Related papers: Phase Space Quantum Mechanics as a Landau Level Pr…
The conceptual problems in quantum mechanics -- related to the collapse of the wave function, the particle-wave duality, the meaning of measurement -- arise from the need to ascribe particle character to the wave function. As will be shown,…
The conditions under which noncommutative quantum mechanics and the Landau problem are equivalent theories is explored. If the potential in noncommutative quantum mechanics is chosen as $V= \Omega \aleph$ with $\aleph$ defined in the text,…
Phase-space techniques are generalized to nonlinear quantum electrodynamics beyond the rotating wave approximation, resulting in an essentially classical picture of radiation dynamics.
Landau levels and states of electrons in a magnetic field are fundamental quantum entities underlying the quantum-Hall and related effects in condensed matter physics. However, the real-space properties and observation of Landau wave…
We revisit the quantum dynamics of a charged particle in a time-dependent magnetic field, a fundamental problem exhibiting rich non-adiabatic behaviour, from the complementary perspective of the Madelung fluid formulation. We first analyse…
We find a quantum group structure in two-dimensional motions of a nonrelativistic electron in a uniform magnetic field and in a periodic potential. The representation basis of the quantum algebra is composed of wavefunctions of the system.…
The spin transitions in the fractional quantum Hall effect provide a direct measure of the tiny energy differences between differently spin-polarized states, and thereby serve as an extremely sensitive test of the quantitative accuracy of…
I present a new approach to the many-body ground state of quantum-Hall systems. The method describes the behavior of a two-dimensional electron system at all Landau-level filling factors $\nu$, continuously as a function of magnetic field,…
Consider a statistical model with an epistemic restriction such that, unlike in classical mechanics, the allowed distribution of positions is fundamentally restricted by the form of an underlying momentum field. Assume an agent (observer)…
We present a simple field transformation which changes the field arguments from the ordinary position-space coordinates to the oblique phase-space coordinates that are linear in position and momentum variables. This is useful in studying…
The quantum dynamics of a two-dimensional charged spin $1/2$ particle is studied for general, symmetry--free curved surfaces and general, nonuniform magnetic fields that are, when different from zero, orthogonal to the defining two surface.…
We examine the visualization of quantum mechanics in phase space by means of the Wigner function and the Wigner function flow as a complementary approach to illustrating quantum mechanics in configuration space by wave functions. The Wigner…
The bootstrap method aims to solve problems by imposing constraints on the space of physical observables, which often follow from physical assumptions such as positivity and symmetry. Here, we employ a bootstrap approach to study…
The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. Existence of the quantum Hall effect requires breaking of the time reversal symmetry caused by an external…
Deformation quantization (sometimes called phase-space quantization) is a formulation of quantum mechanics that is not usually taught to undergraduates. It is formally quite similar to classical mechanics: ordinary functions on phase space…
Starting from the quantum theory of identical particles, we show how to define a classical mechanics that retains information about the quantum statistics. We consider two examples of relevance for the quantum Hall effect: identical…
The unexpected appearance of a fractional quantum Hall effect (FQHE) plateau at $\nu=2+6/13$~ [Kumar \emph{et al.}, Phys. Rev. Lett. {\bf 105}, 246808 (2010)] offers a clue into the physical mechanism of the FQHE in the second Landau level…
A quantum phase space with Wannier basis is constructed: (i) classical phase space is divided into Planck cells; (ii) a complete set of Wannier functions are constructed with the combination of Kohn's method and L\"owdin method such that…
Quantum Hall Dynamics is formulated on von Neumann lattice representation where electrons in Landau levels are defined on lattice sites and are treated systematically like lattice fermions. We give a proof of the integer Hall effect, namely…
We investigate the quantum Hall problem in the lowest Landau level in two dimensions, in the presence of an arbitrary number of $\delta$-function potentials arranged in different geometric configurations. When the number of delta functions…