arXiv subjects

Ding Jia

Publications and source records attributed to Ding Jia.

At least 37 records · Page 2Linked to original sources

arXiv2022

World quantum gravity: Quantum test objects and Synge's world function

A new path integral approach of quantum gravity based on relational variables and quantum test objects is presented. We take as a basic variables the squared invariant distance. This invariant quantity is technically simpler to work with than variant quantities such as the metric tensor. It also facilitates the studies of matter coupling and quantum spacetime causal structures. In contrast to approaches based on piecewise linear geometries, here gravity is captured by its effects on quantum test particles and fields. By an observation of Parker, under a Feynman sum a gravitational phase can be traded into a Van Vleck-Morette determinant term. This leads to a new candidate path integral for gravity, which can potentially be computed efficient in the Lorentzian signature. We discuss some ambiguities left in the path integral measure, which invite further clarifications.

gr-qc↗

arXiv2022

Time-space duality in 2D quantum gravity

An important task faced by all approaches of quantum gravity is to incorporate superpositions and quantify quantum uncertainties of spacetime causal relations. We address this task in 2D. By identifying a global $Z_2$ symmetry of 1+1D quantum gravity, we show that gravitational path integral configurations come in equal amplitude pairs with timelike and spacelike relations exchanged. As a consequence, any two points are equally probable to be timelike and spacelike separated in a universe without boundary conditions. In the context of simplicial quantum gravity we identify a local symmetry of the action which shows that even with boundary conditions causal uncertainties are generically present. Depending on the boundary conditions, causal uncertainties can still be large and even maximal.

gr-qc↗

arXiv2022

Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects

Evaluating gravitational path integrals in the Lorentzian has been a long-standing challenge due to the numerical sign problem. We show that this challenge can be overcome in simplicial quantum gravity. By deforming the integration contour into the complex, the sign fluctuations can be suppressed, for instance using the holomorphic gradient flow algorithm. Working through simple models, we show that this algorithm enables efficient Monte Carlo simulations for Lorentzian simplicial quantum gravity. In order to allow complex deformations of the integration contour, we provide a manifestly holomorphic formula for Lorentzian simplicial gravity. This leads to a complex version of simplicial gravity that generalizes the Euclidean and Lorentzian cases. Outside the context of numerical computation, complex simplicial gravity is also relevant to studies of singularity resolving processes with complex semi-classical solutions. Along the way, we prove a complex version of the Gauss-Bonnet theorem, which may be of independent interest.

gr-qc↗

arXiv2021

Acoustic non-Hermitian skin effect from twisted winding topology

The recently discovered non-Hermitian skin effect (NHSE) manifests the breakdown of current classification of topological phases in energy-nonconservative systems, and necessitates the introduction of non-Hermitian band topology. So far, all NHSE observations are based on one type of non-Hermitian band topology, in which the complex energy spectrum winds along a closed loop. As recently characterized along a synthetic dimension on a photonic platform, non-Hermitian band topology can exhibit almost arbitrary windings in momentum space, but their actual phenomena in real physical systems remain unclear. Here, we report the experimental realization of NHSE in a one-dimensional (1D) non-reciprocal acoustic crystal. With direct acoustic measurement, we demonstrate that a twisted winding, whose topology consists of two oppositely oriented loops in contact rather than a single loop, will dramatically change the NHSE, following previous predictions of unique features such as the bipolar localization and the Bloch point for a Bloch-wave-like extended state. This work reveals previously unnoticed features of NHSE, and provides the observation of physical phenomena originating from complex non-Hermitian winding topology.

physics.app-ph↗

arXiv2021

Observation of dislocation-induced topological modes in a three-dimensional acoustic topological insulator

The interplay between real-space topological lattice defects and the reciprocal-space topology of energy bands can give rise to novel phenomena, such as one-dimensional topological modes bound to screw dislocations in three-dimensional topological insulators. We obtain direct experimental observations of dislocation-induced helical modes in an acoustic analog of a weak three-dimensional topological insulator. The spatial distribution of the helical modes is found through spin-resolved field mapping, and verified numerically by tight-binding and finite-element calculations. These one-dimensional helical channels can serve as robust waveguides in three-dimensional media. Our experiment paves the way to studying novel physical modes and functionalities enabled by topological lattice defects in three-dimensional classical topological materials.

