Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “density matrix”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

The reflected entanglement spectrum for free fermions

We consider the reflected entropy and the associated entanglement spectrum for free fermions reduced to two intervals in 1 + 1 dimensions. Working directly in the continuum theory the reflected entropy can be extracted from the spectrum of a singular integral equation whose kernel is determined by the known free fermion modular evolved correlation function. We find the spectrum numerically and analytically in certain limits. For intervals that almost touch the reflected entanglement spectrum approaches the spectrum of the thermal density matrix. This suggests that the reflected entanglement spectrum is well suited to the task of extracting physical data of the theory directly from the ground state wave function.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Quantum error correction in the black hole interior

We study the quantum error correction properties of the black hole interior in a toy model for an evaporating black hole: Jackiw-Teitelboim gravity entangled with a non-gravitational bath. After the Page time, the black hole interior degrees of freedom in this system are encoded in the bath Hilbert space. We use the gravitational path integral to show that the interior density matrix is correctable against the action of quantum operations on the bath which (i) do not have prior access to details of the black hole microstates, and (ii) do not have a large, negative coherent information with respect to the maximally mixed state on the bath, with the lower bound controlled by the black hole entropy and code subspace dimension. Thus, the encoding of the black hole interior in the radiation is robust against generic, low-rank quantum operations. For erasure errors, gravity comes within an O (1) distance of saturating the Singleton bound on the tolerance of error correcting codes. For typical errors in the bath to corrupt the interior, they must have a rank that is a large multiple of the bath Hilbert space dimension, with the precise coefficient set by the black hole entropy and code subspace dimension.

2D gravity↗
DOE OSTI2024

Lattice realizations of topological defects in the critical (1+1)-d three-state Potts model

Topological/perfectly-transmissive defects play a fundamental role in the analysis of the symmetries of two dimensional conformal field theories (CFTs). In the present work, spin chain regularizations for these defects are proposed and analyzed in the case of the three-state Potts CFT. In particular, lattice versions for all the primitive defects are presented, with the remaining defects obtained from the fusion of the primitive ones. The defects are obtained by introducing modified interactions around two given sites of an otherwise homogeneous spin chain with periodic boundary condition. The various primitive defects are topological on the lattice except for one, which is topological only in the scaling limit. The lattice models are analyzed using a combination of exact diagonalization and density matrix renormalization group techniques. Low-lying energy spectra for different defect Hamiltonians as well as entanglement entropy of blocks located symmetrically around the defects are computed. The latter provides a convenient way to compute the g-function which characterizes various defects. Finally, the eigenvalues of the line operators in the “crossed channel” and fusion of different defect lines are also analyzed. The results are all in agreement with expectations from conformal field theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Quantum error correction from complexity in Brownian SYK

We study the robustness of quantum error correction in a one-parameter ensemble of codes generated by the Brownian SYK model, where the parameter quantifies the encoding complexity. The robustness of error correction by a quantum code is upper bounded by the “mutual purity” of a certain entangled state between the code subspace and environment in the isometric extension of the error channel, where the mutual purity of a density matrix ρAB is the difference $\mathcal{F}$ p ($A : B$) ≡ $\mathrm{T}$r $p^{2}_{AB}$ - $\mathrm{T}$r $p^{2}_{A}$ $\mathrm{T}$r $p^{2}_{B}$. We show that when the encoding complexity is small, the mutual purity is O(1) for the erasure of a small number of qubits (i.e., the encoding is fragile). However, this quantity decays exponentially, becoming O(1/N) for O(log N) encoding complexity. Further, at polynomial encoding complexity, the mutual purity saturates to a plateau of O(e -N ). We also find a hierarchy of complexity scales associated to a tower of subleading contributions to the mutual purity that quantitatively, but not qualitatively, adjust our error correction bound as encoding complexity increases. In the AdS/CFT context, our results suggest that any portion of the entanglement wedge of a general boundary subregion A with sufficiently high encoding complexity is robustly protected against low-rank errors acting on A with no prior access to the encoding map. From the bulk point of view, we expect such bulk degrees of freedom to be causally inaccessible from the region A despite being encoded in it.

