Linear Combinations of Composition Operators on Weighted Dirichlet Spaces

In this paper, linear combinations of composition operators acting on weighted Dirichlet spaces are studied. By using the first derivative of the kernel function, we obtain a lower estimate for the essential norms of these operators acting on the Dirichlet space D and S2. For general weighted Dirichlet space, by using complex interpolation methods, we characterize the compactness of these operators induced by linear fractional self-maps of the disk.

Vibrational frequency of a strong-coupling polaron in a quantum rod at finite temperatures

The Hamiltonian of a quantum rod with a boundary is presented after a coordinate transformation that changes the original ellipsoidal boundary into a spherical one. We then study the effect of temperature on the vibrational frequency and the ground state binding energy of the strong-coupling polaron in the rod. The two quantities are expressed as functions of the aspect ratio of the ellipsoid, the transverse and the longitudinal effective confinement lengths, the temperature and the electron-phonon coupling strength by linear combination operator and unitary transformation methods. It is found that the vibrational frequency and the ground state binding energy will increase rapidly with decreasing transverse and longitudinal effective confinement lengths. They are increasing functions of the electron- phonon coupling strength but become decreasing ones of the temperature and the aspect ratio.

QCSH:A full quantum computer nuclear shell-model package

The nuclear system is a promising area for demonstrating practical quantum advantage.A comprehensive computation of a nuclear system in a classical computer is beyond the capacity of current classical computers.With the rapid development of hardware,the prospect of using quantum computers in nuclear physics is close at hand.In this paper,we report a full quantum package,QCSH,for solving a nuclear shell model in a quantum computer.QCSH uses the linear combination of the unitary formalism of quantum computing and performs all calculations in a quantum computer.The complexities of qubit resource and the number of basic gates of QCSH are both polynomials to the number of nucleons in nuclei.For example,QCSH is used to calculate the binding energies of 12 light nuclei(i.e.,^(2)H,^(3)H,^(3)He,^(4)He,^(6)Li,^(7)Li,^(12)C,^(14)N,^(16)O,^(17)O,^(23)Na,and^(40)Ca).Moreover,we experimentally demonstrate the calculation of deuteron binding energy using a superconducting quantum processor.The result indicates that QCSH can provide meaningful results already in near-term quantum devices.

Effects of magnetic field on the polaron in an asymmetrical Gaussian confinement potential quantum well

The effects of a magnetic field on the vibrational frequency, the ground state energy and the ground state binding energy of a weak-coupling polaron in asymmetrical Gaussian confinement potential quantum well （AGCPQW） are investigated by using linear combination operator and unitary transformation methods. Our cal- culated results show that the vibrational frequency increases with increasing cyclotron frequency of the magnetic field; meanwhile, the absolute value of the ground state energy and the ground state binding energy decrease. The vibrational frequency, the absolute value of the ground state energy and the ground state binding energy are in- creasing functions of the barrier height of the AGCPQW. It is shown that the barrier height of the AGCPQW and the magnetic field are important factors that influence the properties of the magnetopolaron in AGCPQW.

Frequency of the transition spectral line of an electron in quantum rods

The Hamiltonian of a quantum rod with an ellipsoidal boundary is given after a coordinate transformation which changes the ellipsoidal boundary into a spherical one.We then study the first internal excited state energy,the excitation energy and the frequency of the transition spectral line between the first internal excited state and the ground state of the strong-coupling polaron in a quantum rod.The effects of the electron-phonon coupling strength,the aspect ratio of the ellipsoid,the transverse radius of quantum rods and the transverse and longitudinal effective confinement length are taken into consideration by using a linear combination operator and the unitary transformation methods.It is found that the first internal excited state energy,the excitation energy and the frequency of the transition spectral line are increasing functions of the electron-phonon coupling strength,whereas they are decreasing ones of the transverse radius of quantum rods and the aspect ratio.The first internal excited state energy,the excitation energy and the frequency of the transition spectral line increase with decreasing transverse and longitudinal effective confinement length.