arXiv subjects

G. Maglasang

Publications and source records attributed to G. Maglasang.

3 recordsLinked to original sources

arXiv2021

A Mechanical Implementation and Diagrammatic Calculation of Entangled Basis States

We give for the first time a diagrammatic calculational tool of quantum entanglement. We present a pedagogical and simple mechanical implementation of quantum entanglement or "spooky action at a distance" to give a tangible realization of this weird quantum mechanical concept alien to classical physics. When two or more particles are correlated in a certain way, no matter how far apart they are in space, their states remain correlated. Their correlation, which is instantaneous, does not seem to involve any communication which is limited by the speed of light. The same mechanical implementation demonstrates the fundamental physical limits of any computational processes. The analytical derivations of calculational entangled basis states are given and their corresponding diagrammatic representations give an efficient aid in determining the calculational entangled basis states. A quantum Fourier transform for the two-state diagrams representing entangled basis states ('renormalized qubits') can also be formulated. Our results seem to advocate the idea that quantum entanglement generates the extra dimensions of the gravitational theory, indeed quantum entanglement is related to deep issues in the unification of general relativity and quantum mechanics. This extra dimensions of spacetime entanglement are currently being speculated in the literature.

cond-mat.mes-hall↗

arXiv2021

On Hofstadter butterfly spectrum: Chern-Simons theory, subband gap mapping, IQHE and FQHE labelling

The magnetic field affects the Bloch band structure in a couple of ways. First it breaks the Bloch band into magnetic subbands or the Landau levels are broadened into magnetic Bloch bands. The resulting group of subbands in the central portion of the energy scale is associated with the integer quantum Hall effect (IQHE). Then at high fields it changes the integrated density of states of the remaining lowest and topmost subband, respectively, which can be associated with fractional quantum Hall effect (FQHE). Here, we employ the Maxwell Chern-Simons gauge theory to formulate the subband-gap mapping algorithm and to construct the butterfly profile of the Hofstadter spectrum. The two regions in the spectrum responsible for the IQHE are identified. At very high magnetic fields the highest and lowest subband are affected by magnetic-field induced restructuring of the integrated density of states in each subband, respectively. The resulting transformation of each of the two subband is responsible for the FQHE. Thus, in the central regions of the energy scale, the principal group of subbands defined by the gap mapping is responsible for the IQHE. The fine structure of the topmost and lowest subband, which convey an iterative nature of the magnetic spectrum is a result of a hierarchical scaling and restructuring by the magnetic fields on the integrated density of states in each respective subband and is responsible for the FQHE.

cond-mat.mes-hall↗

arXiv2021

On Fractional Quantum Hall Effect (FQHE): A Chern-Simons and nonequilibrium quantum transport Weyl transform approach

We give a simple macroscopic phase-space explanation of fractional quantum Hall effect (FQHE), in a fashion reminiscent of the Landau-Ginsburg macroscopic symmetry breaking analyses. This is in contrast to the more complicated microscopic wavefunction approaches. Here, we employ a nonequilibrium quantum transport in the lattice Weyl transform formalism. This is coupled with the Maxwell Chern-Simons gauge theory for defining fractional filling of Landau levels. Flux attachment concept is inherent in fully occupied and as well as in partially occupied Landau levels. We derived the k-factor scaling hierarchy in Chern-Simons gauge theory, as the scaling hierarchy of the magnetic field or magnetic flux in FQHE. This is crucial in our simple explanation of FQHE as a topological invariant in phase space. For the fundamental scaling hierarchy, the integer k must be a prime number, and for fractions both the numerator and denominator of k must also be prime numbers. The assumption in the literature that a hierarchy of denominators of v = 1 k is given by the expression, (2n + 1), is wrong. Furthermore, even denominators for v cannot belong to fundamental scaling hierarchy and is often absent or less resolved in the experiments.

cond-mat.mes-hall↗