Related papers: Eight-dimensional topological systems simulated us…

We study feedback control of classical Hamiltonian systems with the controlling parameter varying slowly in time. The control aims to change system's energy. We show that the control problems can be solved with help of an adiabatic…

We present a framework for learning Hamiltonian systems using data. This work is based on a lifting hypothesis, which posits that nonlinear Hamiltonian systems can be written as nonlinear systems with cubic Hamiltonians. By leveraging this,…

Nontrivial topological invariant of bulk electronic wavefunctions in two-dimensional quantum crystals leaves its footprints on the edge, dislocation, and corner modes. Here we investigate non-unitary time dynamics of these topological modes…

There is growing interest to investigate states of matter with topological order, which support excitations in the form of anyons, and which underly topological quantum computing. Examples of such systems include lattice spin models in two…

Advances in nanotechnology now allow the creation of artificial atoms - engineered structures whose electronic states closely mimic those of real atoms. Understanding how these artificial atoms interact and bond is key to designing new…

Topological phases supported by quasi-periodic spin-chain models and their bulk-boundary principles are investigated by numerical and K-theoretic methods. We show that, for both the un-correlated and correlated phases, the operator algebras…

Isotropic fluids in two spatial dimensions can break parity symmetry and sustain transverse stresses which do not lead to dissipation. Corresponding transport coefficients include odd viscosity, odd torque, and odd pressure. We consider an…

We propose and analyse an efficient scheme for simulating higher-order topological phases of matter in two dimensional (2D) spin-phononic crystal networks. We show that, through a specially designed periodic driving, one can selectively…

We introduce a family of Hamiltonian systems for measurement-based quantum computation with continuous variables. The Hamiltonians (i) are quadratic, and therefore two body, (ii) are of short range, (iii) are frustration-free, and (iv)…

When a Hamiltonian system is subject to constraints which depend explicitly on time, difficulties can arise in attempting to reduce the system to its physical phase space. Specifically, it is non-trivial to restrict the system in such a way…

Topological phases have been extensively studied primarily in crystalline systems with translational symmetry. Recent theoretical studies, however, have demonstrated the existence of topological phases in quasicrystals that are absent in…

We describe space-time using split octonions over the reals and use their group of automorphisms, the non-compact form of Cartan's exceptional Lie group G2, as the main geometrical group of the model. Connections of the G2-rotations of…

The introduction of topology unravels a new chapter of physics. Topological systems provide unique edge/interfacial quantum states which are expected to contribute to the development of novel spintronics and open the door to robust quantum…

We present the formulation of the problem of the coherent dynamics of quantum mechanical two-level systems in the adiabatic region in terms of the differential geometry of plane curves. We show that there is a natural plane curve…

Higher-order topological crystalline phases in low-dimensional interacting quantum systems represent a challenging and largely unexplored research topic. Here, we derive a Hamiltonian describing fermions interacting through correlated…

The fundamental concept underlying topological phenomena posits the geometric phase associated with eigenstates. In contrast to this prevailing notion, theoretical studies on time-varying Hamiltonians allow for a new type of topological…

In spaces of three or more dimensions, there exists topological physics of significant richness that has no lower-dimensional counterparts. To experimentally explore high-dimensional physics, it is advantageous to augment the physical space…

We give an introduction to topological crystalline insulators, that is, gapped ground states of quantum matter that are not adiabatically connected to an atomic limit without breaking symmetries that include spatial transformations, like…

To define the topology of driven systems, recent works have proposed synthetic dimensions as a way to uncover the underlying parameter space of topological invariants. Using time as a synthetic dimension, together with a momentum dimension,…

This paper is a review of results which have been recently obtained by applying mathematical concepts drawn, in particular, from differential geometry and topology, to the physics of Hamiltonian dynamical systems with many degrees of…