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Nicolas Loizeau
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Nicolas Loizeau
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GitHub - nicolasloizeau/PauliStrings.jl: Quantum many body systems with Pauli strings
Quantum many body systems with Pauli strings. Contribute to nicolasloizeau/PauliStrings.jl development by creating an account on GitHub.
Getting started Â· PauliStrings.jl
Documentation for PauliStrings.jl.
Unveiling Order from Chaos by approximate 2-localization of random matrices
Quantum many-body systems are typically endowed with a tensor product structure. This structure is inherited from probability theory, where the probability of two independent events is the product of the probabilities. The tensor product structure of a Hamiltonian thus gives a natural decomposition of the system into independent smaller subsystems. Considering a particular Hamiltonian and a particular tensor product structure, one can ask: is there a basis in which this Hamiltonian has this desired tensor product structure? In particular, we ask: is there a basis in which an arbitrary Hamiltonian has a 2-local form, i.e. it contains only pairwise interactions? Here we show, using numerical and analytical arguments, that generic Hamiltonian (e.g. a large random matrix) can approximately be written as a linear combination of two-body interactions terms with high precision; that is the Hamiltonian is 2-local in a carefully chosen basis. We show that these Hamiltonians are robust to perturbations. Taken together, our results suggest a possible mechanism for the emergence of locality from chaos.
Channel capacity enhancement with indefinite causal order
Classical communication capacity of a channel can be enhanced either through a device called a ``quantum switch'' or by putting the channel in a quantum superposition. The gains in the two cases, although different, have their origin in the use of a quantum resource, but is it the same resource? Here this question is explored through simulating large sets of random channels. We find that quantum superposition always provides an advantage, while the quantum switch does not: it can either increase or decrease communication capacity. The origin of this discrepancy can be attributed to a subtle combination of superposition and noncommutativity.
Bibliometric projects
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Citation Tree.
Dark matter
Galaxy rotation curves disfavor traditional and self-interacting dark matter halos, preferring a disk component or ad-hoc Einasto function
We use the galaxy rotation curves in the SPARC database to compare 9 different dark matter and modified gravity models on an equal footing, paying special attention to the stellar mass-to-light ratios. We compare three non-interacting dark matter models, a self interacting DM (SIDM) model, two hadronically interacting DM (HIDM) models, and three modified Newtonian dynamics type models: MOND, Radial Acceleration Relation (RAR) and a maximal-disk model. The models with Gas-DM interactions generate a disky component in the dark matter, which significantly improves the fits to the rotation curves compared to all other models except an ad-hoc Einasto halo; the MOND-type models give significantly worse fits.
Non-spherical dark matter structures detection
A rotation curve inequality that holds for spherically symmetric mass distributions is derived, and tested against the SPARC galaxy rotation curves dataset. We identify several Galaxies, eg NGC7793 and UGC05253, which are candidates for hosting non-spherical dark matter structures that could be detected by more precise measurements.
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