Effective-Field Theory on High Spin Systems with Biaxial Crystal Field

Based on the effective-field theory with self-spin correlations and the differential operator technique,physical properties of the spin-2 system with biaxial crystal field on the simple cubic, body-centered cubic, as well as faced-centered lattice have been studied. The influences of the external longitudinal magnetic field on the magnetization,internal energy, specific heat, and susceptibility have been discussed in detail. The phenomenon that the magnetization in the ground state shows quantum effects produced by the biaxial transverse crystal field has been found.     

Effective-Field Theory for Kinetic Ising Model on Honeycomb Lattice

As an analytical method, the effective-field theory （EFT） is used to study the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field. The effective-field equations of motion of the average magnetization are given for the honeycomb lattice （Z = 3）. The Liapunov exponent A is calculated for discussing the stability of the magnetization and it is used to determine the phase boundary. In the field amplitude ho / ZJ-temperature T/ZJ plane, the phase boundary separating the dynamic ordered and the disordered phase has been drawn. In contrast to previous analytical results that predicted a tricritical point separating a dynamic phase boundary line of continuous and discontinuous transitions, we find that the transition is always continuous. There is inconsistency between our results and previous analytical results, because they do not introduce sufficiently strong fluctuations.     

量子场论中的自旋算符

从量子场论的角度对相对论粒子的运动自旋概念作了进一步深入研究.构造了场量子自旋以及场系统运动自旋两个新算符.给出了场量子自旋动量空间的显式表达式以及用Poincar啨群生成元表示的场系统运动自旋的显式表达式.借助这两个算符,可以干净地解决有关场自旋的问题,表明它们才是场自旋的恰当的算符.     

双轴晶体光学参量放大的研究

介绍了新近提出的光学啁啾脉冲参量放大技术,并以高增益、宽谱带的双轴非线性晶体LBO为例,研究了抽运光和信号光的相位匹配的关系、增益、增益带宽、匹配角的选择,以及增益随晶体长度变化的趋势和双曲正割和高斯脉冲输入非线性晶体前后变化的情况。     

Effects of Arbitrarily Directed Field on Spin Phase Oscillations in Biaxial Molecular Magnets

Quantum phase interference and spin-parity effects are studied in biaxial molecular magnets in a magnetic field at an arbitrarily directed angle.The calculations of the ground-state tunnel splitting are performed on the basis of the instanton technique in the spin-coherent-state path-integral representation,and complemented by exactly numerical diagonalization.Both the Wentzel-Kramers-Brillouin exponent and the pre-exponential factor are obtained for the entire region of the direction of the field.Our results show that the tunnel splitting oscillates with the field for the small field angle,while for the large field angle the oscillation is completely suppressed.This distinct angular dependence,together with the dependence of the tunnel splitting on the field strength,provides an independent test for spin-parity effects in biaxial molexular magnets.The analytical results for the molecular Fes magnet are found to be in good agreement with the numerical simulations,which suggests that even the molecular magnet with total spin S=10 is large enough to be treated as a giant spin system.     

Field Theory on Kappa-spacetime

A general formalism is developed, that allows the construction of field theory on quantum spaces which are deformations of ordinary spacetime. The symmetry group of spacetime is replaced by a quantum group. This formalism is demonstrated for the -deformed Poincaré algebra and its quantum space. The algebraic setting is mapped to the algebra of functions of commuting variables with a suitable -product. Fields are elements of this function algebra. As an example, the Klein-Gordon equation is defined and derived from an action.     

光孤子约束系统的量子场论

光孤子系统可用奇异Lagrange量描述,系统含Dirac约束.通常按对应原理写出系统对易关系和量子运动方程时,未计及约束.文中对该系统进行严格的Dirac括号量子化,给出了系统的对易关系和量子运动方程,还对系统进行了路径积分量子化,并根据量子水平的Noether定理,导出了系统在时空平移变换不变性下的量子能量和动量守恒.系统还具有相位变换下的不变性,相应导出了系统的粒子数守恒.     

Analysis of Internal Conical Refraction Using Ray Tracing Formulas for the Biaxial Crystal

Internal or external conical refractions are strange optical phenomena appearing in biaxial crystal. In this paper the analysis of internal conical refraction is derived using the ray tracing formulas for the biaxial crystals, after explaining the theory of the ray tracing for the biaxial or uniaxial crystals. The double rings of conical refraction are also investigated; these are affected by the polarization state or angular intensity distributions of the incident light beam causing conical refraction.     

