The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(...The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(■,...,■),t∈C,b∈C^(N) and A is a linear operator on C^(N).An example of 2-complex symmetric bounded weighted composition operator with the conjugation J_(t,A,b) is given.展开更多
Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_...Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_(ϕ)^(p)(1≤p≤∞),which extends the classical Hörmander Theorem.Furthermore,for a suitable f,we completely characterize the boundedness and compactness of the Hankel operator H_(f):F_(ϕ)^(p)→L^(q)(C,e^(qϕ(·))dm)for all possible 1≤p,q<∞and also characterize the Schatten-p class Hankel operator Hf from F_(ϕ)^(2)to L^(2)(C,E^(-2ϕ)dm) for all 0<p<∞. As an application, we give a complete characterization of the simultaneously bounded, compact and Schatten-p classes Hankel operators H_(f) and h_(f)^(-) on F_(ϕ)^(2).展开更多
本文主要研究了Fock空间Fαp上小Hankel算子hφ的有界性和紧性,得到了hφ在Fαp上有界的充分必要条件是其符号φ属于Fock空间Fα2∞;hφ在Fαp上紧的充分必要条件是φ属于fα2∞。This paper mainly studies the boundedness and compac...本文主要研究了Fock空间Fαp上小Hankel算子hφ的有界性和紧性,得到了hφ在Fαp上有界的充分必要条件是其符号φ属于Fock空间Fα2∞;hφ在Fαp上紧的充分必要条件是φ属于fα2∞。This paper mainly studies the boundedness and compactness of the small Hankel operator hφon Fock space Fαp. It is found that the necessary and sufficient condition for hφbeing bounded on Fαpis that its symbol φbelongs to Fock space Fα2∞;the necessary and sufficient condition for hφbeing compact on Fαpis that φbelongs to fα2∞.展开更多
本文凭借逐点估计、范数估计等相关技巧,给出了指标不同的加权Fock空间中乘法算子有界性与紧性的等价描述。In this paper, by pointwise estimation, norm estimation and other related techniques, the equivalent descriptions of t...本文凭借逐点估计、范数估计等相关技巧,给出了指标不同的加权Fock空间中乘法算子有界性与紧性的等价描述。In this paper, by pointwise estimation, norm estimation and other related techniques, the equivalent descriptions of the boundedness and compactness of multiplication operators in weighted Fock spaces with different indices are presented.展开更多
本文给出了Fock空间上两个Hankel算子乘积的有界性的必要条件描述,且结合反例证明此条件是两个Hankel算子乘积的有界性的必要不充分条件。In this paper, we give a description of the necessary condition for boundedness of the pro...本文给出了Fock空间上两个Hankel算子乘积的有界性的必要条件描述,且结合反例证明此条件是两个Hankel算子乘积的有界性的必要不充分条件。In this paper, we give a description of the necessary condition for boundedness of the product of two Hankel operators on Fock space, and prove that this condition is a necessary and insufficient condition for boundedness of the product of two Hankel operators.展开更多
Photon pairs with large nondegeneracy have recently attracted increasing interest, which gives rise to an urgent demand for revealing their complete and accurate spectral distribution. By thoroughly analyzing parametr...Photon pairs with large nondegeneracy have recently attracted increasing interest, which gives rise to an urgent demand for revealing their complete and accurate spectral distribution. By thoroughly analyzing parametric down-conversion(PDC), we put forward a model to directly describe the spatial-spectral distribution of these photon pairs, which is experimentally demonstrated by a 532-nm pumped type-I PDC in a beta barium borate(BBO) crystal. The measured spectral curves show good agreement with the theoretical predictions over the entire spectral range. We further demonstrate that, as signal wavelength increases, the photon pairs are initially spectrally distinguishable, then partly indistinguishable, finally completely indistinguishable with a maximum bandwidth of approximately 500 nm. Utilizing photon-number-resolving single-photon detectors(SPD), we observe the average photon number decreases significantly more slowly than the spectral intensity as the wavelength deviates from the peak, and the photon numbers follow a quasi-Poisson distribution well for wavelengths around the peak, but a thermal distribution better describes the statistics near the spectral boundaries. Finally,we use the signal photons as the trigger to generate heralded Fock states up to 10 photons in near-infrared range, which are suitable for quantum simulation and quantum key distribution in optical fiber networks.展开更多
The simultaneous description for nuclear matter and finite nuclei has been a long-standing challenge in nuclear ab initio theory.With the success for nuclear matter,the relativistic Brueckner-Hartree-Fock(RBHF)theory ...The simultaneous description for nuclear matter and finite nuclei has been a long-standing challenge in nuclear ab initio theory.With the success for nuclear matter,the relativistic Brueckner-Hartree-Fock(RBHF)theory with covariant chiral interactions is a promising ab initio approach to describe both nuclear matter and finite nuclei.In the description of finite nuclei with the current RBHF theory,the covariant chiral interactions have to be localized to make calculations feasible.In order to examine the reliability and validity,in this letter,the RBHF theory with local and nonlocal covariant chiral interactions at leading order is applied to nuclear matter.The low-energy constants in the covariant chiral interactions determined with the local regularization are close to those with the nonlocal regularization.Moreover,the RBHF theory using covariant chiral interactions with local and nonlocal regulators provides an equally good description of the saturation properties of nuclear matter.The present work paves the way for the implementation of covariant chiral interactions in RBHF theory for finite nuclei.展开更多
基金Supported by Sichuan Science and Technology Program (No.2022ZYD0010)。
文摘The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(■,...,■),t∈C,b∈C^(N) and A is a linear operator on C^(N).An example of 2-complex symmetric bounded weighted composition operator with the conjugation J_(t,A,b) is given.
