Two identities are obtained by Jacobi's triple product identity and some basic operators. By applying these identities, Jacobi's theorem for the number of representations of an integer as a sum of eight square...Two identities are obtained by Jacobi's triple product identity and some basic operators. By applying these identities, Jacobi's theorem for the number of representations of an integer as a sum of eight squares is easily proved.展开更多
We study the critical scaling and dynamical signatures of fractionalized excitations at two different deconfined quantum critical points(DQCPs)in an S=1/2 spin chain using the time evolution of infinite matrix product...We study the critical scaling and dynamical signatures of fractionalized excitations at two different deconfined quantum critical points(DQCPs)in an S=1/2 spin chain using the time evolution of infinite matrix product states.The scaling of the correlation functions and the dispersion of the conserved current correlations explicitly show the emergence of enhanced continuous symmetries at these DQCPs.The dynamical structure factors in several different channels reveal the development of deconfined fractionalized excitations at the DQCPs.Furthermore,we find an effective spin-charge separation at the DQCP between the ferromagnetic(FM)and valence bond solid(VBS)phases,and identify two continua associated with different types of fractionalized excitations at the DQCP between the X-direction and Z-direction FM phases.Our findings not only provide direct evidence for the DQCP in one dimension but also shed light on exploring the DQCP in higher dimensions.展开更多
Based on the vibrational potential curves coupled with the minimum energy reaction path, the partial potential energy surface of the reaction I＋HI→IH＋I was constructed at the QCISD（T）//MP4SDQ level with pseudo po...Based on the vibrational potential curves coupled with the minimum energy reaction path, the partial potential energy surface of the reaction I＋HI→IH＋I was constructed at the QCISD（T）//MP4SDQ level with pseudo potential method. And the formation mechanism of the scattering resonance states of this reaction was well interpreted with the partial potential energy surface. The scattering resonance states of this reaction should belong to Feshbach resonance because of the coupling of the vibrational mode and the translational mode. With the one-dimensional square potential well model, the resonance width and lifetime of the I＋HI（v=0）→IH（v＇=0）＋I state-to-state reaction were calculated, which preferably explained the high-resolved threshold photodetachment spectroscopy of the IHI- anion performed by Neumark et al..展开更多
An instantaneous velocity where a moment of the clock only corresponds to an arbitrary distance or position in space cannot be implied in Axiom 1, but it indicates that there is only one dimensional existence, space o...An instantaneous velocity where a moment of the clock only corresponds to an arbitrary distance or position in space cannot be implied in Axiom 1, but it indicates that there is only one dimensional existence, space or time, where a certain moment only corresponds to itself specifically, not to any other time or any given length of space. Further, a definition of velocity that consists of two dimensions representing the relationship between space and time is not valid and there is only one-dimensional space or time that is independent of each other in Axiom 1. As a result, the principle of relativity and the principle of the constant velocity of light are replaced by the principle of an inertial system and the principle of universal invariant velocity in Axiom 1. Unlike two dimensions whose magnitude is determined by the ratio, the magnitude of a single dimension is determined by the unit values of one dimension, which indicates that an infinitely great velocity is meaningless. Further, if the two inertial systems are infinite versus finite in Axiom 3, then this extension of the infinitely great velocity can be defined as inextensible.展开更多
The existence, multiplicity and infinite solvability of positive solutions are established for some two-point boundary value problems of one-dimensional p-Laplacian. In this paper, by multiplicity we mean the existenc...The existence, multiplicity and infinite solvability of positive solutions are established for some two-point boundary value problems of one-dimensional p-Laplacian. In this paper, by multiplicity we mean the existence of m solutions, where m is an arbitrary natural number.展开更多
文摘Two identities are obtained by Jacobi's triple product identity and some basic operators. By applying these identities, Jacobi's theorem for the number of representations of an integer as a sum of eight squares is easily proved.
基金Project supported by the National Science Foundation of China(Grant No.12174441)the Fundamental Research Funds for the Central Universities,Chinathe Research Funds of Remnin University of China(Grant No.18XNLG24)。
文摘We study the critical scaling and dynamical signatures of fractionalized excitations at two different deconfined quantum critical points(DQCPs)in an S=1/2 spin chain using the time evolution of infinite matrix product states.The scaling of the correlation functions and the dispersion of the conserved current correlations explicitly show the emergence of enhanced continuous symmetries at these DQCPs.The dynamical structure factors in several different channels reveal the development of deconfined fractionalized excitations at the DQCPs.Furthermore,we find an effective spin-charge separation at the DQCP between the ferromagnetic(FM)and valence bond solid(VBS)phases,and identify two continua associated with different types of fractionalized excitations at the DQCP between the X-direction and Z-direction FM phases.Our findings not only provide direct evidence for the DQCP in one dimension but also shed light on exploring the DQCP in higher dimensions.
基金Ⅴ. ACKN0WLEDGMENTS This work was supported by the National Natural Science Foundation of China （No.20573064） and Ph.D. Special Research Foundation of Chinese Education Department.
文摘Based on the vibrational potential curves coupled with the minimum energy reaction path, the partial potential energy surface of the reaction I＋HI→IH＋I was constructed at the QCISD（T）//MP4SDQ level with pseudo potential method. And the formation mechanism of the scattering resonance states of this reaction was well interpreted with the partial potential energy surface. The scattering resonance states of this reaction should belong to Feshbach resonance because of the coupling of the vibrational mode and the translational mode. With the one-dimensional square potential well model, the resonance width and lifetime of the I＋HI（v=0）→IH（v＇=0）＋I state-to-state reaction were calculated, which preferably explained the high-resolved threshold photodetachment spectroscopy of the IHI- anion performed by Neumark et al..
文摘An instantaneous velocity where a moment of the clock only corresponds to an arbitrary distance or position in space cannot be implied in Axiom 1, but it indicates that there is only one dimensional existence, space or time, where a certain moment only corresponds to itself specifically, not to any other time or any given length of space. Further, a definition of velocity that consists of two dimensions representing the relationship between space and time is not valid and there is only one-dimensional space or time that is independent of each other in Axiom 1. As a result, the principle of relativity and the principle of the constant velocity of light are replaced by the principle of an inertial system and the principle of universal invariant velocity in Axiom 1. Unlike two dimensions whose magnitude is determined by the ratio, the magnitude of a single dimension is determined by the unit values of one dimension, which indicates that an infinitely great velocity is meaningless. Further, if the two inertial systems are infinite versus finite in Axiom 3, then this extension of the infinitely great velocity can be defined as inextensible.
文摘The existence, multiplicity and infinite solvability of positive solutions are established for some two-point boundary value problems of one-dimensional p-Laplacian. In this paper, by multiplicity we mean the existence of m solutions, where m is an arbitrary natural number.
