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Measurements of angular correlations between initial and final particles in $\beta$ decay remain one of the most promising ways of probing the Standard Model and looking for new physics. As experiments reach unprecedented precision well…
Random matrix theory yields valuable insights into the universal features of quantum many-body chaotic systems. Although all-to-all interactions are traditionally studied, many interesting dynamical questions, such as transport of a…
We consider random hermitian matrices made of complex blocks. The symmetries of these matrices force them to have pairs of opposite real eigenvalues, so that the average density of eigenvalues must vanish at the origin. These densities are…
It has been known for some years that entanglement entropy obtained from partial trace does not provide the correct entanglement measure when applied to systems of identical particles. Several criteria have been proposed that have the…
A classic feature of gravity is that it is an attractive force. If a source mass is prepared in a localized (classical- like) state, it will cause another probe mass to move towards it. Here we consider the situation in which a source mass…
We consider the effect of a local perturbation on the energy levels of a system described by random matrix theory. An analytic expression for the joint distribution function of initial and final energy levels is obtained. In the case of…
We investigate universal properties of one-dimensional multi-component systems comprised of fermions, bosons, or an arbitrary mixture, with contact interactions and subjected to an external potential. The masses and the coupling strengths…
We revisit the concept of particles as it is used in special relativity. The presented model treats the energy-momentum relation of relativistic particles as the upper branch of a generalized energy-momentum relation of quasi particles.…
We consider a class of rotationally invariant unitary random matrix ensembles where the eigenvalue density falls off as an inverse power law. Under a new scaling appropriate for such power law densities (different from the scaling required…
A new ensemble interpretation of quantum mechanics is proposed according to which the ensemble associated to a quantum state really exists: it is the ensemble of all the systems in the same quantum state in the universe. Individual systems…
Model systems of self-propelled particles reproduce many phenomena observed in laboratory active matter systems that defy our thermal equilibrium-based intuition. In particular, in stationary states of self-propelled systems, it is…
Strongly interacting particles in one dimension subject to external confinement have become a topic of considerable interest due to recent experimental advances and the development of new theoretical methods to attack such systems. In the…
Repulsive self-propelled particles tend to cluster, leading to Motility-Induced Phase Separation (MIPS). By analogy with equilibrium phase separation, the onset of MIPS has been associated with a transition to effective attraction between…
We show that beta ensembles in Random Matrix Theory with generic real analytic potential have the asymptotic equipartition property. In addition, we prove a Central Limit Theorem for the density of the eigenvalues of these ensembles.
We conjecture that for a wide class of interacting particle systems evolving in discrete time, namely conservative cellular automata with piecewise linear flow diagram, relaxation to the limit set follows the same power law at critical…
In finite many-body quantum systems such as nuclei, atoms, mesoscopic systems like quantum dots and small metallic grains, interacting spin systems modeling quantum computing core and BEC, the interparticle interactions are essentially…
This paper studies systems of particles following independent random walks and subject to annihilation, binary branching, coalescence, and deaths. In the case without annihilation, such systems have been studied in our 2005 paper…
In these lectures we discuss some elementary concepts in connection with the theory of symmetric spaces applied to ensembles of random matrices. We review how the relationship between random matrix theory and symmetric spaces can be used in…
The tensor flattenings appear naturally in quantum information when one produces a density matrix by partially tracing the degrees of freedom of a pure quantum state. In this paper, we study the joint $^*$-distribution of the flattenings of…
A new class of electromagnetic composite particles is proposed. The composites are very small (the Compton scale), potentially long-lived, would have unique interactions with atomic and nuclear systems, and, if they exist, could explain a…