1/N expansion↗
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 OSTI2025

First measurement of D* + vector meson spin alignment in Pb–Pb collisions at $\sqrt{{s}_{\text{NN}}}={5}.0{2}$ TeV

The first measurement of prompt D *+ -meson spin alignment in ultrarelativistic heavy-ion collisions with respect to the direction orthogonal to the reaction plane is presented. The spin alignment is quantified by measuring the element ρ 00 of the diagonal spin-density matrix for prompt D *+ mesons with 4 < p T < 30 GeV/c in two rapidity intervals, |y| < 0.3 and 0.3 < |y| < 0.8, in central (0–10%) and midcentral (30–50%) Pb–Pb collisions at $\sqrt{{s}_{\text{NN}}}={5}.0{2}$ TeV. Evidence of spin alignment ρ 00 > 1/3 has been found for p T > 15 GeV/c and 0.3 < |y| < 0.8 with a significance of 3.1σ. The measured spin alignment of prompt D *+ mesons is compared with the one of inclusive J/ψ mesons measured at forward rapidity (2.5 < y < 4).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Effective Field Theory for jet substructure in heavy ion collisions

I develop an Effective Field Theory (EFT) framework to compute jet substructure observables for heavy ion collision experiments. As an example, I consider dijet events that accompany the formation of a weakly coupled long lived Quark Gluon Plasma (QGP) medium in a heavy ion collision and look at an observable insensitive to jet selection bias: the simultaneous measurement of jet mass along with the transverse momentum imbalance between the jets that are groomed to remove soft radiation. Treating the jet as an open quantum system, I write down a factorization formula within the SCET (Soft Collinear Effective Theory) framework in the forward scattering regime. The physics of the medium is encoded in a universal soft field correlator while the jet-medium interaction is captured by a medium induced jet function. The factorization formula leads to a Lindblad type equation for the evolution of the reduced density matrix of the jet in the Markovian approximation. The solution for this equation allows a resummation of large logarithms that arise due to the final state measurements imposed while simultaneously summing over multiple incoherent interactions of the jet with the medium.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Perturbation theory for the logarithm of a positive operator

In various contexts in mathematical physics, such as out-of-equilibrium physics and the asymptotic information theory of many-body quantum systems, one needs to compute the logarithm of a positive unbounded operator. Examples include the von Neumann entropy of a density matrix and the flow of operators with the modular Hamiltonian in the Tomita-Takesaki theory. Often, one encounters the situation where the operator under consideration, which we denote by ∆, can be related by a perturbative series to another operator ∆ 0 , whose logarithm is known. We set up a perturbation theory for the logarithm log ∆. It turns out that the terms in the series possess a remarkable algebraic structure, which enables us to write them in the form of nested commutators plus some “contact terms”.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Symmetry-resolved entanglement entropy, spectra & boundary conformal field theory

We perform a comprehensive analysis of the symmetry-resolved (SR) entanglement entropy (EE) for one single interval in the ground state of a 1 + 1D conformal field theory (CFT), that is invariant under an arbitrary finite or compact Lie group, G. We utilize the boundary CFT approach to study the total EE, which enables us to find the universal leading order behavior of the SREE and its first correction, which explicitly depends on the irreducible representation under consideration and breaks the equipartition of entanglement. We present two distinct schemes to carry out these computations. The first relies on the evaluation of the charged moments of the reduced density matrix. This involves studying the action of the defect-line, that generates the symmetry, on the boundary states of the theory. This perspective also paves the way for discussing the infeasibility of studying symmetry resolution when an anomalous symmetry is present. The second scheme draws a parallel between the SREE and the partition function of an orbifold CFT. This approach allows for the direct computation of the SREE without the need to use charged moments. From this standpoint, the infeasibility of defining the symmetry-resolved EE for an anomalous symmetry arises from the obstruction to gauging. Finally, we derive the symmetry-resolved entanglement spectra for a CFT invariant under a finite symmetry group. We revisit a similar problem for CFT with compact Lie group, explicitly deriving an improved formula for U(1) resolved entanglement spectra. Using the Tauberian formalism, we can estimate the aforementioned EE spectra rigorously by proving an optimal lower and upper bound on the same. In the abelian case, we perform numerical checks on the bound and find perfect agreement.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Accelerated impurity solver for DMFT and its diagrammatic extensions

