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We examine the stick-slip fluctuating response of a rough massive non-rotating cylinder moving on a rough inclined groove which is submitted to weak external perturbations and which is maintained well below the angle of repose. The…
A partially hinged, partially free rectangular plate is considered, with the aim to address the possible unstable end behaviors of a suspension bridge subject to wind. This leads to a nonlinear plate evolution equation with a nonlocal…
The ordinary time-dependent perturbation theory of quantum mechanics, that describes the interaction of a stationary system with a time-dependent perturbation, predicts that the transition probabilities induced by the perturbation are…
We show that time dependent couplings may lead to nontrivial scaling properties of the surface fluctuations of the asymptotic regime in non-equilibrium kinetic roughening models . Three typical situations are studied. In the case of a…
Recent experiments have demonstrated the ability to manipulate nonlinear interactions via time modulation, giving rise to the so-called stroboscopic nonlinearity. To date, however, this phenomenon has not been subjected to a rigorous…
The study of stochastic systems has received considerable interest over the years. Their dynamics can describe many equilibrium and nonequilibrium fluctuating systems. At the same time, nonequilibrium constraints interact with the time…
This article studies the problem of estimating the state variable of non-smooth subdifferential dynamics constrained in a bounded convex domain given some real-time observation. On the one hand, we show that the value function of the…
Two coupled two-level systems placed under external time-dependent magnetic fields are modeled by a general Hamiltonian endowed with a symmetry that enables us to reduce the total dynamics into two independent two-dimensional sub-dynamics.…
Analytic and numerical results for quasiperiodic tight-binding models are reviewed, with emphasis on two and three-dimensional models which so far are beyond a mathematically rigorous treatment. In particular, we consider energy spectra of…
We study the dynamics of a two-qubit system coupled through time dependent anisotropic $XYZ$ Heisenberg interaction in presence of a time varying non-uniform external magnetic field. Exact results are presented for the time evolution of the…
We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and…
With large-scale Monte Carlo simulations, we investigate the nonsteady relaxation at the dynamic depinning transition in the two-dimensional Gaussian random-field Ising model. The dynamic scaling behavior is carefully analyzed, and the…
The entanglement dynamics in a non-Hermitian quantum system is studied numerically and analyzed from the viewpoint of quasiparticle picture. As a concrete model, we consider a one-dimensional tight-binding model with asymmetric hopping…
Many-body approaches to open quantum systems have recently become powerful tools for investigating the detailed role of dissipative environments in diverse non-equilibrium molecular and condensed matter processes. Here, we report the…
In this paper, under an abstract setting we establish the spreading properties and the existence, non-existence and global attractivity of spatially heterogeneous steady states for a large class of monotone evolution systems without the…
We study the topological properties of one dimensional systems undergoing unitary time evolution. We show that symmetries possessed both by the initial wavefunction and by the Hamiltonian at all times may not be present in the…
Discontinuous time derivatives are used to model threshold-dependent switching in such diverse applications as dry friction, electronic control, and biological growth. In a continuous flow, a discon- tinuous derivative can generate multiple…
In this work, the interplay between non-Hermiticity, quasi-disorder, and repulsive interaction is studied for hard-core bosons confined in a one-dimensional optical lattice, where non-Hermiticity is induced by the non-reciprocal hoppings…
The derivation of determinant representations for the space-, time-, and temperature-dependent correlation functions of the impenetrable Gaudin-Yang model in the presence of a trapping potential is presented. These representations are valid…
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…