Related papers: Discrete Quantitative Isocapacitary Inequality: Fl…
This paper studies the oscillatory behavior of solutions to linear nonautonomous impulsive differential equations with piecewise constant arguments, including both advanced and delayed cases \[ x'(t) = a(t)x(t) + b(t)x([t-k]), \quad k \in…
Numerical models based on partial differential equations (PDE), or integro-differential equations, are ubiquitous in engineering and science, making it possible to understand or design systems for which physical experiments would be…
Variational hybrid quantum-classical optimization represents one of the most promising avenue to show the advantage of nowadays noisy intermediate-scale quantum computers in solving hard problems, such as finding the minimum-energy state of…
We study fluctuations of pressure in equilibrium for classical particle systems. In equilibrium statistical mechanics, pressure for a microscopic state is defined by the derivative of a thermodynamic function or, more mechanically, through…
We study the isospin dynamics in fragment formation within the framework of an analytical model based on the spinodal decomposition scenario. We calculate the probability to obtain fragments with given charge and neutron number, focussing…
We present a method for the study of quantum fluctuations of dissipative structures forming in nonlinear optical cavities, which we illustrate in the case of a degenerate, type I optical parametric oscillator. The method consists in (i)…
In systems far from equilibrium, the fluctuation-dissipation relation is violated due to the lack of detailed balance. Recently, for a class of Langevin equations, it has been proved that this violation is related to energy dissipation as…
Quantum fluctuations impose fundamental limits on measurement and space-time probing. Although using optimised probe fields can allow to push sensitivity in a position measurement beyond the "standard quantum limit", quantum fluctuations of…
We study equilibrium fluctuations for a class of totally asymmetric zero-range type interacting particle systems. As a main result, we show that density fluctuation of our process converges to the stationary energy solution of the…
We have developed a theory for inhomogeneous systems that allows for incorporation of effects of mesoscopic fluctuations. A hierarchy of equations relating the correlation and direct correlation functions for the local excess $\phi({\bf…
We consider the isoperimetric inequality involving the $s$-perimeter and the $t$-perimeter with $0<s<t<1$, and show that the ball is a local minimizer of the (scale-invariant) isoperimetric ratio $\mathcal{F}(E):=P_t(E)^{\frac{1}{n-t}}/…
This paper corrects an earlier work suggesting that the quantum expectation value of the proper length is bounded from below by the Planck length. The original calculation examined fluctuations of the conformal factor of Einstein-Hilbert…
We formulate low Mach number fluctuating hydrodynamic equations appropriate for modeling diffusive mixing in isothermal mixtures of fluids with different density and transport coefficients. These equations eliminate the fluctuations in…
Investigation into the applicability of the equivalence principle in quantum mechanics has taken many forms, with varying conclusions. Here, a dynamical semi-classical description of a wave packet in terms of its center of mass and higher…
Gravitational instabilities of isothermal spheres are studied in the presence of a positive or negative cosmological constant, in the Newtonian limit. In gravity, the statistical ensembles are not equivalent. We perform the analysis both in…
We prove several inequalities estimating the distance between volumes of two bodies in terms of the maximal or minimal difference between areas of sections or projections of these bodies. We also provide extensions in which volume is…
We discuss fluctuations in the measurement process and how these fluctuations are related to the dissipational parameter characterising quantum damping or decoherence. On the example of the measuring current of the variable-barrier or QPC…
Fluctuation relations are powerful equalities that hold far from equilibrium. However, the standard approach to include measurement and feedback schemes may become inapplicable in certain situations, including continuous measurements,…
We study quantitative unique continuation for second order elliptic equations with lower-order terms of H\"older regularity via a weighted frequency function method. We establish quantitative three-ball inequalities and corresponding…
The discrete multiscale analysis for boundary value problems in nonlinear discrete systems leads to a first order discrete modulational instability above a threshold amplitude for wave numbers beyond the zero of group velocity dispersion.…