Phase transitions in non-Hermitian systems are at the focus of cutting edge theoretical and experimental research. On the one hand, parity-time- (PT-) and anti-PT-symmetric physics have gained ever-growing interest, due to the existence of non-Hermitian sp ...
Two dynamical systems are topologically equivalent when their phase-portraits can be morphed into each other by a homeomorphic coordinate transformation on the state space. The induced equivalence classes capture qualitative properties such as stability or ...
With ever greater computational resources and more accessible software, deep neural networks have become ubiquitous across industry and academia.
Their remarkable ability to generalize to new samples defies the conventional view, which holds that complex, ...
The present thesis deals with problems arising from discrete mathematics, whose proofs make use of tools from algebraic geometry and topology. The thesis is based on four papers that I have co-authored, three of which have been published in journals, and o ...
We propose a protocol to simulate the evolution of a non-Markovian open quantum system by considering a collisional process with a many-body system, which plays the role of an environment. As a result of our protocol, the environment spatial correlations a ...
By taking inspiration from the backflow transformation for correlated systems, we introduce a tensor network Ansatz which extends the well-established matrix product state representation of a quantum many-body wave function. This structure provides enough ...
We consider the phase retrieval problem of reconstructing a n -dimensional real or complex signal X ⋆ from m (possibly noisy) observations Y μ = | ∑ n i = 1 Φ μ i X ⋆ i / √ n | , for a large class of correlated real and complex random sensing matrices Φ , ...
For any prime power q, Mori and Tanaka introduced a family of q-ary polar codes based on the q x q Reed-Solomon polarization kernels. For transmission over a q-ary erasure channel, they also derived a closed-form recursion for the erasure probability of ea ...
We establish a direct connection between general tensor networks and deep feed-forward artificial neural networks. The core of our results is the construction of neural-network layers that efficiently perform tensor contractions and that use commonly adopt ...
We revisit the problem of constraining the weak field limit of the gravitational lagrangian from S-matrix properties. From unitarity and Lorentz invariance of the S-matrix of massless gravitons, we derive on-shell gauge invariance to consist on the transve ...
