The influence of Fermi surface anisotropy and the charge carrier surface scattering kinetics on the electrical conductivity of a thin metal film in the view of the quantum size effect

The electrical conductivity of a thin metal film in an alternating electric field is calculated considering the quantum size effect. The Fermi surface of the metal has the shape of an ellipsoid of rotation, the main axis of which is parallel to the plane of the film. The quantum kinetic equation obtained from the von Neumann equation (the Liouville quantum equation) is solved. The Soffer model is used as the boundary conditions for the distribution function. The dependence of the electrical conductivity on the film thickness is analyzed. A comparison is made with experimental data on the electrical conductivity of bismuth thin films.

Ulam stability for nonautonomous quantum equations

We establish the Ulam stability of a first-order linear nonautonomous quantum equation with Cayley parameter in terms of the behavior of the nonautonomous coefficient function. We also provide details for some cases of Ulam instability.

Hyers–Ulam Stability for Cayley Quantum Equations and Its Application to h-Difference Equations

The main purpose of this study is to clarify the Hyers–Ulam stability (HUS) for the Cayley quantum equation. In addition, the result obtained for all parameters is applied to HUS of h-difference equations with a specific variable coefficient using a new transformation.

Applications of quantum computing for investigations of electronic transitions in phenylsulfonyl-carbazole TADF emitters

A quantum chemistry study of the first singlet (S1) and triplet (T1) excited states of phenylsulfonyl-carbazole compounds, proposed as useful thermally activated delayed fluorescence (TADF) emitters for organic light emitting diode (OLED) applications, was performed with the quantum Equation-Of-Motion Variational Quantum Eigensolver (qEOM-VQE) and Variational Quantum Deflation (VQD) algorithms on quantum simulators and devices. These quantum simulations were performed with double zeta quality basis sets on an active space comprising the highest occupied and lowest unoccupied molecular orbitals (HOMO, LUMO) of the TADF molecules. The differences in energy separations between S1 and T1 (ΔEST) predicted by calculations on quantum simulators were found to be in excellent agreement with experimental data. Differences of 17 and 88 mHa with respect to exact energies were found for excited states by using the qEOM-VQE and VQD algorithms, respectively, to perform simulations on quantum devices without error mitigation. By utilizing state tomography to purify the quantum states and correct energy values, the large errors found for unmitigated results could be improved to differences of, at most, 4 mHa with respect to exact values. Consequently, excellent agreement could be found between values of ΔEST predicted by quantum simulations and those found in experiments.

On the quantization of a neutron star

This paper deals with quantum gravitation applied to a simple neutron star model. For the quantization process, we use the Weyl prescription that can be used for functions that are not defined in the phase space. The Weyl quantization is applied to the expression of gravitational energy defined in the context of Teleparallelism Equivalent to General Relativity (TEGR). From this, a quantum equation is obtained whose observable is the classical energy. As a consequence, we obtained discretizations for the mass of the star and its angular momentum.

Formulation of a more realistic quantum equation for rectifying the hidden flaws in Planck's black body equation

A thorough investigation of the Planck's black-body radiation reveals several potential flaws. It is found that Planck's final formula suffers from a serious dimensional discrepancy. While it relates to the spectral energy density of the black body radiation, the measured experimental data correspond to the spectral power density. It is shown that Planck's final formula is better written, <mml:math display="inline"> <mml:mi>P</mml:mi> <mml:mo>=</mml:mo> <mml:mi>b</mml:mi> <mml:mi>ν</mml:mi> </mml:math> where <mml:math display="inline"> <mml:mi>P</mml:mi> </mml:math> is power with units <mml:math display="inline"> <mml:mfenced open="[" close="]" separators="|"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:mi>J</mml:mi> </mml:mrow> <mml:mo>/</mml:mo> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:mrow> </mml:mrow> </mml:mfenced> <mml:mo>,</mml:mo> <mml:mo> </mml:mo> <mml:mi>b</mml:mi> </mml:math> is the quantum of energy with units <mml:math display="inline"> <mml:mfenced open="[" close="]" separators="|"> <mml:mrow> <mml:mi>J</mml:mi> </mml:mrow> </mml:mfenced> </mml:math> (numerically equals to Planck's constant, <mml:math display="inline"> <mml:mi>h</mml:mi> </mml:math> ), and <mml:math display="inline"> <mml:mi>ν</mml:mi> </mml:math> is the frequency of the quantum oscillator with units <mml:math display="inline"> <mml:mfenced open="[" close="]" separators="|"> <mml:mrow> <mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mo>/</mml:mo> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:mrow> </mml:mrow> </mml:mfenced> </mml:math> . It is shown that a simple modification in the Planck's black-body radiation formula brought about by replacing “ <mml:math display="inline"> <mml:mi>h</mml:mi> </mml:math> ” by “ <mml:math display="inline"> <mml:mi>b</mml:mi> </mml:math> ” in it could make it absolutely free from any flaws and discrepancies.

Asymptotic behavior of solutions of fractional nabla q-difference equations

We are concerned with the ν-th order nabla fractional q-difference equation (quantum equation) \nabla^{\nu}_{{q,\rho(1)}}x(t)=c(t)x(t),t\in q^{\mathbb{N}_{1}} , where {q>1} , {\mathbb{N}_{1}=\{1,2,\dots\}} , {\rho(1)=q^{-1}} . We prove that for {0<\nu<1} and {c(t)\leq 0} , {t\in\mathbb{N}_{1}} , any solution of the q-difference equation with {x(1)>0} satisfies \lim_{t\to\infty}x(t)=0 . This asymptotic result shows that the solutions of the nabla fractional q-difference equation {{\nabla^{\nu}_{{q,\rho(1)}}}x(t)=cx(t)} , {0<\nu<1} , {c<0} , have asymptotic behavior similar to that of the solutions of the first order nabla q-difference equation {\nabla_{q}x(t)=cx(t)} , {c<0} , {t\in q^{\mathbb{N}_{1}}} .

On Quantization of a Slowly Rotating Kerr Black Hole in Teleparallel Gravity

In this article we calculate the total angular momentum for Kerr space-time for slow rotations in the context of teleparallel gravity. In order to analyze the role of such a quantity, we apply Weyl quantization method to obtain a quantum equation for the z-component of the angular momentum density, and for the squared angular momentum density as well. We present an approximate solution using the Adomian decomposition method (AM), which reveals a discrete characteristic for angular momentum.