双轴晶体光轴角计算的新方法

介绍几何作图计算双轴晶体光轴角的方法、步骤和原理.利用几何作图求得双轴晶体的光轴角,并通过理论推导来证明其正确性.     

Interference in Quantum Field Theory: Detecting Ghosts with Phases

This study discusses the implications of the principle of locality for interference in quantum field theory. As an example, it considers the interaction of two charges via a mediating quantum field and the resulting interference pattern in the Lorenz gauge. Using the Heisenberg picture, it is proposed that detecting relative phases or entanglement between two charges in an interference experiment is equivalent to accessing empirically the gauge degrees of freedom associated with the so-called ghost (scalar) modes of the field in the Lorenz gauge. These results imply that ghost modes are measurable and hence physically relevant, contrary to what is usually thought. They also raise interesting questions about the relation between the principle of locality and the principle of gauge-invariance. This analysis also applies to linearized quantum gravity in the harmonic gauge, and hence has implications for the recently proposed entanglement-based witnesses of non-classicality in gravity.     

Covariant Hamiltonian Field Theory: Path Integral Quantization

The Hamiltonian counterpart of classical Lagrangian field theory is covariant Hamiltonian field theory where momenta correspond to derivatives of fields with respect to all world coordinates. In particular, classical Lagrangian and covariant Hamiltonian field theories are equivalent in the case of a hyperregular Lagrangian, and they are quasi-equivalent if a Lagrangian is almost-regular. In order to quantize covariant Hamiltonian field theory, one usually attempts to construct and quantize a multisymplectic generalization of the Poisson bracket. In the present work, the path integral quantization of covariant Hamiltonian field theory is suggested. We use the fact that a covariant Hamiltonian field system is equivalent to a certain Lagrangian system on a phase space which is quantized in the framework of perturbative quantum field theory. We show that, in the case of almost-regular quadratic Lagrangians, path integral quantizations of associated Lagrangian and Hamiltonian field systems are equivalent.     

Effective Field Theory of Random Quantum Circuits

Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have already been experimentally demonstrated in noisy intermediate-scale quantum (NISQ) devices. On the theory side, properties of random quantum circuits have been studied on a case-by-case basis and for certain specific systems, and a hallmark of quantum chaos—universal Wigner–Dyson level statistics—has been derived. This work develops an effective field theory for a large class of random quantum circuits. The theory has the form of a replica sigma model and is similar to the low-energy approach to diffusion in disordered systems. The method is used to explicitly derive the universal random matrix behavior of a large family of random circuits. In particular, we rederive the Wigner–Dyson spectral statistics of the brickwork circuit model by Chan, De Luca, and Chalker [Phys. Rev. X 8, 041019 (2018)] and show within the same calculation that its various permutations and higher-dimensional generalizations preserve the universal level statistics. Finally, we use the replica sigma model framework to rederive the Weingarten calculus, which is a method of evaluating integrals of polynomials of matrix elements with respect to the Haar measure over compact groups and has many applications in the study of quantum circuits. The effective field theory derived here provides both a method to quantitatively characterize the quantum dynamics of random Floquet systems (e.g., calculating operator and entanglement spreading) and a path to understanding the general fundamental mechanism behind quantum chaos and thermalization in these systems.     

双轴晶体会聚偏光干涉的理论与实验研究

晶体会聚偏光干涉图包含了晶体特性的许多信息,建立偏光干涉图的定量分析方法可以使这些信息得到充分利用。基于双轴晶体折射时满足的波矢关系,导出了两折射光波相位差的精确计算公式。分析了光波在各界面折射时偏振态的变化,提出了会聚偏光干涉合成振幅的计算方法。针对任意取向的双轴晶体,计算了完整的偏光干涉图,反映了相位分布决定等色线、振幅分布决定消光影的规律。用数字图像模似了干涉图,并讨论了干涉图的变化情况。对4块不同取向的KTP晶片进行实验,实验干涉图与理论干涉图的特征完全一致,两者仔细对比可判断现有KTP晶体色散方程的优劣。     

Gravity and Spin Forces in Gravitational Quantum Field Theory

In the new framework of gravitational quantum field theory (GQFT) with spin and scaling gauge invariance developed in Phys. Rev. D 93 (2016) 024012-1, we make a perturbative expansion for the full action in a background field which accounts for the early inflationary universe. We decompose the bicovariant vector fields of gravifield and spin gauge field with Lorentz and spin symmetries SO(1,3) and SP(1,3) in biframe spacetime into SO(3) representations for deriving the propagators of the basic quantum fields and extract their interaction terms. The leading order Feynman rules are presented. A tree-level 2 to 2 scattering amplitude of the Dirac fermions, through a gravifield and a spin gauge field, is calculated and compared to the Born approximation of the potential. It is shown that the Newton's gravitational law in the early universe is modified due to the background field. The spin dependence of the gravitational potential is demonstrated.     

