arXiv subjects

Eugenio Bianchi

Publications and source records attributed to Eugenio Bianchi.

At least 19 recordsLinked to original sources

arXiv2026

On Radiative Fluxes and Coulombic Charges in the Balance Law for Black Hole Evaporation

In asymptotically-flat spacetimes, there is a clear distinction between radiative fluxes and Coulombic charges. Using the Wald-Zoupas prescription, we identify the classical radiative flux of a massless scalar field in 3+1 dimensions. In a spherically-symmetric model of black hole evaporation, the balance law yields a Bondi mass correction related to the entanglement entropy of Hawking radiation. The renormalized flux is nonnegative, differs from the Fulling-Davies formula, and coincides with the Ashtekar-Taveras-Varadarajan flux. We discuss implications for 3+1 black hole evaporation.

gr-qc↗

arXiv2026

Observables are glocal

We show that the problem of observables can be fully resolved for background independent theories defined on graphs, through the explicit construction of complete observables. The appropriate analogue of coordinate independence is argued to be the invariance under changes of graph labels, a kind of permutation invariance. Invariants are formed by group averaging and they probe the entire graph -- they are global. Strikingly, sets of complete observables can be constructed so that each of the invariants comprising them seeks a connected subgraph structure -- local correlations. Geometrical information is fully encoded through this subtle interplay of global and local graph notions, a behavior we term glocal. This provides physically meaningful complete sets of observables for discrete general relativity, and a permutation invariant reformulation of the spin networks state space of loop quantum gravity. Our analysis reveals an important new aspect of the problem of observables, demonstrating a deep connection between the theory of spacetime and computational complexity theory: the construction of a complete set of observables for discrete spacetime theories is computationally costly, as it corresponds to solving a graph isomorphism problem.

gr-qc↗

arXiv2026

Minimum lifetime of a black hole

We derive bounds on the lifetime of an evaporating black hole. The bound follows from energy conservation and purification, within the framework of `asymptotically semiclassical spacetimes'. We use the recently derived expression for the Bondi flux of Hawking radiation, together with the expression for the entanglement entropy of Hawking radiation at null infinity, to investigate the purification phase after the last semiclassical ray. We discuss the energy-cost of entanglement purification and we find a lower bound on the purification time of the black hole, which scales as $M_0^4/\hbar^{3/2}$, where $M_0$ is the initial black hole mass. Additionally, motivated by quantum gravity considerations, we include the additional assumption that a Planck mass black hole is metastable. With this assumption, we find that the the purification time is extended to be exponential in the square of the initial black hole mass, i.e. in its initial area. We find that the redshift exponent is negative in this purification phase, which indicates the existence of a white-hole remnant which releases information slowly. We comment on phenomenological implications for primordial black hole remnants.

gr-qc↗

arXiv2026

Typical entanglement entropy with charge conservation

We consider a many-body Hilbert space with a fixed global charge and show that the typical entanglement entropy of a subsystem, at the leading and subleading order in the thermodynamic limit, can be expressed in terms of a single quantity which represents the local thermal entropy at fixed charge density. We find a general formula which applies both to abelian U(1) symmetry and non-abelian SU(2) symmetry, including the case of a local Hilbert space which transforms under a general reducible representation of the symmetry group. We illustrate the general formula with model systems and discuss the relevance of the results as a probe of quantum chaos for physical Hamiltonians.

