Related papers: Universal threshold for the dynamical behavior of …
In quantum/wave systems with chaotic classical analogs, wavefunctions evolve in highly complex, yet deterministic ways. A slight perturbation of the system, though, will cause the evolution to diverge from its original behavior increasingly…
Limit theorems for a linear dynamical system with random interactions are established. These theorems enable us to characterize the dynamics of a large complex system in details and assess whether a large complex system is stable or…
We investigate numerically the relaxation dynamics of an elastic string in two-dimensional random media by thermal fluctuations starting from a flat configuration. Measuring spatial fluctuations of its mean position, we find that the…
We investigate the non-equilibrium dynamics of a class of isolated one-dimensional systems possessing two degenerate ground states, initialized in a low-energy symmetric phase. We report the emergence of a time-scale separation between fast…
We propose and study a one-dimensional $2\times 2$ hyperbolic Eulerian system with local relaxation from critical threshold phenomena perspective. The system features dynamic transition between strictly and weakly hyperbolic. For different…
Scalar field theories regularized on a $D$ dimensional lattice are found to exhibit double scaling for a class of critical behaviors labeled by an integer $m\geq 2$. The continuum theory reached in the double scaling limit defines a…
Gravitational and electrostatic interactions are fundamental examples of systems with long-range interactions. Equilibrium properties of simple models with long-range interactions are well understood and exhibit exotic behaviors : negative…
Cell monolayers and epithelial tissues display slow dynamics during the liquid-glass transitions, a phenomenon with direct relevance to embryogenesis, tumor metastases, and wound healing. In active cells, persistent motion and cell…
Long-range interactions and, in particular, two-body potentials with power-law long-distance tails are ubiquitous in nature. For two bosons or fermions in one spatial dimension, the latter case being formally equivalent to three-dimensional…
In the first part of the thesis we consider the constraints of causality and unitarity for particles interacting via strictly finite-range interactions. We generalize Wigner's causality bound to the case of non-vanishing partial-wave…
Physical kinetic roughening processes are well known to exhibit universal scaling of observables that fluctuate in space and time. Are there analogous dynamic scaling laws that are unique to the chemical reaction mechanisms available…
Quantum spin models with variable-range interactions can exhibit certain quantum characteristics that a short-ranged model cannot possess. By considering the quantum XYZ model whose interaction strength between different sites varies either…
Quantum quenches to or near criticality give rise to the phenomenon of \textit{aging}, manifested by glassy-like dynamics at short times and far from equilibrium. The recent surge of interest in the dynamics of quantum many-body systems has…
We give a prescription to perform the continuum limit of the $d$-dimensional Hubbard model in the presence of a harmonic trap at zero temperature. We perform the continuum limit at fixed number of particles. In $d\geq3$ the lattice system…
When interpersonal interactions between individuals are described by the (discrete or continuous) dynamical systems, the interactions are usually assumed to be instantaneous: the rates of change of the actual states of the actors at given…
Long-range interacting systems such as nitrogen vacancy centers in diamond and trapped ions serve as useful experimental setups to probe a range of nonequilibrium many-body phenomena. In particular, via driving, various effective…
In this work we investigate the phenomena associated with the new thresholds in the spectrum of excitations arising when different one-dimensional strongly interacting systems are voltage biased and weakly coupled by tunneling. We develop…
Uncovering and understanding universal dynamics in matter far from equilibrium remains a key challenge. In this work, we identify a so far unrecognized form of universal behavior that emerges after a sudden symmetry-breaking quench at…
We consider a one-dimensional lattice of Ising-type variables where the ferromagnetic exchange interaction J between neighboring sites is frustrated by a long-ranged anti-ferromagnetic interaction of strength g between the sites i and j,…
The equilibrium properties of the lattice fluid with the repulsion between the nearest neighbors on the two-level planar triangular lattice are investigated. The numerical results obtained from the analytical expressions are compared with…