A simple model for short-range correlations in nuclear matter

It is shown that Pauli blocking and short-range correlation effects, which strongly renormalize the bare nucleon-nucleon interaction in the medium, can be summarized in a correlation operator which has an extremely simple structure. The use of such a simple correlation operator leads to a form of Brueckner's reaction-matrix interaction which is very convenient for applications. The effective interaction introduced by the Jülich-Stony Brook group and extensively used in the study of the spin-isospin excitation modes in nuclei is derived from a meson exchange potential.     

Retardation effects from quark confinement on low-energy nucleon dynamics

We investigate effects from quark confinement on low-energy nucleon dynamics. These effects are shown to give rise to a peculiar dynamical situation: Low-energy nucleon dynamics is not Hamiltonian and is governed by a nonlocal-in-time interaction operator. In the leading order of the two-nucleon EFT we show that after renormalization the nucleon dynamics is governed by the same interaction operator.     

On the calculation of the classical Liouville operator for the step-type interparticle interaction

A new method of the determination of the Liouville operator for the step-type interparticle interaction is presented. The interaction part of the Liouville operator is calculated for the particles interacting via a spherical repulsive and spherical attractive barrier. Limiting cases of an infinitely high (hard core) and infinitely deep barrier are discussed. These results can be used for the determination of the interaction part of the Liouville operator for an arbitrary step-type interaction which can be expressed as a sum of several attractive and repulsive barriers.     

New Representation of Rotation Operator and Its Application

By employing the technique of integration within an ordered product of operators, we derive natural representations of the rotation operator, the two-mode Fourier transform operator and the two-mode parity operator in entangled state representations. As an application, it is proved that the rotation operator constructed by the entangled state representation is a useful tool to solve the exact energy spectra of the two-mode harmonic oscillators with coordinat-momentum interaction.     

原子-辐射场相互作用系统 Heisenberg运动方程的相干态表述

用Heisenberg-Weyle(简称H-W)群直积SU(2)群上的相干态表述了原 子-辐射场相互作用系统的Heisenberg运动方程。引入一个算符振幅函数,将Heisenberg绘 景中算符运动方程转化成可分离变量的偏微分方程,给出了方程的形式解以及时间演化算符 在该表述下的表示。     

A system with two photon states and two polarization-entangled photon modes as configuration of minimal coupling to a classical pump field

The configuration of minimum interaction energy between two polarization-entangled photon modes and a classical pump field is determined by treating the corresponding interaction Hamiltonian operator. In fact, the above configuration is found to be of two photon states.     

Generalization of the Hecke theorem for the nonlinear Boltzmann collision integral in the axisymmetric case

The properties of the nonlinear collision integral in the Boltzmann equation are studied. Expansions in spherical Hermitean polynomials are used. It was shown [1] that the nonlinear matrix elements of the collision operator are related to each other by simple expressions, which are valid for arbitrary cross sections of particle interaction. The structure of the collision operator and the properties of the matrix elements are studied for the case when the interaction potential is spherically symmetric. In this case, the linear Boltzmann operator satisfies the Hecke theorem. The generalized Hecke theorem, from which it follows that many nonlinear matrix elements vanish, is proved with recurrence relations derived. It is shown that the generalized Hecke theorem is a consequence of the ordinary Hecke theorem.     

Calculation of transitions in intense laserfields with the Magnus expansion

For bound quantum systems in presence of strong long wavelength electromagnetic fields the time evolution operator is calculated by application of the Magnus expansion in the interaction picture. We find that the first two orders of the Magnus expansion of the interaction picture time evolution operator contain both the momentum-translation transform of H.R. Reiss and terms which give rise to a non-static Stark-effect.     

Geometric Phase Gate Based on Both Displacement Operator and Squeezed Operators with a Superconducting Circuit Quantum Electrdynamics

We give the brief review on the related definition of the geometric phase independent of specific physical system based on the displacement opreator and
the sqeezed operator, then show how the displacement operator and the squeezed operator can induce the general geometric phase. By means of the displacement operator and the squeezed operator concerning the circuit cavity mode state along a closed path in the phase space, we discuss specifically how to implement a two-qubit geometric phase gate in circuit quantum electrodynamics with both single photon interaction and two-photon interaction between the superconducting qubits and the circuit cavity modes. The experimental feasibility is discussed in detail.     

Physical Realization of Quantum C-Not Gate

We investigate a Heisenberg spin cluster with two particles controlled by a time-dependent magnetic field. The system is controlled by tuning the amplitude, frequency, and interaction time of the three-step time-dependent magnetic field. Then we solve the time-dependent Schrodinger equation of the two-particle system, and obtain the time evolution operator. By the three-timestep interaction, the wavefunction evolves from the initial state to the final state, and the total evolution operator can be expressed as a product of the three evolution operators. By adjusting the physical parameters, the key two-qubit logic gate, the C-Not gate, can be realized physically.     

