In the mutual transform between the number-difference state and the phase state corresponding to the operational phase operator we find that there exists an end-point ambiguousness. This problem can be avoided by Ligh...In the mutual transform between the number-difference state and the phase state corresponding to the operational phase operator we find that there exists an end-point ambiguousness. This problem can be avoided by Lighthill's method.展开更多
Pricing variance swaps under stochastic volatility has been an important subject pursued recently. Various approaches have been proposed, mainly due to the substantially increased trading activities of volatility-rela...Pricing variance swaps under stochastic volatility has been an important subject pursued recently. Various approaches have been proposed, mainly due to the substantially increased trading activities of volatility-related derivatives in the past few years. In this note, the authors develop analytical method for pricing variance swaps under stochastic volatility with an Ornstein-Uhlenbeck(OU) process. By using Fourier transform algorithm, a closed-form solution for pricing variance swaps with stochastic volatility is obtained, and to give a comparison of fair strike value based on the discrete model, continuous model, and the Monte Carlo simulations.展开更多
We consider two typical approximations that are used in the microscopic calculations of double-quantum dot spin qubits, namely,the Heitler-London(HL) and the Hund-Mulliken(HM) approximations, which use linear combinat...We consider two typical approximations that are used in the microscopic calculations of double-quantum dot spin qubits, namely,the Heitler-London(HL) and the Hund-Mulliken(HM) approximations, which use linear combinations of Fock-Darwin states to approximate the two-electron states under the double-well confinement potential. We compared these results to a case in which the solution to a one-dimensional Schr ¨odinger equation was exactly known and found that typical microscopic calculations based on Fock-Darwin states substantially underestimate the value of the exchange interaction, which is the key parameter that controls the quantum dot spin qubits. This underestimation originates from the lack of tunneling of Fock-Darwin states, which is accurate only in the case with a single potential well. Our results suggest that the accuracies of the current two-dimensional molecularorbit-theoretical calculations based on Fock-Darwin states should be revisited since underestimation could only deteriorate in dimensions that are higher than one.展开更多
基金the Ph. D Tutoring Programme of the Educational Ministry of China
文摘In the mutual transform between the number-difference state and the phase state corresponding to the operational phase operator we find that there exists an end-point ambiguousness. This problem can be avoided by Lighthill's method.
基金supported by the National Social Science Fund of China under Grant No.14ATJ005Anhui Provincial Natural Science Foundation under Grant Nos.1308085MF93 and 1408085MKL84the National Natural Science Foundations of China under Grant No.11401556
文摘Pricing variance swaps under stochastic volatility has been an important subject pursued recently. Various approaches have been proposed, mainly due to the substantially increased trading activities of volatility-related derivatives in the past few years. In this note, the authors develop analytical method for pricing variance swaps under stochastic volatility with an Ornstein-Uhlenbeck(OU) process. By using Fourier transform algorithm, a closed-form solution for pricing variance swaps with stochastic volatility is obtained, and to give a comparison of fair strike value based on the discrete model, continuous model, and the Monte Carlo simulations.
基金supported by the Research Grants Council of the Hong Kong Special Administrative Region of China(Grant No.City U 21300116)the National Natural Science Foundation of China(Grant No.11604277)the Guangdong Innovative and Entrepreneurial Research Team Program(Grant No.2016ZT06D348)
文摘We consider two typical approximations that are used in the microscopic calculations of double-quantum dot spin qubits, namely,the Heitler-London(HL) and the Hund-Mulliken(HM) approximations, which use linear combinations of Fock-Darwin states to approximate the two-electron states under the double-well confinement potential. We compared these results to a case in which the solution to a one-dimensional Schr ¨odinger equation was exactly known and found that typical microscopic calculations based on Fock-Darwin states substantially underestimate the value of the exchange interaction, which is the key parameter that controls the quantum dot spin qubits. This underestimation originates from the lack of tunneling of Fock-Darwin states, which is accurate only in the case with a single potential well. Our results suggest that the accuracies of the current two-dimensional molecularorbit-theoretical calculations based on Fock-Darwin states should be revisited since underestimation could only deteriorate in dimensions that are higher than one.
