Authors: Damiano Anselmi, Eugenio Bianchi and Marco Piva
We derive the predictions of quantum gravity with fakeons on the amplitudes and spectral indices of the scalar and tensor fluctuations in inflationary cosmology. The action is R+R2 plus the Weyl-squared term. The ghost is eliminated by turning it into a fakeon, that is to say a purely virtual particle. We work to the next-to-leading order of the expansion around the de Sitter background. The consistency of the approach puts a lower bound (mχ>mϕ/4) on the mass mχ of the fakeon with respect to the mass mϕ of the inflaton. The tensor-to-scalar ratio r is predicted within less than an order of magnitude (4/3
Authors: Lucas Hackl and Eugenio Bianchi
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 J2=−11. Mixed Gaussian states can also be identified with such a triple, but with J2≠−11. 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.
Authors: Eugenio Bianchi, Lucas Hackl and Mario Kieburg
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 NA out of N degrees of freedom is given by ⟨SA⟩G=(N−12)Ψ(2N)+(14−NA)Ψ(N)+(12+NA−N)Ψ(2N−2NA)−14Ψ(N−NA)−NA, where Ψ is the digamma function. Its asymptotic behavior in the thermodynamic limit is given by ⟨SA⟩G=N(log2−1)f+N(f−1)log(1−f)+12f+14log(1−f)+O(1/N), where f=NA/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 limN→∞(ΔSA)2G=12(f+f2+log(1−f)).