Related papers: A note on the uniqueness result for the inverse He…
Two identical particles driven by the same steady force through a viscous fluid may move relative to one another due to hydrodynamic interactions. The presence or absence of this relative translation has a profound effect on the dynamics of…
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we…
We show that fractional exclusion statistics is manifested in general in interacting systems and we discuss the conjecture recently introduced (J. Phys. A: Math. Theor. 40, F1013, 2007), according to which if in a thermodynamic system the…
It is shown that elementary indistinguishability properties of partially polarized mixtures are consistent only with the conventional Hilbert space model of quantum mechanics and a few exotic alternatives. This applies even in low…
In this note we revisit the recent developments concerning rigorous results on the virial series of a continuous system of classical particles interacting via a stable and tempered pair potential and we provide new lower bounds for its…
An inverse problem is considered for an inhomogeneous Schr\"odinger equation. Assuming that the potential vanishes outside a finite interval and satisfies some other technical assumptions, one proves the uniqueness of the recovery of this…
Statistical thermodynamics is valuable as a conceptual structure that shapes our thinking about equilibrium thermodynamic states. A cloud of unresolved questions surrounding the foundations of the theory could lead an impartial observer to…
The Calder\'on problem is an inverse problem with applications to electrical impedance tomography and geophysical prospection. We prove uniqueness in the Calder\'on problem in spatial dimension $n \geq 3$ for scalar conductivities in the…
We investigate the existence of bound states in a one-dimensional quantum system of $N$ identical particles interacting with each other through an inverse square potential. This system is equivalent to the Calogero model without the…
The Gibbs paradox of the first kind (GP1) refers to the false increase in entropy which, in statistical mechanics, is calculated from the process of combining two gas systems S1 and S2 consisting of distinguishable particles. Presented in a…
We consider the dynamics of a tagged particle in an infinite particle environment moving according to a stochastic gradient dynamics. For singular interaction potentials this tagged particle dynamics was constructed first in [FG11], using…
Considering two static, electrically charged, elementary particles, we demonstrate a possible way of proving that all known fundamental forces in the nature are the manifestations of the single, unique interaction. We re-define the gauging…
The issue of irreversibility in a universe with time-reversal-symmetric laws is a central problem in physics. % , and, in particular, to statistical mechanics, information theory and quantum thermodynamics. In this letter, we discuss for…
We consider irreversible translation-invariant interacting particle systems on the $d$-dimensional cubic lattice with finite local state space, which admit at least one Gibbs measure as a time-stationary measure. Under some mild degeneracy…
This work explores fundamental statistical and thermodynamic properties of short-and long-range-interacting systems. The purpose of this study is twofold. Firstly, we rigorously prove that the probability distribution of arbitrary few-body…
In this paper, we survey our recent results on the variational formulation of nonequilibrium thermodynamics for the finite dimensional case of discrete systems as well as for the infinite dimensional case of continuum systems. Starting with…
In this paper the uncertainty principle is found via characteristics of continuous and nowhere differentiable functions. We prove that any physical system that has a continuous and nowhere differentiable position function is subject to an…
We consider the problem of a single particle interacting with $N$ identical fermions, at zero temperature and in one dimension. We calculate the binding energy as well as the effective mass of the single particle. We use an approximate…
These lecture notes present an overview of equilibrium statistical mechanics of classical fluids, with special applications to the structural and thermodynamic properties of systems made of particles interacting via the hard-sphere…
We numerically analyze the dynamical generation of quantum entanglement in a system of 2 interacting particles, started in a coherent separable state, for decreasing values of $\hbar$. As $\hbar\to 0$ the entanglement entropy, computed at…