For classical Hamiltonian with general form H = 1/2∑ijMijpipj+1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator (...For classical Hamiltonian with general form H = 1/2∑ijMijpipj+1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator (IEO) method (Fan et al. 2004 Phys. Lett. A 321 75) to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived.展开更多
Noticing that the equation with double-Poisson bracket, where On is normal coordinate, Hc is classical Hamiltonian, is the classical correspondence of the invariant eigen-operator equation (2004 Phys. Left. A. 321 75...Noticing that the equation with double-Poisson bracket, where On is normal coordinate, Hc is classical Hamiltonian, is the classical correspondence of the invariant eigen-operator equation (2004 Phys. Left. A. 321 75), we can find normal coordinates in harmonic crystal by virtue of the invaxiant eigen-operator method.展开更多
This paper reports that the mesoscopic inductance and capacitance coupling LC circuit is quantized by means of the canonical quantization method. Using the 'invariant eigen-operator' method, it deduces the energy-le...This paper reports that the mesoscopic inductance and capacitance coupling LC circuit is quantized by means of the canonical quantization method. Using the 'invariant eigen-operator' method, it deduces the energy-level transition rule when the system is disturbed by an external electromagnetic field. At the same time, the quantum fluctuations for the system at finite temperature are examined by virtue of the generalized Hellmann-Feynman theorem.展开更多
We used the Jordan-Wigner transform and the invariant eigenoperator method to study the magnetic phase diagram and the magnetization curve of the spin-1/2 alternating ferrimagnetic diamond chain in an external magneti...We used the Jordan-Wigner transform and the invariant eigenoperator method to study the magnetic phase diagram and the magnetization curve of the spin-1/2 alternating ferrimagnetic diamond chain in an external magnetic field at finite temperature.The magnetization versus external magnetic field curve exhibits a 1/3 magnetization plateau at absolute zero and finite temperatures,and the width of the 1/3 magnetization plateau was modulated by tuning the temperature and the exchange interactions.Three critical magnetic field intensities H_(CB),H_(CE)and H_(CS) were obtained,in which the H_(CB) and H_(CE)correspond to the appearance and disappearance of the 1/3 magnetization plateau,respectively,and the higher H_(CS) correspond to the appearance of fully polarized magnetization plateau of the system.The energies of elementary excitation hω_(σ,k)(σ=1,2,3)present the extrema of zero at the three critical magnetic fields at 0 K,i.e.,[hω_(3,k)(H_(CB)]_(min)=0,[hω_(2,k)(H_(CE)]_(max)=0 and[hω_(2,k)(H_(CS)]_(min)=0,and the magnetic phase diagram of magnetic field versus different exchange interactions at 0 K was established by the above relationships.According to the relationships between the system’s magnetization curve at finite temperatures and the critical magnetic field intensities,the magnetic field-temperature phase diagram was drawn.It was observed that if the magnetic phase diagram shows a three-phase critical point,which is intersected by the ferrimagnetic phase,the ferrimagnetic plateau phase,and the Luttinger liquid phase,the disappearance of the 1/3 magnetization plateau would inevitably occur.However,the 1/3 magnetization plateau would not disappear without the three-phase critical point.The appearance of the 1/3 magnetization plateau in the low temperature region is the macroscopic manifestations of quantum effect.展开更多
基金supported by the National Natural Science Foundation of China (Grant No.10874174)the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20070358009)
文摘For classical Hamiltonian with general form H = 1/2∑ijMijpipj+1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator (IEO) method (Fan et al. 2004 Phys. Lett. A 321 75) to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived.
基金supported by the National Natural Science Foundation of China (Grant No. 10574060)the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A23)the Shandong Province Higher Educational Science and Technology Program (Grant No. J09LA07)
文摘Noticing that the equation with double-Poisson bracket, where On is normal coordinate, Hc is classical Hamiltonian, is the classical correspondence of the invariant eigen-operator equation (2004 Phys. Left. A. 321 75), we can find normal coordinates in harmonic crystal by virtue of the invaxiant eigen-operator method.
基金supported by the National Natural Science Foundation of China(Grant No 10574060)the Natural Science Foundation of Shandong Province of China(Grant No Q2007A01)
文摘This paper reports that the mesoscopic inductance and capacitance coupling LC circuit is quantized by means of the canonical quantization method. Using the 'invariant eigen-operator' method, it deduces the energy-level transition rule when the system is disturbed by an external electromagnetic field. At the same time, the quantum fluctuations for the system at finite temperature are examined by virtue of the generalized Hellmann-Feynman theorem.
基金the National Natural Science Foundation of China(Grant Nos.11374215 and 11704262)the Scientific Study Project from Education Department of Liaoning Province of China(Grant No.LJ2019004)the Natural Science Foundation Guidance Project of Liaoning Province of China(Grant No.2019-ZD-0070).
文摘We used the Jordan-Wigner transform and the invariant eigenoperator method to study the magnetic phase diagram and the magnetization curve of the spin-1/2 alternating ferrimagnetic diamond chain in an external magnetic field at finite temperature.The magnetization versus external magnetic field curve exhibits a 1/3 magnetization plateau at absolute zero and finite temperatures,and the width of the 1/3 magnetization plateau was modulated by tuning the temperature and the exchange interactions.Three critical magnetic field intensities H_(CB),H_(CE)and H_(CS) were obtained,in which the H_(CB) and H_(CE)correspond to the appearance and disappearance of the 1/3 magnetization plateau,respectively,and the higher H_(CS) correspond to the appearance of fully polarized magnetization plateau of the system.The energies of elementary excitation hω_(σ,k)(σ=1,2,3)present the extrema of zero at the three critical magnetic fields at 0 K,i.e.,[hω_(3,k)(H_(CB)]_(min)=0,[hω_(2,k)(H_(CE)]_(max)=0 and[hω_(2,k)(H_(CS)]_(min)=0,and the magnetic phase diagram of magnetic field versus different exchange interactions at 0 K was established by the above relationships.According to the relationships between the system’s magnetization curve at finite temperatures and the critical magnetic field intensities,the magnetic field-temperature phase diagram was drawn.It was observed that if the magnetic phase diagram shows a three-phase critical point,which is intersected by the ferrimagnetic phase,the ferrimagnetic plateau phase,and the Luttinger liquid phase,the disappearance of the 1/3 magnetization plateau would inevitably occur.However,the 1/3 magnetization plateau would not disappear without the three-phase critical point.The appearance of the 1/3 magnetization plateau in the low temperature region is the macroscopic manifestations of quantum effect.