Related papers: Chopping time of the FPU $\alpha$-model
We show interaction between high- and low-frequency modes in periodic $\alpha$-FPU chains with alternating large masses. The treatment discusses the difficult case where the number of particles $N=2p$ involves $p$ prime. A key role is…
The purpose of this paper is to investigate several analytical methods of solving first passage (FP) problem for the Rouse model, a simplest model of a polymer chain. We show that this problem has to be treated as a multi-dimensional…
Quantum phase transitions occur when quantum fluctuation destroys order at zero temperature. With an increase in temperature, normally the thermal fluctuation wipes out any signs of this transition. Here we identify a physical quantity that…
A switching-off process very similar to those in real high-voltage self-blast circuit-breakers is emulated in a model chamber to study the arc properties by optical emission spectroscopy. The arc is operated in a chamber filled with SF$_6$…
This paper is devoted to the study of the flatness property of linear time-invariant fractional systems. In the framework of polynomial matrices of the fractional derivative operator, we give a characterization of fractionally flat outputs…
Thermalization in nonlinear systems is a central concept in statistical mechanics and has been extensively studied theoretically since the seminal work of Fermi, Pasta and Ulam (FPU). Using molecular dynamics and continuum modeling of a…
The well known FPU phenomenon (lack of attainment of equipartition of the mode--energies at low energies, for some exceptional initial data) suggests that the FPU model does not have the mixing property at low energies. We give numerical…
The front dynamics in the Harper (or Aubry-Andr\'e) model (which has a localization transition) is investigated using two different settings, particle number front where the system is at zero temperature, and initially, the particle numbers…
We show that Kramers rate theory gives a straightforward, accurate estimate of the closing time $\tau_c$ of a semiflexible polymer that is valid in cases of physical interest. The calculation also reveals how the time scales of chain…
We consider the thermal breakage of a tethered polymer chain of discrete segments coupled by Morse potentials under constant tensile stress. The chain dynamics at the onset of fracture is studied analytically by Kramers-Langer…
By analytically continuing the time variable in a black hole background, and requiring unitary evolution, it is found that quantum mechanical states at the horizon develop a thermal factor under suitable identification of the physical time.…
Linear-scaling electronic structure methods based on the calculation of moments of the underlying electronic Hamiltonian offer a computationally efficient and numerically robust scheme to drive large-scale atomistic simulations, in which…
We show by means of the theory of the order parameter phase fluctuations that the temperature of "closing" (or "opening") of the gap (and pseudogap) in the electron spectra of superconductors with anisotropic order parameter takes place…
The article provides upper bounds for the blow-up time of a system of fractional differential equations in the Caputo sense. Furthermore, concrete examples of blow-up time estimation are given using a numerical algorithm of the…
We demonstrate the measurement and manipulation of the temperature of cold CO molecules in a microchip environment. Through the use of time-resolved spatial imaging, we are able to observe the phase-space distribution of the molecules, and…
Breakage is generally understood in mechanical terms, yet nano-structures can rupture not only under external loads but also via thermal activation. Here we treat in a general framework the statistical mechanics of thermally induced…
We study the exchange of energy between the modes of the optical branch and those of the acoustic one in a diatomic chain of particles, with masses $m_1$ and $m_2$. We prove that, at small temperature and provided $m_1\gg m_2$, for the…
Breaking of an atomic chain under stress is a collective many-particle tunneling phenomenon. We study classical dynamics in imaginary time by using conformal mapping technique, and derive an analytic formula for the probability of breaking.…
The study of blow-up solution of time-fractional heat equations is of significant and wide-ranging interest for its multitude of applications. These types of equations are used to model several real problems in science and engineering. This…
The phase structure of a four- and eight-fermion interaction model is investigated at finite temperature and chemical potential in arbitrary space-time dimensions, $2\leq D<4$. The effective potential and the gap equation are calculated in…