Related papers: Nonlinear level crossing models
We study a class of multistate Landau-Zener model which cannot be solved by integrability conditions or other standard techniques. By analyzing analytical constraints on its scattering matrix and performing fitting to results from numerical…
Current deep neural networks are highly overparameterized (up to billions of connection weights) and nonlinear. Yet they can fit data almost perfectly through variants of gradient descent algorithms and achieve unexpected levels of…
We revisit the problem of an elastic line (e.g. a vortex line in a superconductor) subject to both columnar disorder and point disorder in dimension $d=1+1$. Upon applying a transverse field, a delocalization transition is expected, beyond…
We determine the propagation properties of a quantum particle in a d-dimensional lattice with hopping disorder, delta-correlated in time. The system is delocalized: the averaged transition probability shows a diffusive behavior. Then,…
We studied how the inhomogeneity of a sequence affects the phase transition that takes place at DNA melting. Unlike previous works, which considered thermodynamic quantities averaged over many different inhomogeneous sequences, we focused…
The study of crossing probabilities - i.e. probabilities of existence of paths crossing rectangles - has been at the heart of the theory of two-dimensional percolation since its beginning. They may be used to prove a number of results on…
We study the effect of an environment consisting of noninteracting two level systems on Landau-Zener transitions with an interest on the performance of an adiabatic quantum computer. We show that if the environment is initially at zero…
We investigate dynamical aspects of the discrete nonlinear Schr\"{o}dinger equation (DNLS) in finite lattices. Starting from a periodic chain with nearest neighbor interactions, we insert randomly links connecting distant pairs of sites…
We study the applicability of the Zhu-Nakamura theory to a class of time-dependent quantum mechanical level-crossing models called superparabolic level-glancing models. The phenomenon of a level glancing, being on the borderline between a…
The degenerate Landau-Zener-Majorana-St\"uckelberg model consists of two degenerate energy levels whose energies vary with time and in the presence of an interaction which couples the states of the two levels. In the adiabatic limit, it…
A simple mechanical analog describing Landau-Zener tunneling effect is proposed using two weakly coupled chains of nonlinear oscillators with gradually decreasing (first chain) and increasing (second chain) masses. The model allows to…
One dimensional pinning models have been widely studied in the physical and mathematical literature, also in presence of disorder. Roughly speaking, they undergo a transition between a delocalized phase and a localized one. In mathematical…
Dynamical phase transitions (DPTs) characterize critical changes in system behavior occurring at finite times, providing a lens to study nonequilibrium phenomena beyond conventional equilibrium physics. While extensively studied in quantum…
It is pointed out that there exists an interesting strong and weak duality in the Landau-Zener-Stueckelberg potential curve crossing. A reliable perturbation theory can thus be formulated in the both limits of weak and strong interactions.…
Dynamical phase transitions (DPT) occur after quenching some global parameters in quantum systems and are signalled by the non-analytical time evolution of the dynamical free energy, which is calculated from the Loschmidt overlap between…
We discuss the application of the adiabatic perturbation theory to analyze the dynamics in various systems in the limit of slow parametric changes of the Hamiltonian. We first consider a two-level system and give an elementary derivation of…
This study examines anomalous diffusion and dynamical phase transitions in a nonlinear bouncer model with short-range interactions leading to velocity-dependent (adiabatic) collisions. By varying a control parameter, transitions between…
Random walks serve as important tools for studying complex network structures, yet their dynamics in cases where transition probabilities are not static remain under explored and poorly understood. Here we study nonlinear random walks that…
For the hopping dynamics in a one-dimensional model, containing energy and barrier disorder, we determine the linear and nonlinear response to an external field for arbitrary external frequencies. The calculation is performed in analytical…
A transition between energy levels at an avoided crossing is known as a Landau-Zener transition. When a two-level system (TLS) is subject to periodic driving with sufficiently large amplitude, a sequence of transitions occurs. The phase…