quant-ph↗

arXiv2026

Toller matrices and the Feynman $i\varepsilon$ in spinfoams

We study the analytic properties and three equivalent representations of the Toller matrices $T^{(\pm)}$ which appear in the causal formulation of spinfoam transition amplitudes for 4d Lorentzian quantum gravity. These are polynomially bounded functions on the Lorentz group which satisfy the relation $T^{(+)}+T^{(-)}=D$, where the Wigner matrix $D$ provides a unitary irreducible representation of $SL(2,C)$. Ruhl's definition of $T^{(\pm)}$ in terms of analyticity and asymptotic properties is shown to be equivalent to the recently introduced Feynman $i\varepsilon$ prescription in spinfoams. We show that, equivalently, they can be represented as an integral over eigenvalues of the boost operator, which results in a sum over residues. The latter reproduces the Wick rotation relating Euclidean $Spin(4)$ to Lorentzian $SL(2,C)$ spinfoams studied by Dona, Gozzini and Nicotra. We provide explicit expressions in terms of hypergeometric functions and specialize them to the $γ$-simple representations relevant for spinfoams.

gr-qc↗

arXiv2026

Spinfoams, $γ$-duality and parity violation in primordial gravitational waves

The Barbero-Immirzi parameter $γ$ appears as a coupling constant in the spinfoam dynamics of loop quantum gravity. In this work, we highlight that $γ$ can be understood as a measure of gravitational parity violation via a duality rotation for the EPRL spinfoam model. We call this property $γ$-duality, and we investigate an effective field theory for gravity and a scalar field with the same degree of parity violation. The resulting relation between the coupling constants of parity-even and parity-odd higher-curvature terms in the effective action is determined by $γ$, opening the possibility of its measurement in the semiclassical regime. For a choice of $γ$-dual effective action, we study cosmic inflation and show that the observation of a primordial tensor polarization, together with the tensor tilt and the tensor-to-scalar ratio, provides a measurement of the Barbero-Immirzi parameter and, therefore, of the scale of discreteness of the quantum geometry of space.

gr-qc↗

arXiv2026

Causal structure in spin-foams

The metric field of general relativity is almost fully determined by its causal structure. Yet, in spin-foam models for quantum gravity, the role played by the causal structure is still largely unexplored. The goal of this paper is to clarify how causality is encoded in such models. The quest unveils the physical meaning of the orientation of the two-complex and its role as a dynamical variable. We propose a causal version of the EPRL spin-foam model and discuss the role of the causal structure in the reconstruction of a semiclassical spacetime geometry.

gr-qc↗

arXiv2026

Causal spinfoam vertex for 4d Lorentzian quantum gravity

We introduce a new causal spinfoam vertex for $4$d Lorentzian quantum gravity. The causal data are encoded in Toller $T$-matrices, which add to Wigner $D$-matrices $T^{(+)}+T^{(-)}=D$, and for which we provide a Feynman $\mathrm{i}\varepsilon$ representation. We discuss how the Toller poles cancel in the EPRL vertex, how the Livine-Oriti model is obtained in the Barrett-Crane limit, and how spinfoam causal data are distinct from Regge causal data. In the large-spin limit, we show that only Lorentzian Regge geometries with causal data compatible with the spinfoam data are selected, resulting in a single exponential $\exp(+\mathrm{i}\, S_{\mathrm{Regge}}/\hbar)$ and a new form of causal rigidity.

gr-qc↗

arXiv2026

A Maximum Entropy Conjecture for Black Hole Mergers

The final state of a binary black hole merger is predicted with high precision by numerical relativity, but could there be a simple thermodynamic principle within general relativity that governs the selection of the remnant? Using post-Newtonian relations between the mass M (including the binding energy) and angular momentum J of quasi-circular, nonspinning binaries, we uncover a puzzling result: When the binary's instantaneous M and J are mapped to those of a hypothetical Kerr black hole, the corresponding entropy exhibits a maximum during the evolution. This maximum occurs at values of M and J strikingly close to those of the final remnant predicted by numerical relativity. Consistent behavior is observed when using the relation between M and J obtained from numerical relativity evolution. Although this procedure is somewhat ad hoc, the agreement between the masses and spins of the final state obtained from numerical relativity and the results of this maximum entropy procedure is remarkable, with agreement to within a few percent when using either post-Newtonian or numerical relativity results for M and J. These findings allow us to propose an entropy maximization conjecture for binary black hole mergers, hinting that thermodynamic principles may govern the selection of the final black hole state.

