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We investigate, both analytically and with numerical simulations, a Monte Carlo dynamics at zero temperature, where a random walker evolving in continuous space and discrete time seeks to minimize its potential energy, by decreasing this quantity at each jump. The resulting dynamics is universal in the sense that it does not depend on the underlying potential energy landscape, as long as it admits a unique minimum; furthermore, the long time regime does not depend on the details of the jump distribution, but only on its behaviour for small jumps. We work out the scaling properties of this dynamics, as embodied by the walker probability density. Our analytical predictions are in excellent agreement with direct Monte Carlo simulations., J. Phys. A: Math. Theor (2021)

In this paper, we prove that the large scale properties of a number of two-dimensional lattice models are rotationally invariant. More precisely, we prove that the random-cluster model on the square lattice with cluster-weight $1\le q\le 4$ exhibits rotational invariance at large scales. This covers the case of Bernoulli percolation on the square lattice as an important example. We deduce from this result that the correlations of the Potts models with $q\in\{2,3,4\}$ colors and of the six-vertex height function with $\Delta\in[-1,-1/2]$ are rotationally invariant at large scales., Comment: 92 pages, 29 pictures

We prove the existence of orbitally stable standing waves with prescribed $L^2$-norm for the following Schr\"odinger-Poisson type equation \label{intro} %{%{ll} i\psi_{t}+ \Delta \psi - (|x|^{-1}*|\psi|^{2}) \psi+|\psi|^{p-2}\psi=0 \text{in} \R^{3}, %-\Delta\phi= |\psi|^{2}& \text{in} \R^{3},%. when $p\in \{8/3\}\cup (3,10/3)$. In the case $3

We consider non-negative solutions to a class of second order degenerate Kolmogorov operators L in non-divergence form, defined in a bounded open domain Omega contained in R^{N+1}. Let K be a compact subset of the closure of Omega, let z be a point of Omega, and let Sigma be a subset of the boundary of Omega. We give sufficient geometric conditions for the validity of the following Carleson type estimate: There exists a positive constant C, depending only on the Kolmogorov operator L, on Omega, Sigma, K and z, such that sup_K u < C u(z), for every non-negative solution u of Lu = 0 in Omega such that u vanishes on Sigma.

The LHCb Muon system performance is presented using cosmic ray events collected in 2009. These events allowed to test and optimize the detector configuration before the LHC start. The space and time alignment and the measurement of chamber efficiency, time resolution and cluster size are described in detail. The results are in agreement with the expected detector performance., Comment: Submitted to JINST and accepted

A new mean field statistical mechanics model of two interacting groups of spins is introduced, and the phase transition is studied in terms of their relative size. A jump of the average magnetization is found for large values of the mutual interaction when the relative percentage of the two populations crosses a critical threshold. It is shown how the critical percentage depends on internal interactions and on the initial magnetizations. The model is interpreted as a prototype of resident-immigrant cultural interaction, and conclusions from the social sciences perspectives are drawn.

We analyse a quantum system consisting of a particle travelling in a model-environment made up of a net of localised two-level subsystems. We examine the dynamics of the entanglement through which the environment acquires information about the direction of propagation of the particle. Our study reproduces, within a nonperturbative investigation, an old result obtained by N. F. Mott in the early days of quantum mechanics.

We study noncommutative geometry at the Quantum Mechanics level by means of a model where noncommutativity of both configuration and momentum spaces is considered. We analyze how this model affects the problem of the two-dimensional gravitational quantum well and use the latest experimental results for the two lowest energy states of neutrons in the Earth's gravitational field to establish an upper bound on the fundamental momentum scale introduced by noncommutativity, namely $\sqrt{\eta}\lesssim1\ \mathrm{meV/c}$, a value that can be improved in the future by up to 3 orders of magnitude. We show that the configuration space noncommutativity has, in leading order, no effect on the problem. We also analyze some features introduced by the model, specially a correction to the presently accepted value of Planck's constant to 1 part in $10^{24}$., Comment: Revtex4, 9 pages

In this paper we study the gauge invariance of the time-dependent Ginzburg–Landau equations through the introduction of a model which uses observable variables. We observe that the various choices of gauge lead to a different representation of such variables and therefore to a different definition of the weak solution of the problem. With a suitable decomposition of the unknown fields, related to the choice of London gauge, we examine the Ginzburg–Landau equations and deduce some energy estimates which prove the existence of a maximal attractor for the system.

We derive thermodynamic Bethe ansatz equations describing the vacuum energy of the SU(2N)/Sp(N) nonlinear sigma model on a cylinder geometry. The starting points are the recently-proposed amplitudes for the scattering among the physical, massive excitations of the theory. The analysis fully confirms the correctness of the S-matrix. We also derive closed sets of functional relations for the pseudoenergies (Y-systems). These relations are shown to be the k-->infinity limit of the Sp(k+1)-related systems studied some years ago by Kuniba and Nakanishi in the framework of lattice models., 11 pages, 1 figure, Latex 2e, uses amssymb, graphicx. v2: typos corrected

We prove existence and multiplicity of T-periodic solutions (for any given T) for the N-body problem in R(m) (any m >= 2) where one of the bodies has mass equal to 1 and the others have masses epsilon alpha(2), ... , epsilon alpha(N), epsilon small. We find solutions such that the body of mass 1 moves close to x = 0 while the body of mass epsilon alpha(i) moves close to one of the circular solutions of the two body problem of period T/k(i), where k(i) is any odd number. No relation has to be satisfied by k(2), ... , k(N).

We give a formulation of the static gauge $$\dot A_0 = 0$$ , on a lattice with periodic boundary conditions. We discuss a complete gauge fixing and as an application we compute the running coupling constant and the Debye mass, showing how in computing gauge invariant quantities no problem arises with the singularity of the propagator.