Related papers: Topological quantum mechanics and the first Chern …
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
We study the quantum mechanics of a system of topologically interacting particles in 2+1 dimensions, which is described by coupling the particles to a Chern-Simons gauge field of an inhomogeneous group. Analysis of the phase space shows…
A topological pump of the $SU(Q)$ quantum chain is proposed associated with a current due to a local $[U(1)]^{\otimes Q}$ gauge invariance of colored fermions. The $SU(Q)$ invariant dimer phases are characterized by the $Z_Q$ Berry phases…
We calculate a topological invariant, whose value would coincide with the Chern number in case of integer quantum Hall effect, for fractional quantum Hall states. In case of Abelian fractional quantum Hall states, this invariant is shown to…
These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by…
Topological quantum state described by the global invariant has been extensively studied in theory and experiment. In this letter, we investigate the relationship between \emph{Zitterbewegung} and the topology of systems that reflect the…
Topology of the spatial coherence function is considered in details. The phase singularity (coherence vortices) structures of coherence function are classified by Hopf index and Brouwer degree in topology. The coherence flux quantization…
The integral and fractional quantum Hall effects are among the most important discoveries in condensed matter physics in 1980s. The main results can be summarized in the conductance matrix. When the filling factor is an integer or some…
We propose the velocity field approach to characterize topological invariants of quantum states. We introduce the indexes of the velocity field flow based on the zero modes of the velocity field and find that these zero modes play the role…
Few level quantum systems driven by $n_\mathrm{f}$ incommensurate fundamental frequencies exhibit temporal analogues of non-interacting phenomena in $n_\mathrm{f}$ spatial dimensions, a consequence of the generalisation of Floquet theory in…
Topological transforms are parametrized families of topological invariants, which, by analogy with transforms in signal processing, are much more discriminative than single measurements. The first two topological transforms to be defined…
We theoretically study the effects of isotropic dissipation in a topological mechanical system which is an analogue of Chern insulator in mechanical vibrational lattice. The global gauge invariance is still conserved in this system albeit…
Topological quantum pumps are topologically equivalent to the quantum Hall state: In these systems, the charge pumped during each pumping cycle is quantized and coincides with the Chern invariant. However, differently from quantum Hall…
Topological superconductors are characterized by topological invariants that describe the number and nature of their robust boundary modes. These invariants must also have observable consequences in the bulk of the system, akin to the…
We introduce the velocity field of the Bloch electrons and propose the velocity field approach to characterize the topological invariants of quantum states. We find that the zero modes of the velocity field flow play the roles of effective…
Here, we reveal our recent progress on a geometrical approach of quantum physics and topological crystals linking with Dirac magnetic monopoles and gauge fields through classical electrodynamics. The Bloch sphere of a quantum spin-1/2…
The Chern topological numbers of a material platform are usually written in terms of the Berry curvature, which depends on the normal modes of the system. Here, we use a gauge invariant Green's function method to determine from first…
When a two-dimensional electron gas is exposed to a perpendicular magnetic field and an in-plane electric field, its conductance becomes quantized in the transverse in-plane direction: this is known as the quantum Hall (QH) effect. This…
Topological quantum numbers account for the precise quantization that occurs in the integer Hall effect. In this theory, Kubo's formula for the conductance acquires a topological interpretation in terms of Chern numbers and their…
The topological structure of the wavefunctions of particles in periodic potentials is characterized by the Berry curvature $\Omega_{kn}$ whose integral on the Brillouin zone is a topological invariant known as the Chern number. The…