gr-qc↗

arXiv2025

Precision predictions of Starobinsky inflation with self-consistent Weyl-squared corrections

Starobinsky's $R+αR^2$ inflation provides a compelling one-parameter inflationary model that is supported by current cosmological observations. However, at the same order in spacetime derivatives as the $R^2$ term, an effective theory of spacetime geometry must also include the Weyl-squared curvature invariant $W^2$. In this paper, we study the inflationary predictions of the gravitational theory with action of the form $R+αR^2 - βW^2$, where the coupling constant $α$ sets the scale of inflation, and corrections due to the $W^2$ term are treated self-consistently via reduction of order in an expansion in the coupling constant $β$, at the linear order in $β/α$. Cosmological perturbations are found to be described by an effective action with a nontrivial speed of sound $c_{\textrm{s}}$ for scalar and $c_{\textrm{t}}$ for tensor modes, satisfying the relation $c_{\textrm{t}}/c_{\textrm{s}} \simeq 1+ \fracβ{6\, α}$ during the inflationary phase. Within this self-consistent framework, we compute several primordial observables up to the next-to-next-to-next-to leading order (N3LO). We find the tensor-to-scalar ratio $r \simeq 3(1-\fracβ{6α})(n_\textrm{s}-1)^2$, the tensor tilt $n_{\textrm{t}}\simeq-\frac{r}{8}$ and the running of the scalar tilt $\mathfrak{a}_{\textrm{s}}\simeq-\frac{1}{2} (n_{\textrm{s}} - 1)^2$, all expressed in terms of the observed scalar tilt $n_{\textrm{s}}$. We also provide the corresponding corrections up to N3LO, $\mathcal{O}((n_{\textrm{s}} - 1)^3)$.

gr-qc↗

arXiv2025

Adiabatic vacua from linear complex structures

Adiabatic vacua play a central role in quantum fields in cosmological spacetimes, where they serve as distinguished initial conditions and as reference states for the renormalization of observables. In this paper we introduce new methods based on linear complex structures which provide a powerful tool for determining adiabatic vacua. The new methods generalize both the standard WKB appoach and the Lewis-Riesenfeld invariants, and allow us to study the problem of many coupled bosonic degrees of freedom with general quadratic time-dependent Hamiltonian. We show that the adiabatic number operator and the adiabatic vacuum of finite order can be expressed in terms of the adiabatic complex structure of the same order. We compare our results to standard techniques which apply only to a single degree of freedom, and comment on its applicability to problems in quantum fields in cosmological spacetimes, many-body systems and quantum thermodynamics, where the Hamiltonian is time dependent with slowly-changing parameters.

gr-qc↗

arXiv2025

Squeezed vacua and primordial features in effective theories of inflation at N2LO

A finite duration of cosmic inflation can result in features $\mathcal{P}_{\mathcal{R}}(k) = |α_k-β_k\,\mathrm{e}^{\mathrm{i}δ_k}|^2 \,\mathcal{P}_{\mathcal{R}}^{(0)}(k)$ in the primordial power spectrum that carry information about a quantum gravity phase before inflation. While the almost scale-invariant power spectrum $\mathcal{P}_{\mathcal{R}}^{(0)}$ for the quasi-Bunch-Davies vacuum is fully determined by the inflationary background dynamics, the Bogoliubov coefficients $α_k$ and $β_k$ for the squeezed vacuum depend on new physics beyond inflation and have been used to produce phenomenological templates for the features. The phase $δ_k$ vanishes in de Sitter space and therefore is often neglected, but it results in non-trivial effects in quasi-de Sitter inflationary geometries. Here we consider a large class of effective theories of inflation and provide a closed-form expression for $δ_k$ and for the fully expanded power spectrum up to next-to-next-leading order (N2LO) in the Hubble-flow expansion. In particular, for the Starobinsky model of inflation we find that this relative phase can be expressed in terms of the scalar tilt $n_\mathrm{s}$ as $δ_{k\ast}=\fracπ{2}(n_\mathrm{s}-1)-\fracπ{4}(n_\mathrm{s}-1)^2\,\ln(k/k_*)$. The relative phase results in a negative shift and a running frequency that have been considered in the most studied phenomenological templates for primordial features, thus providing precise theoretical predictions for upcoming cosmological observations.

