相关论文: The quantum-mechanical position operator and the p…
The position operator (defined within the Schroedinger representation in the standard way) becomes meaningless when periodic boundary conditions are adopted for the wavefunction, as usual in condensed matter physics. We show how to define…
The quantum mechanical position operators, and their products, are not well-defined in systems obeying periodic boundary conditions. Here we extend the work of Resta who developed a formalism to calculate the electronic polarization as an…
The dipole moment of any finite and neutral system, having a square-integrable wavefunction, is a well defined quantity. The same quantity is ill-defined for an extended system, whose wavefunction invariably obeys periodic (Born-von Karman)…
A perturbation theory of the static response of insulating crystals to homogeneous electric fields, that combines the modern theory of polarization (MTP) with the variation-perturbation framework is developed, at unrestricted order of…
The standard quantum mechanical electronic state calculations for molecules and solids uses the Schroedinger representation where the momentum conjugate to the coordinate $q_r$ is given by $-hbar {partial over {partial q_r}}$. This…
We discuss characterization of the polarization for insulators under the periodic boundary condition in terms of the Berry phase, clarifying confusing subtleties. For band insulators, the Berry phase can be formulated in terms of the Bloch…
Recently, it has been established that Chern insulators possess an intrinsic two-dimensional electric polarization, despite having gapless edge states and non-localizable Wannier orbitals. This polarization, $\vec{P}_{\text{o}}$, can be…
In translationally invariant semiconductors that host exciton bound states, one can define an infinite number of possible exciton Berry connections. These correspond to the different ways in which a many-body exciton state, at fixed total…
The physics of a quantum dot with electron-electron interactions is well captured by the so called "Universal Hamiltonian" if the dimensionless conductance of the dot is much higher than unity. Within this scheme interactions are…
We define a deformed kinetic energy operator for a discrete position space with a finite number of points. The structure may be either periodic or nonperiodic with well-defined end points. It is shown that for the nonperiodic case the…
The many-body Berry phase formula for the macroscopic polarization is approximated by a sum of natural orbital geometric phases with fractional occupation numbers accounting for the dominant correlation effects. This reduced formula…
The components of the position operator, at a fixed time, for a massless and spinning particle with given helicity $\lambda$ described in terms of bosonic degrees of freedom have an anomalous commutator proportional to $\lambda$. The…
We discuss an extension of the Resta's electronic polarization to non-Hermitian systems with periodic boundary conditions. We introduce the ``electronic polarization'' as an expectation value of the exponential of the position operator in…
A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique…
The polarization operator is investigated at arbitrary photon energy in a constant and homogeneous magnetic field for the strength H less than the Schwinger critical value. The effective mass of a real photon with a preset polarization is…
We generalize the modern theory of electric polarization to the case of one-dimensional non-Hermitian systems with line-gapped spectrum. In these systems, the electronic position operator is non-Hermitian even when projected into the…
We consider the flow of polarization current J(t)=dP/dt produced by a homogeneous electric field E(t) or by rapidly varying some other parameter in the Hamiltonian of a solid. For an initially insulating system and a collisionless time…
It is first shown that when the Schr\"{o}dinger equation for a wave function is written in the polar form, complete information about the system's {\em quantum-ness} is separated out in a single term $Q$, the so called `quantum potential'.…
The expectation value of the twist operator has been widely used as a polarization-based index for gapped and gapless phases in interacting quantum many-body systems. Although numerous studies support this usage in specific settings and…
For a bi-partite quantum system defined in a finite dimensional Hilbert space we investigate in what sense entanglement change and interactions imply each other. For this purpose we introduce an entanglement operator, which is then shown to…