Talks

Scaling and Universality in Quantum Reaction-Transport Systems

Quantum reaction-transport systems consist of coherently propagating particles that irreversibly react upon encounter. Their relaxation is commonly classified as reaction-limited or transport-limited, depending on the relative timescales of reaction and particle transport. In this talk, first we will briefly introduce classical reaction-diffusion phenomena and their scaling behavior in different spatial dimensions. Then we will discuss quantum binary annihilation, where we show that reaction processes are dominated by fluctuations at and below two dimensions. In one dimension, they render mean-field relaxation transient and drive the system toward a transport-limited regime, governed by a quantum-Zeno scale even for arbitrarily weak loss. In two dimensions, the kinetics acquires logarithmic corrections, whereas above two dimensions mean-field scaling is asymptotically restored. At and below the upper critical dimension, mean-field behavior can nevertheless persist over parametrically long crossover times before the asymptotic fluctuation-dominated regime emerges. We also show that the same fluctuations generate effective elastic collisions despite the absence of microscopic coherent interactions.

Low-temperature transition of 2d random-bond Ising model and quantum infinite randomness

At low temperatures, the classical two-dimensional random bond Ising model undergoes a frustration-driven ferromagnet-to-paramagnet transition controlled by a zero-temperature fixed point separating ferromagnet and spin glass phases. We show that this critical point can be understood through a renormalization group transformation that constructs the ground state of the Ising model through a sequence of Hamiltonians that, starting with an unfrustrated model, iteratively adds in frustration until the target Hamiltonian is reached. Via a mapping of the thermodynamics of the 2d Ising model to the spectral properties of a related Hermitian matrix -- the Hamiltonian of a noninteracting quantum problem -- this RG procedure corresponds to an iterative diagonalization of the quantum Hamiltonian. The flow toward zero temperature in the Ising picture manifests as a flow toward infinite randomness in the spectrum of the quantum Hamiltonian.

Chaotic behavior of disordered nonlinear lattices - Part II

We discuss the chaotic dynamics and wave packet spreading in disordered nonlinear Hamiltonian lattices, focusing on the disordered Klein-Gordon (DKG) and discrete nonlinear Schrödinger (DDNLS) models in one and two spatial dimensions. Through extensive numerical simulations, we employ a range of complementary techniques, including the maximum Lyapunov exponent (MLE), deviation vector distributions (DVDs), frequency map analysis (FMA), the Generalized Alignment Index (GALI), as well as symplectic integration schemes based on split Hamiltonians and the tangent-map method. For both models, we identify weak and strong chaos spreading regimes and find similar dynamical behaviors in one and two dimensions, highlighting the generality of the underlying chaotic mechanisms. The MLE reveals a systematic algebraic decrease of chaoticity strength with time, but chaos persists on the largest timescales investigated and does not cross over to regular dynamics, remaining sufficiently strong to sustain the subdiffusive spreading of initially localized wave packets. The DVD and FMA analyses provide complementary information on the propagation and spatial organization of chaos, while the GALI method allows us to distinguish localized from spreading chaos and to identify energy thresholds associated both with global chaotic spreading and the disappearance of chaos. We also briefly consider a one-dimensional disordered nonlinear stub lattice, showing that the characteristic weak and strong chaos subdiffusive spreading observed in conventional disordered nonlinear lattices can also occur in flat-band network geometries.

TBA

TBA

Life at High Reynolds Number

Unlike coffee and cream that homogenize when stirred, growing micro-organisms (e.g., bacteria and unicellular marine organisms) can actively kill each other and avoid mixing. How do such antagonistic interactions impact the growth and survival of competing strains, while being spatially advected by turbulent flows? By using analytic arguments and numerical simulations of a continuum model, we describe the dynamics of two antagonistic strains that are dispersed by both compressible and incompressible turbulent flows in two spatial dimensions. A key parameter is the ratio of the fluid transport time to that of biological reproduction, which determines the winning organism that ultimately takes over the whole population from an initial heterogeneous state, a process known as fixation. By quantifying the probability and mean time for fixation, we discuss how turbulence raises the threshold for biological nucleation and antagonism suppresses flow-induced mixing by depleting the population at interfaces. We highlight the unusual biological consequences of the interplay of turbulent fluid flows with antagonistic population dynamics, with potential implications for marine microbial ecology and origins of biological chirality.

ATOM26 Colloquium

Quantum Dynamics Seminar: tba