Quantum Field Theory and Dense Measurement

We show, using quantum field theory (QFT), that performing a large number of identical repetitions of the same measurement does not only preserve the initial state of the wave function (the Zeno effect), but also produces additional physicaleffects. We first discuss the Zeno effect in the framework of QFT, that is, as a quantum field phenomenon. We then derive it from QFT for the general case in which the initial and final states are different. We use perturbation theory and Feynman diagrams and refer to the measurement act as an external constraint upon the system that corresponds to the perturbative diagram that denotes this constraint. The basic physical entities dealt with in this work are not the conventional once-perfomed physical processes, but their n times repetition where n tends to infinity. We show that the presence of these repetitions entails the presence of additional excited state energies, and the absence of them entails the absence of these excited energies.     

Field Theory Approaches to Relativistic Hydrodynamics

Just as non-relativistic fluids, oftentimes we find relativistic fluids in situations where random fluctuations cannot be ignored, with thermal and turbulent fluctuations being the most relevant examples. Because of the theory’s inherent nonlinearity, fluctuations induce deep and complex changes in the dynamics of the system. The Martin–Siggia–Rose technique is a powerful tool that allows us to translate the original hydrodynamic problem into a quantum field theory one, thus taking advantage of the progress in the treatment of quantum fields out of equilibrium. To demonstrate this technique, we shall consider the thermal fluctuations of the spin two modes of a relativistic fluid, in a theory where hydrodynamics is derived by taking moments of the Boltzmann equation under the relaxation time approximation.     

Quantum Field Theory with a Minimal Length Induced from Noncommutative Space

From the inspection of noncommutative quantum mechanics, we obtain an approximate equivalent relation for the energy dependence of the Planck constant in the noncommutative space, which means a minimal length of the space. We find that this relation is reasonable and it can inherit the main properties of the noncommutative space. Based on this relation, we derive the modified Klein-Gordon equation and Dirac equation. We investigate the scalar field and φ4 model and then quantum electrodynamics in our theory, and derive the corresponding Feynman rules. These results may be considered as reasonable approximations to those of noncommutative quantum field theory. Our theory also shows a connection between the space with a minimal length and the noncommutative space.     

非均匀外磁场下海森堡自旋链的热纠缠

研究了两量子比特海森堡XXX自旋链处于x方向的非均匀磁场时系统的纠缠特性,并用负度N来度量.得到N的解析表达式,并在此基础上进行数值计算.仔细讨论了均匀磁场B、非均匀磁场b、温度T和自旋耦合系数J对纠缠度N的影响.结果表明:N会随着■和T的增大而减小,但会随着J的增大而增大.同时,增大的J和b还会使临界磁场■和临界温度T_th变大,从而使系统中热纠缠存在的磁场范围和温度范围都变大.这一点在较大磁场和较高温度下需要纠缠具有实际意义.由此,我们可以通过调节B、b、T和J来控制热纠缠,这对固态系统中通过构建和选择参数调整系统的纠缠度具有一定的作用和意义.     

On Field Theory Methods in Singular Perturbation Theory

Singular and supersingular finite rank perturbations of self-adjoint operators are studied using methods from renormalization theory for quantum fields. It is shown that the ideas from dimensional and Pauli–Villars regulatizations can be applied to determine uniquely certain finite rank supersingular perturbations. Approach is based on the regularization of homogeneous singular quadratic forms.     

Toward a Finite-Dimensional Formulation of Quantum Field Theory

Rules of quantization and equations of motion for a finite-dimensional formulation of quantum field theory are proposed which fulfill the following properties: (a) Both the rules of quantization and the equations of motion are covariant; (b) the equations of evolution are second order in derivatives and first order in derivatives of the spacetime coordinates; and (c) these rules of quantization and equations of motion lead to the usual (canonical) rules of quantization and the (Schrödinger) equation of motion of quantum mechanics in the particular case of mechanical systems. We also comment briefly on further steps to fully develop a satisfactory quantum field theory and the difficuties which may be encountered when doing so.