Here, we present ComCTQMC, a GPU accelerated quantum impurity solver. It uses the continuous-time quantum Monte Carlo (CTQMC) algorithm wherein the partition function is expanded in terms of the hybridisation function (CT-HYB). ComCTQMC supports both partition and worm-space measurements, and it uses improved estimators and the reduced density matrix to improve observable measurements whenever possible. ComCTQMC efficiently measures all one and two-particle Green's functions, all static observables which commute with the local Hamiltonian, and the occupation of each impurity orbital. ComCTQMC can solve complex-valued impurities with crystal fields that are hybridized to both fermionic and bosonic baths. Most importantly, ComCTQMC utilizes graphical processing units (GPUs), if available, to dramatically accelerate the CTQMC algorithm when the Hilbert space is sufficiently large. We demonstrate acceleration by a factor of over 600 (100) in a simulation of δ-Pu at 600 K with (without) crystal fields. In easier problems, the GPU offers less impressive acceleration or even decelerates the CTQMC. Here we describe the theory, algorithms, and structure used by ComCTQMC in order to achieve this set of features and level of acceleration.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

QuDPy: A Python-based tool for computing ultrafast non-linear optical responses

Nonlinear Optical Spectroscopy is a well-developed field with theoretical and experimental advances that have benefited multiple disciplines, including chemistry, biology, and physics. However, for the accurate interpretation of the corresponding multi-dimensional spectra, there is a need for precise quantum dynamical simulations based on model Hamiltonians. In this article, we present the initial release of our code, QuDPy (Quantum Dynamics in Python), which provides a robust numerical platform for performing quantum dynamics simulations based on model systems, including open quantum systems. Furthermore, a distinguishing feature of our approach is the ability to specify various high-order optical response pathways in the form of double-sided Feynman diagrams through a straightforward input syntax. This syntax outlines the time-ordering of ket-sided or bra-sided optical interactions acting on the time-evolving density matrix of the system. We utilize the quantum dynamics capabilities of QuTip to simulate the spectral response of complex systems, allowing us to compute virtually any $n$-th order optical response of the model system. To illustrate the utility of our approach, we provide a series of example calculations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Mutual information prediction for strongly correlated systems

We have trained a new machine-learning (ML) model which predicts mutual information (MI) for strongly correlated systems. This is a complex quantity, which is much more difficult to predict than one-site entropies, but carries important information about the correlation structure inside electronic systems. In this work, we replaced the expensive density matrix renormalization group (DMRG) calculations by newly trained ML model for prediction of the mutual information. We show the performance of the model on two important tasks: (a) to determine the correlation structure and (b) to determine ordering of orbitals for accurate DMRG calculations. In conclusion, the results are compared with the MI obtained from accurate DMRG calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Thermal diffusivity and thermal conductivity of SiC composite tubes: the effects of microstructure and irradiation

Cladding thermal conductivity is an important physical property in assessing the performance of silicon carbide (SiC)-cladded fuels for nuclear reactors. However, there is a significant lack of reliable data, particularly for irradiated materials, because the geometry complicates the measurement. This study investigates the thermal diffusivity of coupons with a curvature, machined from SiC fiber–reinforced SiC matrix composite tubes, with and without neutron irradiation under light water reactor–relevant temperature and dose conditions. The tested materials included full composite and duplex SiC composite tubes. The measurements were conducted using a modern flash diffusivity apparatus. The analyzed area on the specimen during diffusivity testing was reduced for improved measurement accuracy due to sample curvature. Post-irradiation measurements showed that the effects of neutron irradiation on thermal conductivity (e.g. thermal defect resistivity) are different between SiC composite plates versus tubes. The difference was explained by higher matrix density of the tube than the plate. This study provides reliable thermal properties of prototypic SiC composite tubes useful for fuel performance modeling of SiC-based cladding.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

On the connection between perturbation theory and new semiclassical expansion in quantum mechanics