gr-qc↗

arXiv2024

Bosonic and fermionic Gaussian states from Kähler structures

We show that bosonic and fermionic Gaussian states (also known as "squeezed coherent states") can be uniquely characterized by their linear complex structure $J$ which is a linear map on the classical phase space. This extends conventional Gaussian methods based on covariance matrices and provides a unified framework to treat bosons and fermions simultaneously. Pure Gaussian states can be identified with the triple $(G,Ω,J)$ of compatible Kähler structures, consisting of a positive definite metric $G$, a symplectic form $Ω$ and a linear complex structure $J$ with $J^2=-1\!\!1$. Mixed Gaussian states can also be identified with such a triple, but with $J^2\neq -1\!\!1$. We apply these methods to show how computations involving Gaussian states can be reduced to algebraic operations of these objects, leading to many known and some unknown identities. We apply these methods to the study of (A) entanglement and complexity, (B) dynamics of stable systems, (C) dynamics of driven systems. From this, we compile a comprehensive list of mathematical structures and formulas to compare bosonic and fermionic Gaussian states side-by-side.

quant-ph↗

arXiv2024

Primordial power spectrum at N3LO in effective theories of inflation

We develop a systematic framework to compute the primordial power spectrum up to next-to-next-to-next to leading order (N3LO) in the Hubble-flow parameters for a large class of effective theories of inflation. We assume that the quadratic action for perturbations is characterized by two functions of time, the kinetic amplitude and the speed of sound, that are independent of the Fourier mode $k$. Using the Green's function method introduced by Stewart and Gong and extended by Auclair and Ringeval, we determine the primordial power spectrum fully expanded around a pivot scale up to N3LO, starting from a given generic action for perturbations. As a check, we reproduce the state-of-the-art results for scalar and the tensor power spectra of the simplest "vanilla" models of single-field inflation. The framework applies to Weinberg's effective field theory of inflation (with the condition of no parity violation) and to the effective theory of spontaneous de Sitter-symmetry breaking. As a concrete application, we provide the expression for the N3LO power spectrum of $R+R^2$ Starobinsky inflation in metric variables. All expressions are provided in terms of an expansion in one single parameter, the number of inflationary e-foldings $N_\ast$. Surprisingly, we find that, compared to previous leading-order calculations, for $N_\ast = 55$ the N3LO correction results in a $7\%$ decrease of the predicted tensor-to-scalar ratio, in addition to a deviation from the consistency relation and a prediction of a negative running $α_\mathrm{s}=-\frac{1}{2}(n_\mathrm{s}-1)^2+\ldots$ of the scalar tilt. These results provide precise theoretical predictions for the next generation of CMB observations.

gr-qc↗

arXiv2024

Non-abelian symmetry-resolved entanglement entropy

We introduce a mathematical framework for symmetry-resolved entanglement entropy with a non-abelian symmetry group. To obtain a reduced density matrix that is block-diagonal in the non-abelian charges, we define subsystems operationally in terms of subalgebras of invariant observables. We derive exact formulas for the average and the variance of the typical entanglement entropy for the ensemble of random pure states with fixed non-abelian charges. We focus on compact, semisimple Lie groups. We show that, compared to the abelian case, new phenomena arise from the interplay of locality and non-abelian symmetry, such as the asymmetry of the entanglement entropy under subsystem exchange, which we show in detail by computing the Page curve of a many-body system with SU(2) symmetry.

