic/quantum chaotic regime of the phase diagram. Using simple scaling arguments and an analysis of various models for which rigorous results are available, we find that these measures can be particularly adversely affected by the strong finite-size effects observed in nearly all numerical studies of many-body localization. This severely impacts their utility in probing the transition and the localized phase. In light of this analysis, we discuss a recent study (Šuntajs et al., 2020) of the behaviour of the Thouless energy and level repulsion in disordered spin chains, and its implications for the question of whether MBL is a true phase of matter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

On the generalised equipartition law

We observe that the so-called Generalised Equipartition Law for hamiltonian systems is actually valid only under specific hypotheses – unfortunately omitted in some textbooks – which limit its applicability when dealing with nonlinear systems. We introduce a new coordinate-independent generalisation which overcomes this problem and can be applied to a larger set of functions. A simple example of application is discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Gravitational wave scattering theory without large-distance asymptotics

In conventional gravitational wave scattering theory, a large-distance asymptotic approximation is employed. In this approximation, the gravitational wave is approximated by its large-distance asymptotics. In this paper, we establish a gravitational wave scattering theory without the large-distance asymptotic approximation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

On restricting first order form of gauge theories to one-loop order

Highlights: • We prove the equivalence of the first and second-order formalism. • We use Lagrange multiplier fields to limit radiative effects to one-loop order. • We prove that the quantized theory is both renormalizable and unitary. The first order form of the Yang–Mills and Einstein–Hilbert actions are quantized, and it is shown how Green’s functions computed using the first and the second order form of these theories are related. Next we show how by use of Lagrange multiplier fields (LM), radiative effects beyond one-loop order can be eliminated. This allows one to compute Green’s functions exactly without loss of unitarity. The consequences of this restriction on radiative effects are examined for the Yang–Mills and Einstein–Hilbert actions. In these two gauge theories, we find that the quantized theory is both renormalizable and unitary once the LM field is used to eliminate effects beyond one-loop order.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Low-frequency and Moiré–Floquet engineering: A review

Highlights: • Review of theoretical and experimental advances in Floquet engineering. • Review of theories to derive effective Floquet Hamiltonians, with a focus on the low-frequency regime. • Review of the theoretical effects of light in Moiré materials. We review recent work on low-frequency Floquet engineering and its application to quantum materials driven by light, focusing on van der Waals systems hosting Moiré superlattices. These non-equilibrium systems combine the twist-angle sensitivity of the band structure with the flexibility of light drives. The frequency, amplitude, and polarization of light can be tuned in experimental setups, leading to platforms with on-demand properties. First, we review recent theoretical developments to derive effective Floquet Hamiltonians, emphasizing the low-frequency regime. We then review applications of some of these theories to study twisted graphene and transition metal dichalcogenide systems irradiated by light in free space and inside a waveguide. We study the changes induced in the quasienergies and steady-states, which can lead to topological transitions. Next, we consider van der Waals magnetic materials driven by low-frequency light pulses in resonance with the phonons. We discuss the phonon dynamics induced by the light and the resulting magnetic transitions from a Floquet perspective. We finish by outlining new directions for Moiré–Floquet engineering in the low-frequency regime and their relevance for technological applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