Quantum Hall Effect: A Perspective

2015

JMP

Electrodynamics of the one-electron currents due to the circular orbital motion of the electron particle in the hydrogen atom has been examined. The motion is assumed to be induced by the time change of the magnetic field in the atom. A characteristic point is that the electric resistance calculated for the motion is independent of the orbit index and its size is similar to that obtained earlier experimentally for the planar free-electron-like structures considered in the integer quantum Hall effect. Other current parameters like conductivity and the relaxation time behave in a way similar to that being typical for metals. A special attention was attached to the relations between the current intensity and magnetic field. A correct reproduction of this field with the aid of the Biot-Savart law became possible when the geometrical microstructure of the electron particle has been explicitly taken into account. But the same microstructure properties do influence also the current velocity. In fact the current suitable for the Biot-Savart law should have a speed characteristic for a spinning electron particle and not that of a spinless electron circulating along the orbit of the original Bohr model.

Section: Discussionmentioning

confidence: 99%

“…In effect R is the same constant number for all orbits n. Moreover, the value of R is equal to one-half of the electric resistance associated with the integer quantum Hall effect; see e.g. [10].…”

Section: Electric Resistance Of the Orbital Motionmentioning

confidence: 99%

Electrodynamics of the Electron Orbital Motion in the Hydrogen Atom Considered in Reference to the Microstructure of the Electron Particle and Its Spin

2015

JMP

“…to the first component entering (14). In this case the formula (17) accompanied by (18) is obtained.…”

Section: Entropy Change and The Specific Heatmentioning

confidence: 96%

“…In Sec. 4 (see (14)) the problem-for the sake of simplicity-was reduced to a situation of a very low T by limiting the Planck's probability expression for the temperature bath of T…”

Section: Entropy Change and The Specific Heatmentioning

confidence: 99%

The de Broglie Waves and Joule-Lenz Law Applied in Examining the Electron Transitions in Small Quantum Systems

2019

JMP

A transformation of the electron states-say those enclosed in a potential box-into the de Broglie waves done in the paper, enabled us to calculate the energy change between two quantum levels as a function of the specific heat and difference of the temperature between the states. In consequence, the energy difference and that of entropy between the levels could be examined in terms of the appropriate classical parameters. In the next step, the time interval necessary for the electron transition between the levels could be associated with the classical electrodynamical parameters like the electric resistance and capacitance connected with the temporary formation of the electric cell in course of the transition. The parameters characterizing the mechanical inertia of the electron were next used as a check of the electrodynamical formulae referring to transition. Journal of Modern Physics the electron transitions, and their properties, approximately on the level presented by Einstein. A step forwards was here the wave functions of the stationary states applied in calculating the transition probabilities between different quantum levels.Another feature of the probabilistic Einstein theory was the assumption that a large, though rather undefined, number of the quantum objects should enter a given transition. This difficulty seems to be not involved in the Planck's approach where the number of the states which participate in transition can be definited and not necessarily large. This property allows us to consider also transitions in which the number of participating objects is relatively small. Moreover, when the Joule-Lenz classical approach [3] is applied on the quantum footing [4], the intensity of the energy emission can be estimated for a transition of a single particle without any reference to the probabilistic theory.In effect, the aim of the present paper became to examine a single electron transition in small quantum systems on both probabilistic and non-probabilisticfooting. An analysis of the classical physical parameters of mechanics, thermodynamics and electrodynamics which can be connected with the transition seems to be then of use. Notion of Temperature Applied for a Small Number of Quantum SystemsHistorically the quantum theory began as a statistics of photons emitted in course of the black-body radiation. Here the notion of temperature does accompany systematically the presentation of the energy distribution among the quantum levels. Somewhat later a concurrent quantum theory by Schrödinger banned essentially the notion of temperature and that of particle oscillations from the basic idea of the quantum states: the spectrum of levels has been replaced by a set of discrete entities being in general essentially different in their individualproperties. The temperature is then assumed to be close to zero.Nevertheless, for less or more numerous ensembles of particles, a reference between the temperature and energy remained of importance. The point became especially sound for the case of very low temperatur...

“…The formula of (4) is characteristic for the magnetoresistance of the integer quantum Hall effect, but also the magnetoresistance values specific for the fractional quantum Hall effect can be obtained [6][7][8]. Here the coefficient  is a simple fraction like 1 2 2 , , ,…”

Section: Ementioning

confidence: 99%

Quantum of the Magnetic Flux Characteristic forExperiments Performed on the Integer and Fractional Quantum Hall Effects

2013

JMP

Experimentally the plateaus characteristic for the integer quantum Hall effect is obtained in vicinity of specific values of the magnetic induction. The paper demonstrates that the ratios of these induction values to carrier concentration in the planar crystalline samples approach systematically the quanta of the magnetic flux important for the behavior of superconductors. Moreover, the same quanta can be deduced from the Landau levels theory and their application in the magnetoresistance theory gives results being in accordance with experiments. The quanta of the magnetic flux similar to those for the integer quantum Hall effect can be obtained also for the fractional quantum Hall effect. This holds on condition the experimental ratio of the magnetic flux to carrier concentration is multiplied by the filling factor of the Landau level.