cond-mat.mes-hall↗

arXiv2021

Vortex states in an acoustic Weyl crystal with a topological lattice defect

We design and implement a three dimensional acoustic Weyl metamaterial hosting robust modes bound to a one-dimensional topological lattice defect. The modes are related to topological features of the bulk bands, and carry nonzero orbital angular momentum locked to the direction of propagation. They span a range of axial wavenumbers defined by the projections of two bulk Weyl points to a one-dimensional subspace, in a manner analogous to the formation of Fermi arc surface states. We use acoustic experiments to probe their dispersion relation, orbital angular momentum locked waveguiding, and ability to emit acoustic vortices into free space. These results point to new possibilities for creating and exploiting topological modes in three-dimensional structures through the interplay between band topology in momentum space and topological lattice defects in real space.

cond-mat.mes-hall↗

arXiv2021

Correlational quantum theory and correlation constraints

A correlational dialect is introduced within the quantum theory language to give a unified treatment of finite-dimensional informational/operational quantum theories, infinite-dimensional relativistic quantum theories, and quantum gravity. Theories are written in terms of correlation diagrams which specify correlation types and weights. Grouping similar correlation diagrams leads to generalized Feynman diagrams, which in special cases reduce to the familiar Feynman diagrams from quantum field theories. The correlational formalism is applied in a study of correlation constraints, revealing new classes of quantum processes that evade previous characterizations of general quantum processes. The results apply to quantum theories of various kinds, including time-asymmetric theories, time-symmetric theories, theories without predefined time, and theories with indefinite causal structures.

quant-ph↗

arXiv2021

Demonstration of negative refraction induced by synthetic gauge fields

The phenomenon of negative refraction generally requires negative refractive indices or phase discontinuities, which can be realized using metamaterials or metasurfaces. Recent theories have proposed a novel mechanism for negative refraction based on synthetic gauge fields, which affect classical waves as if they were charged particles in electromagnetic fields, but this has not hitherto been demonstrated in experiment. Here, we report on the experimental demonstration of gauge-field-induced negative refraction in a twisted bilayer acoustic metamaterial. The bilayer twisting produces a synthetic gauge field for sound waves propagating within a projected two-dimensional geometry, with the magnitude of the gauge field parameterized by the choice of wavenumber along the third dimension. Waveguiding with backward propagating modes is also demonstrated in a trilayer configuration that implements strong gauge fields. These results provide an alternative route to achieving negative refraction in synthetic materials.

physics.app-ph↗

arXiv2020

Ultraviolet regularity from quantum gravitational indefinite causal structure

Indefinite causal structure is generically present in theories of quantum gravity admitting a path integral formulation. We show that summing over causal structures eliminates ultraviolet divergences of matter QFT and resolves spacetime singularities using the non-perturbative World Quantum Gravity approach. Independent information-theoretic and model-independent considerations suggest that the mechanism of ultraviolet regularization by indefinite causal structure also applies to other theories of quantum gravity.

gr-qc↗

arXiv2019

Causally neutral quantum physics

In fundamental theories that accounts for quantum gravitational effects, the spacetime causal structure is expected to be quantum uncertain. Previous studies of quantum causal structure focused on finite-dimensional systems. Here we present an algebraic framework that incorporates both finite- and infinite-dimensional systems including quantum fields. Thanks to the absence of a definite spacetime causal structure, Lagrangian quantum field theories can be studied on a quantum superposition of spacetimes with a point identification structure.

quant-ph↗

arXiv2019

Causal order as a resource for quantum communication

In theories of communication, it is usually presumed that the involved parties perform actions in a fixed causal order. However, practical and fundamental reasons can induce uncertainties in the causal order. Here we show that a maximal uncertainty in the causal order forbids asymptotic quantum communication, while still enabling the noisy transfer of classical information. Therefore causal order, like shared entanglement, is an additional resource for communication. The result is formulated within an asymptotic setting for processes with no fixed causal order, which sets a basis for a quantum information theory in general quantum causal structures.

