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We study general singular value shrinkage estimators in high-dimensional regression and classification, when the number of features and the sample size both grow proportionally to infinity. We allow models with general covariance matrices…
We propose an experimental protocol for using cold atoms to create and probe quantum dimer models, thereby exploring the Pauling-Anderson vision of a macroscopic collection of resonating bonds. This process can allow the study of exotic…
We consider the two-dimensional (2d) Ising model on a infinitely long cylinder and study the probabilities $p_i$ to observe a given spin configuration $i$ along a circular section of the cylinder. These probabilities also occur as…
The particle-physics nature of dark matter (DM) remains one of the central open questions in modern physics. A widely used framework to investigate DM properties is provided by simplified models (DMSimps), which extend the Standard Model…
This paper study the hyperexponential stabilization for infinite-dimensional system on Hilbert space by a distributed time depending control law. The well-posedness of the closed loop for every time is obtained through the use of maximal…
Following our previous work of 1905.10745 [hep-th], 2003.11217 [hep-th], we study heterotic interpolating models $D$ dimensionally compactified with constant background fields that include the full set of Wilson lines and radii. Focusing on…
We consider one-dimensional discrete Dirac models in vanishing random environments. In a previous work [6], we showed that these models exhibit a rich phase diagram in terms of their spectrum as a function of the rate of decay of the random…
The Kronig-Penney model with random Dirac potentials on the lattice $\ZM$ has critical energies at which the Lyapunov exponent vanishes and the density of states has a van Hove singularity. This leads to a non-trivial quantum diffusion even…
The cosmological relic density of a Bino-like Lightest Supersymmetric Particle is calculated in the framework of the Minimal Supersymmetric Standard Model. We include annihilation and coannihilation effects of the Bino with the lightest…
This paper discusses the boundary feedback stabilization of a reaction-diffusion equation with Robin boundary conditions and in the presence of a time-varying state-delay. The proposed control design strategy is based on a…
We study the classical dimer model on a square lattice with a single vacancy by developing a graph-theoretic classification of the set of all configurations which extends the spanning tree formulation of close-packed dimers. With this…
We consider the reduced density matrix of a large block of consecutive spins in the ground states of the XY spin chain on an infinite lattice. We derive the spectrum of the density matrix using the expression of the Renyi entropy in terms…
We numerically investigate the momentum-space entanglement entropy and entanglement spectrum of the random-dimer model and its generalizations, which circumvent Anderson localization, after a quench in the Hamiltonian parameters. The type…
Expressions for the density of states $D(E)$, where $D(E)$ is the number of states of energy $E$, are well known. The present paper offers the expressions for generalized density of states $D_N(E,m)$, where $D_N(E,m)$ is the number of…
The development of diffusion-based generative models over the past decade has largely proceeded independently of progress in representation learning. These diffusion models typically rely on regression-based objectives and generally lack…
A numerical study of the statistics of transmission ($t$) and reflection ($r$) of quasi-particles from a one-dimensional disordered lasing or amplifying medium is presented. The amplification is introduced via a uniform imaginary part in…
Using arguments built on ergodicity, we derive an analytical expression for the Renyi entanglement entropies corresponding to the finite-energy density eigenstates of chaotic many-body Hamiltonians. The expression is a universal function of…
A microscopic formalism is developed that includes the coupling to two particle-hole phonons in the particle-hole propagator by extending the dressed random phase approximation (DRPA) equation for a finite system. The resulting formalism is…
The spatial extension and complexity of the eigenfunctions of an open finite-size two-dimensional (2D) random system are systematically studied for a random collection of systems ranging from weakly scattering to localized. The…
A basic theoretical framework is developed in which elementary particles have a component of their wave function extending into higher spatial dimensions. This model postulates an extension of the Schrodinger equation to include a 4th and…