当能级间隔较小时三能级核四极共振自旋系统对脉冲的响应

用虚拟自旋—１／２算符理论考察了Ｉ＝１的核四极共振自旋系统在其能级间隔较小时对１—２个脉冲的响应．由于核四极相互作用表象中的射频场与核自旋的相互作用（Ｈｎ）包含时间．因而用Ｄｙｓｏｎ时序算符来计算密度算符在Ｈｎ作用下的演化．     

Spin-other-orbit interaction in highly excited configurations with p and g electrons in outer shells

The matrix of the operator of the spin-other-orbit interaction energy is constructed for npn’g and np ⁵ n’g configurations. The matrix elements of this operator are calculated in the single-configuration approximation with wave functions in the LSJM representation and in the representation of uncoupled angular momenta using the known general formulas. The spin-other-orbit interaction is represented by three direct and three exchange radial Marvin spin interaction integrals.     

当能级间隔较小时三能级核四极共振自旋系统对脉冲的响应

用虚拟自旋-1/2算符理论考察了I=1的核四极共振自旋系统在其能级间隔较小时对1-2个脉冲的响应.由于核四极相互作用表象中的射频场与核自旋的相互作用(H_rf)包含时间,因而用Dyson时序算符来计算密度算符在H_rf作用下的演化.     

Higher-order spin-orbit interaction in photoelectron spectra of mercury halides

Spin-orbit interaction is introduced into the semi-empirical Extended Hückel MO scheme by adding the spin-orbit interaction operator to the effective     

Spectral splitting method for nonlinear Schrödinger equations with singular potential

We consider the time-dependent one-dimensional nonlinear Schrödinger equation with pointwise singular potential. By means of spectral splitting methods we prove that the evolution operator is approximated by the Lie evolution operator, where the kernel of the Lie evolution operator is explicitly written. This result yields a numerical procedure which is much less computationally expensive than multi-grid methods previously used. Furthermore, we apply the Lie approximation in order to make some numerical experiments concerning the splitting of a soliton, interaction among solitons and blow-up phenomenon.     

Connection between the eigenvalues of the energy operator and the s matrix in quantum field theory

A formula that connects the eigenvalues of the energy operator of a system of interacting fields with the S matrix generated by the operator of the interaction energy is derived.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 11–15, June, 1980.     

A quasi-energy operator in the Jaynes-Cummings model in a polychromatic classical field

A perturbation theory is developed for constructing the quasi-energy operator Q of the Tavis-Cummings Hamiltonian, which includes the interaction of atoms with a classical quasi-monochromatic field. The operator Q of the first order in the interaction δ of an atom with a resonator mode has a form of the generalized Tavis-Cummings Hamiltonian (in the interaction representation) to which the oppositely rotating terms with a changed interaction constant are added. Such a Hamiltonian has a singularity in the dimensionless amplitude σ of a classical field. In the vicinity of this singularity, the Hamiltonian spectrum tends to a continuous one, while the degree of squeezing of field quadratures (in its eigenstates) increases infinitely. In the case of one atom and the biharmonic perturbation, the operator Q is obtained up to the third order of the perturbation theory. The spectral problem for Q is studied. The features of the dependence of the quasi-energy spectrum on σ are explained by the presence of an efficient barrier between the regions of the “coordinate” space. It is found that the above-mentioned singularity corresponds to the beginning of the parametric resonance zone. Analytic expressions for the top and bottom of this zone in the δσ plane are presented.     

Ward-Takahashi identity for the electromagnetic current of two-particle systems on the light front

The problem of nonconservation of the electromagnetic current for two-boson systems on the light front obtained by truncation of the quasi-potential expansion is studied. We found that current conservation can be restored by a subtle choice of the truncation of the expansion of the current operator, while the naive truncation of the expansion of both current and effective interaction violates covariance and current conservation. The framework allows to treat at the same level the current operator for bound and scattering states. The generalization to two-fermion systems is briefly discussed.     

Spectral Theory of Perturbative Decays

We propose a complex approach to evaluating afunction sum of two noncommuting non-Hermitianoperators. We propose an explicit expansion of theevolution operator in the case of the neutral K-mesonsystem influenced by an external interaction. Theimportance is pointed out of considering the algebraicexpansion of the time evolution operator whenever thedynamics decouples the internal transitions andcenter-of-mass motion.