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Luca Molinari

Publications and source records attributed to Luca Molinari.

3 recordsLinked to original sources

The burden of Fundamentality: Metaphysical ambiguities and the issue of Superdeterminism

In this paper we approach the problem of superdeterminism from a novel point of view, highlighting its character as a more metaphysical than scientific proposition. First, we introduce a distinction between two types of superdeterministic theories, na\"ive (NSD) and metaphysical (MSD), and argue how NSD presents significant epistemic flaws. We show how NSD justifies itself through claims to fundamentality, thus connoting itself as a metaphysical theory rather than a scientific one. We finally illustrate that the most developed MSD model so far, Invariant Set Theory, implicitly proposes a confused form of priority monism. Our paper thus reinforces the thesis that theories should demonstrate rather than assume fundamentality and that it is methodologically flawed for a theory to assume its own fundamentality for the sole purpose of defending against criticisms.

physics.hist-ph

Transfer matrices, non-Hermitian Hamiltonians and Resolvents: some spectral identities

I consider the N-step transfer matrix T for a general block Hamiltonian, with eigenvalue equation L_n ψ_{n+1} + H_n ψ_n + L_{n-1}^\dagger ψ_{n-1} = E ψ_n where H_n and L_n are matrices, and provide its explicit representation in terms of blocks of the resolvent of the Hamiltonian matrix for the system of length N with boundary conditions ψ_0 =ψ_{N+1} =0. I then introduce the related Hamiltonian for the case ψ_0 = z^{-1} ψ_N and ψ_{N+1} = z ψ_1, and provide an exact relation between the trace of its resolvent and Tr(T-z)^{-1}, together with an identity of Thouless type connecting Tr(\log |T|) with the Hamiltonian eigenvalues for z=e^{iϕ}. The results are then extended to T^\dagger T by showing that it is itself a transfer matrix. Besides their own mathematical interest, the identities should be useful for an analytical approach in the study of spectral properties of a physically relevant class of transfer matrices. P.A.C.S.: 02.10.Sp (theory of matrices), 05.60 (theory of quantum transport), 71.23 (Anderson model), 72.17.Rn (Quantum localization)

math-ph

Universality of the Tearing Phase in Matrix Models

The spontaneous symmetry breaking associated to the tearing of a random surface, where large dynamical holes fill the surface, was recently analized obtaining a non-universal critical exponent on a border phase. Here the issue of universality is explained by an independent analysis. The one hole sector of the model is useful to manifest the origin of the (limited) non-universal behaviour, that is the existence of two inequivalent critical points.

hep-th