Related papers: Topological Pauli Phase and Fractional Quantizatio…
We consider the quantum mechanics of a spinless charged particle on a 2-dimensional sphere. When threaded with a magnetic monopole field, this is the well-known Haldane sphere that furnishes a translationally-invariant, incompressible…
Topology is now securely established as a means to explore and classify electronic states in crystalline solids. This review provides a gentle but firm introduction to topological electronic band structure suitable for new researchers in…
Modern theory of electric polarization is formulated by the Berry phase, which, when quantized, leads to topological phases of matter. Such a formulation has recently been extended to higher electric multipole moments, through the discovery…
In noncommutative space to maintain Bose-Einstein statistics for identical particles at the non-perturbation level described by deformed annihilation-creation operators when the state vector space of identical bosons is constructed by…
When superimposing the potentials of external fields on the Coulomb potential of the hydrogen atom a saddle point appears, which is called the Stark saddle point. For energies slightly above the saddle point energy one can find classical…
We introduce a quantum like representation of a Spiral Phase Plate, acting on an electromagnetic field, as a two mode phase operator. The representation is based on the Newton binomial expansion and on properties of rational power of…
We develop a semiclassical framework for studying quantum particles constrained to curved surfaces using the momentous quantum mechanics formalism, which extends classical phase-space to include quantum fluctuation variables (moments). In a…
We introduce topological gauge fields as nontrivial field configurations enforced by topological currents. These fields crucially determine the form of statistical gauge fields that couple to matter and transmute their statistics. We…
I review why and how physical states with fractional quantum numbers can occur, emphasizing basic mechanisms in simple contexts. The general mechanism of charge fractionalization is the passage from states created by local action of fields…
Suppose a classical electron is confined to move in the $xy$ plane under the influence of a constant magnetic field in the positive $z$ direction. It then traverses a circular orbit with a fixed positive angular momentum $L_z$ with respect…
Quantum mechanics states that a particle emitted at point (x_1,t_1) and detected at point (x_2,t_2) does not travel along a definite path between the two points. This conclusion arises essentially from the analysis of the two-slit…
The angular momentum formalism provides a powerful way to classify atomic states. Yet, requiring a spherical symmetry from the very first line, this formalism cannot be used for periodic systems, even though cubic semiconductor states are…
In the helium case of the classical Coulomb three-body problem in two dimensions with zero angular momentum, we develop a procedure to find periodic orbits applying two symbolic dynamics for one-dimensional and planar problems. A sequence…
The major conceptual difficulties of quantum mechanics are analyzed. They are: the notion "wave-particle", the probabilistic interpretation of the Schroedinger wave \psi-function and hence the probability amplitude and its phase, long-range…
A semiclassical method for the calculation of tunneling exponent in systems with many degrees of freedom is developed. We find that corresponding classical solution as function of energy form several branches joint by bifurcation points. A…
We prove the existence of time quasi-periodic vortex patch solutions of the 2$d$-Euler equations in $\mathbb{R}^2$, close to uniformly rotating Kirchhoff elliptical vortices, with aspect ratios belonging to a set of asymptotically full…
Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…
A quantum field theory approach is put forward to generalize the concept of classical spatial light beams carrying orbital angular momentum to the single-photon level. This quantization framework is carried out both in the paraxial and…
A triaxial particle-rotor Hamiltonian for three mutually perpendicular angular momentum vectors corresponding to two high-$j$ quasiparticles and the rotation of a triaxial collective core, is treated within a time-dependent variational…
We investigate the quantum behavior of a quark-antiquark bound system under the influence of a magnetic field within the symplectic formulation of quantum mechanics. Employing a perturbative approach, we obtain the ground and first excited…