Abstract
We introduce and study a model for the movement of surfaces, namely the conserved, restricted solid-on-solid model. The surface configurations are restricted such that the difference between ...the heights at adjacent sites is no more than one. In addition, the total number of particles is preserved by the dynamics of the model. Mean-field approximations are used to approximate the one-site probability function of the model in both time-independent and time-dependent regimes. In the time-dependent regime, we found that for the height at one site, the average evolves like
t
1/6
and squared fluctuations like
t
1/3
.
Abstract
We investigate the dynamical Casimir-Polder force between an atom and a conducting wall during the time evolution of the system from a partially dressed state. This state is obtained by a ...sudden change of the atomic position with respect to the plate. To evaluate the time-dependent atom-plate Casimir-Polder force we solve the Heisenberg equations for the field and atomic operators by an iterative technique. We find that the dynamical atom-plate Casimir-Polder interaction exhibits oscillation in time, and can be attractive or repulsive depending on time and the atom-wall distance. We also investigate the time dependence of global observables, such as the field and atomic Hamiltonians, and discuss some interesting features of the dynamical process bringing the interaction energy to the equilibrium configuration.
Abstract In this paper, the improved localized method of approximated particular solutions (ILMAPS) using polyharmonic splines with constant polynomial basis is used to approximate solutions of ...nonlinear time-dependent PDEs. The discretization process is done through a simple implicit time stepping and a collocation technique on a set of points in local domains of influence. Resulted system of nonlinear algebraic equations is solved by Newton’s method. Numerical experiments suggest that the proposed method yields superior accuracy than other RBFs as well as FDM for solving nonlinear PDEs.
We analyze quantum dynamics of strongly interacting, kinetically constrained many-body systems. Motivated by recent experiments demonstrating surprising long-lived, periodic revivals after quantum ...quenches in Rydberg atom arrays, we introduce a manifold of locally entangled spin states, representable by low-bond dimension matrix product states, and derive equations of motion for them using the time-dependent variational principle. We find that they feature isolated, unstable periodic orbits, which capture the recurrences and represent nonergodic dynamical trajectories. Our results provide a theoretical framework for understanding quantum dynamics in a class of constrained spin models, which allow us to examine the recently suggested explanation of "quantum many-body scarring" Nat. Phys. 14, 745 (2018)NPAHAX1745-247310.1038/s41567-018-0137-5, and establish a possible connection to the corresponding phenomenon in chaotic single-particle systems.
Neutrinos are key to probing the deep structure of matter and the high-energy Universe. Yet, until recently, their interactions had only been measured at laboratory energies up to about 350 GeV. An ...opportunity to measure their interactions at higher energies opened up with the detection of high-energy neutrinos in IceCube, partially of astrophysical origin. Scattering off matter inside Earth affects the distribution of their arrival directions-from this, we extract the neutrino-nucleon cross section at energies from 18 TeV to 2 PeV, in four energy bins, in spite of uncertainties in the neutrino flux. Using six years of public IceCube High-Energy Starting Events, we explicitly show for the first time that the energy dependence of the cross section above 18 TeV agrees with the predicted softer-than-linear dependence, and reaffirm the absence of new physics that would make the cross section rise sharply, up to a center-of-mass energy sqrts≈1 TeV.
Quantum simulation has the potential to investigate gauge theories in strongly interacting regimes, which are currently inaccessible through conventional numerical techniques. Here, we take a first ...step in this direction by implementing a Floquet-based method for studying \{\Bbb Z}_2\ lattice gauge theories using two-component ultracold atoms in a double-well potential. For resonant periodic driving at the on-site interaction strength and an appropriate choice of the modulation parameters, the effective Floquet Hamiltonian exhibits \{\Bbb Z}_2\ symmetry. We study the dynamics of the system for different initial states and critically contrast the observed evolution with a theoretical analysis of the full time-dependent Hamiltonian of the periodically driven lattice model. We reveal challenges that arise due to symmetry-breaking terms and outline potential pathways to overcome these limitations. Our results provide important insights for future studies of lattice gauge theories based on Floquet techniques.
Supramolecular gels are formed by the self-assembly of small molecules under the influence of various non-covalent interactions. As the interactions are individually weak and reversible, it is ...possible to perturb the gels easily, which in turn enables fine tuning of their properties. Synthetic supramolecular gels are kinetically trapped and usually do not show time variable changes in material properties after formation. However, such materials potentially become switchable when exposed to external stimuli like temperature, pH, light, enzyme, redox, and chemical analytes resulting in reconfiguration of gel matrix into a different type of network. Such transformations allow gel-to-gel transitions while the changes in the molecular aggregation result in alteration of physical and chemical properties of the gel with time. Here, we discuss various methods that have been used to achieve gel-to-gel transitions by modifying a pre-formed gel material through external perturbation. We also describe methods that allow time-dependent autonomous switching of gels into different networks enabling synthesis of next generation functional materials. Dynamic modification of gels allows construction of an array of supramolecular gels with various properties from a single material which eventually extend the limit of applications of the gels. In some cases, gel-to-gel transitions lead to materials that cannot be accessed directly. Finally, we point out the necessity and possibility of further exploration of the field.
Stimuli responsive dynamic changes in the networks of self-assembled gels result in an alteration of physical and chemical properties of the gel with time.
PDF