quant-ph↗

arXiv2023

Loop Quantum Gravity and Quantum Information

We summarize recent developments at the interface of quantum gravity and quantum information, and discuss applications to the quantum geometry of space in loop quantum gravity. In particular, we describe the notions of link entanglement, intertwiner entanglement, and boundary spin entanglement in a spin-network state. We discuss how these notions encode the gluing of quanta of space and their relevance for the reconstruction of a quantum geometry from a network of entanglement structures. We then focus on the geometric entanglement entropy of spin-network states at fixed spins, treated as a many-body system of quantum polyhedra, and discuss the hierarchy of volume-law, area-law and zero-law states. Using information theoretic bounds on the uncertainty of geometric observables and on their correlations, we identify area-law states as the corner of the Hilbert space that encodes a semiclassical geometry, and the geometric entanglement entropy as a probe of semiclassicality.

gr-qc↗

arXiv2022

Volume-law entanglement entropy of typical pure quantum states

The entanglement entropy of subsystems of typical eigenstates of quantum many-body Hamiltonians has been recently conjectured to be a diagnostic of quantum chaos and integrability. In quantum chaotic systems it has been found to behave as in typical pure states, while in integrable systems it has been found to behave as in typical pure Gaussian states. In this tutorial, we provide a pedagogical introduction to known results about the entanglement entropy of subsystems of typical pure states and of typical pure Gaussian states. They both exhibit a leading term that scales with the volume of the subsystem, when smaller than one half of the volume of the system, but the prefactor of the volume law is fundamentally different. It is constant (and maximal) for typical pure states, and it depends on the ratio between the volume of the subsystem and of the entire system for typical pure Gaussian states. Since particle-number conservation plays an important role in many physical Hamiltonians, we discuss its effect on typical pure states and on typical pure Gaussian states. We prove that while the behavior of the leading volume-law terms does not change qualitatively, the nature of the subleading terms can change. In particular, subleading corrections can appear that depend on the square root of the volume of the subsystem. We unveil the origin of those corrections. Finally, we discuss the connection between the entanglement entropy of typical pure states and analytical results obtained in the context of random matrix theory, as well as numerical results obtained for physical Hamiltonians.

quant-ph↗

arXiv2021

The Page Curve for Fermionic Gaussian States

In a seminal paper, Page found the exact formula for the average entanglement entropy for a pure random state. We consider the analogous problem for the ensemble of pure fermionic Gaussian states, which plays a crucial role in the context of random free Hamiltonians. Using recent results from random matrix theory, we show that the average entanglement entropy of pure random fermionic Gaussian states in a subsystem of $N_A$ out of $N$ degrees of freedom is given by $\langle S_A\rangle_\mathrm{G}\!=\!(N\!-\!\tfrac{1}{2})Ψ(2N)\!+\!(\tfrac{1}{4}\!-\!N_A)Ψ(N)\!+\!(\tfrac{1}{2}\!+\!N_A\!-\!N)Ψ(2N\!-\!2N_A)\!-\!\tfrac{1}{4}Ψ(N\!-\!N_A)\!-\!N_A$, where $Ψ$ is the digamma function. Its asymptotic behavior in the thermodynamic limit is given by $\langle S_A\rangle_\mathrm{G}\!=\! N(\log 2-1)f+N(f-1)\log(1-f)+\tfrac{1}{2}f+\tfrac{1}{4}\log{(1-f)}\,+\,O(1/N)$, where $f=N_A/N$. Remarkably, its leading order agrees with the average over eigenstates of random quadratic Hamiltonians with number conservation, as found by Lydzba, Rigol and Vidmar. Finally, we compute the variance in the thermodynamic limit, given by the constant $\lim_{N\to\infty}(ΔS_A)^2_{\mathrm{G}}=\frac{1}{2}(f+f^2+\log(1-f))$.

quant-ph↗