Here, it is shown that for the one-dimensional anharmonic oscillator with potential V(x) = ax 2 + bgx 3 + ... = $\frac{1}{g^2}$ $\hat{V}$ (gx), as well as for the radial oscillator V(r) = $\frac{1}{g^2}$ $\hat{V}$ (gr) and for the perturbed Coulomb problem V(r) = $\frac{a}{r}$ + βgr + ... = g $\tilde{V}$ (gr), the Perturbation Theory in powers of the coupling constant g (weak coupling regime) and the semiclassical expansion in powers of $\hbar$ 1/2 for the energies coincide. This is related to the fact that the dynamics developed in two spaces: x (r)-space and gx (gr)-space, lead to the same energy spectra. The equations which govern dynamics in these two spaces, the Riccati-Bloch equation and the Generalized Bloch equation, respectively, are presented. It is shown that the perturbation theory for the logarithmic derivative of the wavefunction in - space leads to (true) semiclassical expansion in powers of $\hbar$ 1/2 ; for the one-dimensional case this corresponds to the flucton calculus for the density matrix in the path integral formalism in Euclidean (imaginary) time proposed by one of the authors. Matching the perturbation theory in powers of g and the semiclassical expansion in powers of $\hbar$ 1/2 for the wavefunction leads to a highly accurate local approximation in the entire coordinate space, its expectation value for the Hamiltonian provides a prescription for the summation of the perturbative (trans)-series.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Impact of globally spin-aligned vector mesons on the search for the chiral magnetic effect in heavy-ion collisions

In high-energy heavy-ion collisions, the chiral magnetic effect (CME) is predicted to arise from the interplay between the chirality imbalance of quarks in the nuclear medium and the intense magnetic field, and will cause a charge separation along the magnetic field direction. While the search for the CME is still ongoing in experiments at Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC), the CME-sensitive observables need to be scrutinized to exclude the non-CME contributions. In this work, we examine the influence of globally spin-aligned ρ mesons on the γ 112 correlator, the R Ψ 2 (ΔS) correlator, and the signed balance functions, via a toy model and a multiphase transport model (AMPT). The global spin alignment of vector mesons could originate from non-CME mechanisms in heavy-ion collisions, and is characterized by the 00-component of the spin density matrix, ρ 00 . Here, we find that the CME observables show similar dependence on ρ 00 , and could receive a positive (negative) contribution from ρ-decay pions, if the ρ 00 of ρ mesons is larger (smaller) than 1/3. Since pions are the most abundant particles in such collisions, the ρ 00 measurements for ρ mesons become crucial to the interpretation of the CME data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Multireference Embedding and Fragmentation Methods for Classical and Quantum Computers: From Model Systems to Realistic Applications

One of the primary challenges in quantum chemistry is the accurate modeling of strong electron correlation. While multireference methods effectively capture such correlation, their steep scaling with system size prohibits their application to large molecules and extended materials. Quantum embedding offers a promising solution by partitioning complex systems into manageable subsystems. In this Review, we highlight recent advances in multireference density matrix embedding and localized active space self-consistent field approaches for complex molecules and extended materials. We discuss both classical implementations and the emerging potential of these methods on quantum computers. Here, by extending classical embedding concepts to the quantum landscape, these algorithms have the potential to expand the reach of multireference methods in quantum chemistry and materials.

Algorithms↗
DOE OSTI2024

Site Suitability and Air Pollution Impacts of Composting Infrastructure for California’s Organic Waste Diversion Law

The emerging field of polaritonic chemistry explores the behavior of molecules under strong coupling with cavity modes. Despite recent developments in ab initio polaritonic methods for simulating polaritonic chemistry under electronic strong coupling, their capabilities are limited, especially in cases where the molecule also features strong electronic correlation. To bridge this gap, we have developed a novel method for cavity QED calculations utilizing the Density Matrix Renormalization Group (DMRG) algorithm in conjunction with the Pauli–Fierz Hamiltonian. Our approach is applied to investigate the effect of the cavity on the S0–S1 transition of n-oligoacenes, with n ranging from 2 to 5, encompassing 22 fully correlated π orbitals in the largest pentacene molecule. Our findings indicate that the influence of the cavity intensifies with larger acenes. Additionally, we demonstrate that, unlike the full determinantal representation, DMRG efficiently optimizes and eliminates excess photonic degrees of freedom, resulting in an asymptotically constant computational cost as the photonic basis increases.

54 ENVIRONMENTAL SCIENCES↗