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We discuss a new strategy for treating the complex action problem of lattice field theories with a $\theta$-term based on density of states (DoS) methods. The key ingredient is to use open boundary conditions where the topological charge is…
We study two-electron states confined in two coupled quantum dots formed by a short-range potential in a two-dimensional topological insulator. It is shown that there is a fairly wide range of the system parameters, where the ground state…
A double quantum dot device is a tunable two-level system for electronic energy states. A dc electron current directly measures the rates for elastic and inelastic transitions between the two levels. For inelastic transitions energy is…
The properties of two-state nearest-neighbour cellular automata (CA) that are capable of density classification are discussed. It is shown that these CA actually conserve the total density, rather than merely classifying it. This is also…
In finite systems driven unitarily across topological phase transitions, the Chern number and the Bott index have been found to exhibit different behaviors depending on the boundary conditions and on the commensurability of the lattice. For…
We focus on quantum systems that can be effectively described as a localized spin-$s$ particle subject to a static magnetic field coplanar to a coexisting elliptically rotating time-periodic field. Depending on the values taken on by the…
Scanning tunneling microscopy and spectroscopy have been used to investigate the femtosecond dynamics of Dirac fermions in the topological insulator Bi$_2$Se$_3$ ultrathin films. At two-dimensional limit, bulk electrons becomes quantized…
For a wide class of noninteracting tight-binding models in one dimension we present an analytical solution for all scattering and edge states on a half-infinite system. Without assuming any symmetry constraints we consider models with…
We show that band topology can dramatically change the photophysics of two-dimensional (2D) semiconductors. For systems in which states near the band extrema are of multiple orbitals character and the spinors describing the orbital…
In this paper a duality between the d=2 Wen-plaquette model in a transverse field and the d=1 Ising model in a transverse field is used to learn the nature of the quantum phase transition (QPT) between a spin-polarized phase and a…
We consider coupling an ordinary quantum field theory with an infinite number of degrees of freedom to a topological field theory. On R^d the new theory differs from the original one by the spectrum of operators. Sometimes the local…
Dimensional evolution between one- ($1D$) and two-dimensional ($2D$) topological phases is investigated systematically. The crossover from a $2D$ topological insulator to its $1D$ limit shows oscillating behavior between a $1D$ ordinary…
The relativistic ``no pair'' model of quantum electrodynamics uses the Dirac operator, D(A), for the electron dynamics together with the usual self-energy of the quantized ultraviolet cutoff electromagnetic field A -- in the Coulomb gauge.…
We consider steady states of the incompressible Euler equation on two-dimensional domains. For non-radial analytic steady states on bounded simply connected domains, it was shown previously that there must be a global functional…
The rheology of biological tissues is important for their function, and we would like to better understand how single cells control global tissue properties such as tissue fluidity. A confluent tissue can fluidize when cells diffuse by…
We present a generalization of the double semion topological quantum field theory to higher dimensions, as a theory of $d-1$ dimensional surfaces in a $d$ dimensional ambient space. We construct a local Hamiltonian which is a sum of…
A theory of the static electron polarizability of crystals whose energy spectrum is modified by quantizing magnetic fields is presented. It is argued that The polarizability is strongly affected by non-dissipative Hall currents induced by…
An electric-field-induced phase transition and pattern formation in a binary dielectric fluid layer are studied using a coarse-grained free energy functional. The electrostatic part of the free energy is a nonlinear functional of the…
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…
We study how the \theta -term is affected by interactions in certain one-dimensional gapped systems that preserve charge-conjugation, parity, and time-reversal invariance. We exploit the relation between the chiral anomaly of a fermionic…