research

I study non‑equilibrium quantum systems where periodic driving (Floquet control) and topology meet. A central object is the one‑period evolution \(U(T)=\mathcal{T}\exp\bigl(-\tfrac{i}{\hbar}\int_0^T H(t)\,dt\bigr)\) and its effective generator \(H_{\mathrm{eff}}=\tfrac{i\hbar}{T}\log U(T)\approx H_0+\tfrac{1}{\Omega}[H_{-1},H_{+1}]+\cdots\) which organize dynamics in powers of the drive frequency \(\Omega\).

In driven rotors, the angular momentum basis forms an angular-momentum lattice that lets us port concepts from band topology; responses follow from band geometry, with Chern numbers \(\nu=\tfrac{1}{2\pi}\int_{\mathrm{BZ}}\operatorname{Tr}\,\mathcal{F}[\mathcal{A}]\) when applicable.

On laser‑kicked molecules, this lattice picture reveals Dirac cones protected by symmetries. Their topological charges control inter‑band transport and produce fingerprints in alignment/orientation correlators \(\langle \cos\theta\rangle,\;\langle \cos^2\theta\rangle\) measurable in pump–probe protocols. See topological charges in kicked molecules: project.

In quantum rotors with multiple quasienergy gaps, braiding of band degeneracies reshapes topology across gaps. We characterize these phases using frame/Euler‑class structure and non‑Abelian charges; for a band pair over a domain \(D\) one representative quantity is the Euler class \(\chi^D_{n,n+1}=\tfrac{1}{2\pi}\!\left(\int_D Eu(k)\,dk\wedge d\alpha-\int_{\partial D}\!A\cdot dk\right)\) and nodal lines acquire quaternion‑valued charges that flip under braiding. This physics underlies anomalous multi‑gap behavior on the angular‑momentum lattice. See anomalous multi‑gap topology: project.

I also work on entanglement structure of highly excited eigenstates. For local Hamiltonians with anti‑commuting symmetries, extensive zero‑energy nullspaces allow construction of low‑entropy eigenstates with area‑law scaling connecting to many‑body scars. See area‑law eigenstates from nullspaces: project.

Earlier, I studied coupled superfluidity in 2D Bose mixtures. Inter‑species vortex binding modifies BKT physics; schematic RG flows \(\tfrac{dK_i^{-1}}{dl}\sim y_i^2+\lambda y_1y_2,\; \tfrac{dy_i}{dl}\sim (2-\pi K_i)\,y_i+\cdots\) predict correlated criticality and shifted temperatures. See coupled 2D superfluids: project.

Beyond quantum matter, I explored how interactions between climate/eco “tipping elements” reshape thresholds and produce cascades in networks governed by \(\dot x_i=f_i(x_i,\mu_i)+\sum_j K_{ij}\,g_{ij}(x_j)\) informing compound‑risk assessments. See cascading tipping dynamics: project. I also examined classical analogs of dynamical localization by discretizing phase space in kicked‑rotor maps, clarifying minimal ingredients for transport suppression; see classical localization: project.

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