quant-ph↗

arXiv2018

Topological triply-degenerate point with double Fermi arcs

Unconventional chiral particles have recently been predicted to appear in certain three dimensional (3D) crystal structures containing three- or more-fold linear band degeneracy points (BDPs). These BDPs carry topological charges, but are distinct from the standard twofold Weyl points or fourfold Dirac points, and cannot be described in terms of an emergent relativistic field theory. Here, we report on the experimental observation of a topological threefold BDP in a 3D phononic crystal. Using direct acoustic field mapping, we demonstrate the existence of the threefold BDP in the bulk bandstructure, as well as doubled Fermi arcs of surface states consistent with a topological charge of 2. Another novel BDP, similar to a Dirac point but carrying nonzero topological charge, is connected to the threefold BDP via the doubled Fermi arcs. These findings pave the way to using these unconventional particles for exploring new emergent physical phenomena.

cond-mat.other↗

arXiv2018

Quantum from principles without assuming definite causal structure

There has been a body of works deriving the complex Hilbert space structure of quantum theory from axioms/principles/postulates to deepen our understanding about quantum theory and to reveal ways to go beyond it to resolve foundational issues. Recent progresses in incorporating indefinite causal structure into physical theories suggest that a more comprehensive understanding of both quantum theory and the theory beyond it accounts for indefinite causal structure. We formulate a framework of physical theories without assuming definite causal structure and identify postulates that single out the complex Hilbert space structure. More than one complex Hilbert space theory is compatible with the postulates, which leaves the room for the further search of the best among these theories.

quant-ph↗

arXiv2018

Reduction of correlations by quantum indefinite causal structure

We show that quantum indefinite causal structure generically reduce two-party correlations. For significant indefiniteness in the causal structure captured by some general conditions, the correlation is shown to be reduced down to zero. The result offers an operational model-independent ultraviolet regularization mechanism. It may be applied to various approaches of quantum gravity that allow quantum indefinite spacetime causal structure.

quant-ph↗

arXiv2018

Quantum field theory with indefinite causal structure

Quantum field theory (QFT) in classical spacetime has revealed interesting and puzzling aspects about gravitational systems, in particular black hole thermodynamics and its information processing. Although quantum gravitational effects may be relevant for a better understanding of these topics, a commonly accepted framework for studying QFT with quantum gravitational effects is missing. We present a theory for studying quantum fields in the presence of quantum indefinite causal structure. This theory incorporates quantum properties of spacetime causal structure in a model independent way, and exposes universal features of quantum spacetime which are independent of the details about its microscopic degrees of freedom (strings, loops, causal sets...).

quant-ph↗

arXiv2018

Generalizing Entanglement

The expected indefinite causal structure in quantum gravity poses a challenge to the notion of entanglement: If two parties are in an indefinite causal relation of being spacelike and timelike, can they still be entangled? If so, how does one measure the amount of entanglement? We propose to generalize the notions of entanglement and entanglement measure to address these questions. Incidentally but importantly, the generalization opens the path to study quantum entanglement of states, channels, networks and processes with definite or indefinite causal structure in a unified fashion, e.g., we show that the entanglement distillation capacity of a state, the quantum communication capacity of a channel, and the entanglement generation capacity of a network or a process are different manifestations of one and the same entanglement measure.

quant-ph↗

arXiv2018

Analogue of Null Geodesic in Quantum Spacetime

In classical spacetime null geodesics give information on where free massless particles travel. In quantum spacetime where quantum indefiniteness renders spacetime fuzzy null geodesics as sharp trajectories cannot be retained. We propose a "tendency postulate" that gives information on where free massless objects tend to travel based exclusively on meaningful notions in quantum spacetime. It says that free massless objects tend to trace large quantum causal fluctuations. We implement the tendency postulate in concrete models of quantum spacetime that describe causal fluctuation. The tendency postulate supports the suggestion that information can leak out of black holes in a quantum spacetime without introducing superluminal signalling.

quant-ph↗

arXiv2018

Quantifying Causality in Quantum and General Models

In studies of entanglement, finding out if a state is entangled and quantifying the amount of entanglement contained in a state are related but different questions. Similarly in studies of causality, finding out the causal structures compatible with a model and quantifying the causal strengths are related but different questions. Recently much research have been directed towards the first question but considerably less attention is paid to the second one. In this paper we propose axioms for all reasonable quantitative measures of causality to obey. The axioms apply to a broad family of operational probabilistic theories with and without definite causal structure. For quantum models, we study causality measures based on one-shot quantum capacities in detail. These measures are used to define the notions of quantum signalling and quantum causality measures in order to quantify quantum causality.

quant-ph↗