文摘Letϕbe a smooth radial weight that decays faster than the class Gaussian ones.We obtain certain estimates for the reproducing kernels and the Lp-estimates for solutions of theδ-equation on the weighted Fock spaces F_(ϕ)^(p)(1≤p≤∞),which extends the classical Hörmander Theorem.Furthermore,for a suitable f,we completely characterize the boundedness and compactness of the Hankel operator H_(f):F_(ϕ)^(p)→L^(q)(C,e^(qϕ(·))dm)for all possible 1≤p,q<∞and also characterize the Schatten-p class Hankel operator Hf from F_(ϕ)^(2)to L^(2)(C,E^(-2ϕ)dm) for all 0<p<∞. As an application, we give a complete characterization of the simultaneously bounded, compact and Schatten-p classes Hankel operators H_(f) and h_(f)^(-) on F_(ϕ)^(2).
文摘本文主要研究了Fock空间Fαp上小Hankel算子hφ的有界性和紧性,得到了hφ在Fαp上有界的充分必要条件是其符号φ属于Fock空间Fα2∞;hφ在Fαp上紧的充分必要条件是φ属于fα2∞。This paper mainly studies the boundedness and compactness of the small Hankel operator hφon Fock space Fαp. It is found that the necessary and sufficient condition for hφbeing bounded on Fαpis that its symbol φbelongs to Fock space Fα2∞;the necessary and sufficient condition for hφbeing compact on Fαpis that φbelongs to fα2∞.
文摘本文凭借逐点估计、范数估计等相关技巧,给出了指标不同的加权Fock空间中乘法算子有界性与紧性的等价描述。In this paper, by pointwise estimation, norm estimation and other related techniques, the equivalent descriptions of the boundedness and compactness of multiplication operators in weighted Fock spaces with different indices are presented.
文摘本文给出了Fock空间上两个Hankel算子乘积的有界性的必要条件描述,且结合反例证明此条件是两个Hankel算子乘积的有界性的必要不充分条件。In this paper, we give a description of the necessary condition for boundedness of the product of two Hankel operators on Fock space, and prove that this condition is a necessary and insufficient condition for boundedness of the product of two Hankel operators.
基金Project supported by the National Natural Science Foundation of China (Grant No. 62075010)。
文摘Photon pairs with large nondegeneracy have recently attracted increasing interest, which gives rise to an urgent demand for revealing their complete and accurate spectral distribution. By thoroughly analyzing parametric down-conversion(PDC), we put forward a model to directly describe the spatial-spectral distribution of these photon pairs, which is experimentally demonstrated by a 532-nm pumped type-I PDC in a beta barium borate(BBO) crystal. The measured spectral curves show good agreement with the theoretical predictions over the entire spectral range. We further demonstrate that, as signal wavelength increases, the photon pairs are initially spectrally distinguishable, then partly indistinguishable, finally completely indistinguishable with a maximum bandwidth of approximately 500 nm. Utilizing photon-number-resolving single-photon detectors(SPD), we observe the average photon number decreases significantly more slowly than the spectral intensity as the wavelength deviates from the peak, and the photon numbers follow a quasi-Poisson distribution well for wavelengths around the peak, but a thermal distribution better describes the statistics near the spectral boundaries. Finally,we use the signal photons as the trigger to generate heralded Fock states up to 10 photons in near-infrared range, which are suitable for quantum simulation and quantum key distribution in optical fiber networks.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.12435006,12435007,12475117,12141501,and 123B2080)the National Key R&D Program of China(Grant No.2024YFE0109803)the National Key Laboratory of Neutron Science and Technology(Grant No.NST202401016)。
文摘The simultaneous description for nuclear matter and finite nuclei has been a long-standing challenge in nuclear ab initio theory.With the success for nuclear matter,the relativistic Brueckner-Hartree-Fock(RBHF)theory with covariant chiral interactions is a promising ab initio approach to describe both nuclear matter and finite nuclei.In the description of finite nuclei with the current RBHF theory,the covariant chiral interactions have to be localized to make calculations feasible.In order to examine the reliability and validity,in this letter,the RBHF theory with local and nonlocal covariant chiral interactions at leading order is applied to nuclear matter.The low-energy constants in the covariant chiral interactions determined with the local regularization are close to those with the nonlocal regularization.Moreover,the RBHF theory using covariant chiral interactions with local and nonlocal regulators provides an equally good description of the saturation properties of nuclear matter.The present work paves the way for the implementation of covariant chiral interactions in RBHF theory for finite nuclei.
