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The inter-molecular structure of semidilute polymer solutions is studied theoretically. The low density limit of a generalized Ornstein-Zernicke integral equation approach to polymeric liquids is considered. Scaling laws for the…
The Heisenberg-Ising spin ladder is one of the few short-range models showing confinement of elementary excitations without the need of an external field, neither transverse nor longitudinal. This feature makes the model suitable for an…
The Bethe-Salpeter eigenvalue problem is a structured eigenvalue problem arising in many-body physics. In practice, a few of the smallest positive eigenvalues and the corresponding eigenvectors need to be computed. In principle, the LOBPCG…
We explore the energy spectrum of a non-relativistic particle bound in a linear finite range, attractive potential, envisaged as a quark-confining potential. The intricate transcendental eigenvalue equation is solved numerically to obtain…
This note extends the modulated entropy and free energy methods for proving mean-field limits/propagation of chaos to the whole space without any confining potential, in contrast to previous work limited to the torus or requiring…
We use the structure of conditionally independent states to analyze the stability of topological entanglement entropy. For the ground state of quantum double or Levin-Wen model, we obtain a bound on the first order perturbation of…
We investigate stability of both localized time-periodic coherent states (pulsons) and uniformly distributed coherent states (oscillating condensate) of a real scalar field satisfying the Klein-Gordon equation with a logarithmic…
We compile some easily deducible information on the discrete eigenvalue spectra of spinless Salpeter equations encompassing, besides a relativistic kinetic term, interactions which are expressible as superpositions of an attractive Coulomb…
This work presents the continuation of the recent article "The Lorenz system: hidden boundary of practical stability and the Lyapunov dimension", published in the Nonlinear Dynamics journal. In this work, in comparison with the results for…
A simple system of two particles in a bidimensional configurational space $S$ is studied. The possibility of breaking in $S$ the time independent Schr\"{o}dinger equation of the system into two separated one-dimensional one-body…
The Poincar\'e-covariant quantum-field-theoretic description of bound states by the homogeneous Bethe-Salpeter equation usually exhibits an intrinsic complexity that can be attenuated by allowing this formalism to undergo various…
In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…
We present a bouquet of continuity bounds for quantum entropies, falling broadly into two classes: First, a tight analysis of the Alicki-Fannes continuity bounds for the conditional von Neumann entropy, reaching almost the best possible…
We derive a version of the so-called "best Fokker-Planck approximation" (BFPA) to describe the spatial properties of interacting active Ornstein-Uhlenbeck particles (AOUPs) in arbitrary spatial dimensions. In doing so, we also take into…
The Freud ensemble of random matrices is the unitary invariant ensemble corresponding to the weight $\exp(-n |x|^{\beta})$, $\beta>0$, on the real line. We consider the local behaviour of eigenvalues near zero, which exhibits a transition…
We derive the self-consistent random phase approximations (sc-RPA) from the projective truncation approximation (PTA) for the equation of motion of two-time Green's function. The obtained sc-RPA applies to arbitrary temperature and recovers…
We investigate the lifted TASEP and its generalization, the GL-TASEP. We analyze the spectral properties of the transition matrix of the lifted TASEP using its Bethe ansatz solution, and use them to determine the scaling of the relaxation…
We present a model where the lepton masses are the eigenvalues of relativistic nonlinear field equations. The eigenfunctions correspond in the model to lepton states with inner structure. In this picture the self-interaction leads to the…
The approximation of the eigenvalues and eigenfunctions of an elliptic operator is a key computational task in many areas of applied mathematics and computational physics. An important case, especially in quantum physics, is the computation…
Conserved quantities such as energy or the electric charge of a closed system, or the Runge-Lenz vector in Kepler dynamics are determined by its global, local, or accidental symmetries. They were instrumental to advances such as the…