Demonstration and operation of quantum harmonic oscillators in an AlGaAs–GaAs heterostructure

The quantum harmonic oscillator(QHO),one of the most important and ubiquitous model systems in quantum mechanics,features equally spaced energy levels or eigenstates.Here we present a new class of nearly ideal QHOs formed by hydrogenic substitutional dopants in an AlGaAs/GaAs heterostructure.On the basis of model calculations,we demonstrate that,when aδ-doping Si donor substitutes the Ga/Al lattice site close to AlGaAs/GaAs heterointerface,a hydrogenic Si QHO,characterized by a restoring Coulomb force producing square law harmonic potential,is formed.This gives rise to QHO states with energy spacing of~8–9 meV.We experimentally confirm this proposal by utilizing gate tuning and measuring QHO states using an aluminum single-electron transistor(SET).A sharp and fast oscillation with period of~7–8 mV appears in addition to the regular Coulomb blockade(CB)oscillation with much larger period,for positive gate biases above 0.5 V.The observation of fast oscillation and its behavior is quantitatively consistent with our theoretical result,manifesting the harmonic motion of electrons from the QHO.Our results might establish a general principle to design,construct and manipulate QHOs in semiconductor heterostructures,opening future possibilities for their quantum applications.

A Model Effective Mass Quantum Anharmonic Oscillator and Its Thermodynamic Characterization

Using a model anharmonic oscillator with asymptotically decreasing effective mass to study the effect of compositional grading on the quantum mechanical properties of a semiconductor heterostructure, we determine the exact bound states and spectral values of the system. Furthermore, we show that ordering ambiguity only brings about a spectral shift on the quantum anharmonic oscillator with spatially varying effective mass. A study of thermodynamic properties of the system reveals a resonance condition dependent on the magnitude of the anharmonicity parameter. This resonance condition is seen to set a critical value on the said parameter beyond which a complex valued entropy which is discussed, emerges.

Option Pricing beyond Black-Scholes Model:Quantum Mechanics Approach

Based on the analog between the stochastic dynamics and quantum harmonic oscillator,we propose a market force driving model to generalize the Black-Scholes model in finance market.We give new schemes of option pricing,in which we can take various unexpected market behaviors into account to modify the option pricing.As examples,we present several market forces to analyze their effects on the option pricing.These results provide us two practical applications.One is to be used as a new scheme of option pricing when we can predict some hidden market forces or behaviors emerging.The other implies the existence of some risk premium when some unexpected forces emerge.

Virial Theorem for a Class of Quantum Nonlinear Harmonic Oscillators

In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ■/■λ,where the λ is a real number.When λ = 0,the nonlinear harmonic oscillator naturally reduces to the usual quantum linear harmonic oscillator,and the Virial Theorem also reduces to the usual Virial Theorem.

N-particles intermediate coordinate-momentum representation and its application

This paper constructs the new common eigenvectors of n intermediate coordinate-momentum operators which are complete and orthonormal. The intermediate coordinate-momentum representation of a multi-particles system is proposed and applied to a generaln-mode quantum harmonic oscillators system with coordinate-momentum coupling.

模拟城际人口流动的量子谐振子模型

The simulation of intercity population mobility helps to deepen the understanding of intercity population mobility and its underlying laws,which has great importance for epidemic prevention and control,social management,and even urban planning.There are many factors that affect intercity population mobility,such as socioeconomic attributes,geographical distance,and industrial structure.The complexity of the coupling among these factors makes it difficult to simulate intercity population mobility.To address this issue,we propose a novel method named the quantum harmonic oscillator model for simulation of intercity population mobility(QHO-IPM).QHO-IPM describes the intercity population mobility as being affected by coupled driving factors that work as a multioscillator-coupled quantum harmonic oscillator system,which is further transformed by the oscillation process of an oscillator,namely,the breaking point of intercity population mobility.The intercity population mobility among seven cities in the Beijing-Tianjin-Hebei region and its surrounding region is taken as an example for verifying the QHO-IPM.The experimental results show that(1)compared with the reference methods(the autoregressive integrated moving average(ARIMA)and long and short-term memory(LSTM)models),the QHO-IPM achieves better simulation performance regarding intercity population mobility in terms of both overall trend and mutation.(2)The simulation error in the QHO-IPM for different-level intercity population mobility is small and stable,which illustrates the weak sensitivity of the QHO-IPM to intercity population mobility under different structures.(3)The discussion regarding the influence degree of different driving factors reveals the significant“one dominant and multiple auxiliary”factor pattern of driving factors on intercity population mobility in the study area.The proposed method has the potential to provide valuable support for understanding intercity population mobility laws and related decision-making on intercity population mobility control.