Dual charged solution in curved space-time

A dual charged solution carrying both electric and magnetic charge is formulated in SU(2) × U(1) gauge theory without making use of the topological characteristics of Higgs fields. When Dirac quantisation condition is imposed, two consequences follow: (i) Weinberg angle is restricted to the value sin² θ = 1/2 and (ii) the solution cannot have fractional electric change, but must have integer items the basic electric charge of the theory. The infinity inherent in the theory is removed at the classical level by the use of gravitational effects by obtaining the same solution in the curved space-time. The resultant metric is of Reissner-Nordström form.     

弯曲时空几何光学中的聚焦定理

严格、详细地证明了弯曲时空几何光学中的聚焦定理.     

Noncommutative space-time models

The FRT quantum Euclidean spaces O _q ^N are formulated in terms of Cartesian generators. The quantum analogs of N-dimensional Cayley-Klein spaces are obtained by contractions and analytical continuations. Noncommutative constant-curvature spaces are introduced as spheres in the quantum Cayley-Klein spaces. For N = 5 part of them is interpreted as the noncommutative analogs of (1+3) space-time models. As a result the quantum (anti) de Sitter, Minkowski, Newton, Galilei kinematics with the fundamental length and the fundamental time are suggested. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Photon counting statistics in single multi-level quantum system

<正>We theoretically study the statistics of photon emission of a single multi-level quantum system by employing the generating functions approach developed recently.The generalized decay constants are included in a single multi-level quantum system with quasi-degenerated levels in this work although they are normally neglected in the absence of (quasi-)degeneracies in a multi-level quantum system within the rotating wave approximation.The quantum beats,the line shapes and the Mandel's Q parameters,etc.are studied.     

Probabilistic teleportation of an arbitrary GHZ-class state with a pure entangled two-particle quantum channel and its application in quantum state sharing

This paper presents a scheme for probabilistic teleportation of an arbitrary GHZ-class state with a pure entangled two-particle quantum channel. The sender Alice first teleports the coefficients of the unknown state to the receiver Bob, and then Bob reconstructs the state with an auxiliary particle and some unitary operations if the teleportation succeeds. This scheme has the advantage of transmitting much less particles for teleporting an arbitrary GHZ-class state than others. Moreover, it discusses the application of this scheme in quantum state sharing.     

硅量子点的形状及其弯曲表面效应

硅量子点的弯曲表面引起系统的对称性破缺, 致使某些表面键合在能带的带隙中形成局域电子态.计算结果表明:硅量子点的表面曲率不同形成的表面键合结合能和电子态分布明显不同. 例如, Si–O–Si桥键在曲率较大的表面键合能够在带隙中形成局域能级, 而在硅量子点曲率较小的近平台表面上键合不会形成任何局域态, 但此时的键合结合能较低. 用弯曲表面效应(CS)可以解释较小硅量子点的光致荧光光谱的红移现象. CS效应揭示了纳米物理中又一奇妙的特性. 实验证实, CS效应在带隙中形成的局域能级可以激活硅量子点发光. 关键词： 硅量子点 弯曲表面效应 表面键合 局域能级     

Role of quantum statistics in multi-particle decay dynamics

The role of quantum statistics in the decay dynamics of a multi-particle state, which is suddenly released from a confining potential, is investigated. For an initially confined double particle state, the exact dynamics is presented for both bosons and fermions. The time-evolution of the probability to measure two-particle is evaluated and some counterintuitive features are discussed. For instance, it is shown that although there is a higher chance of finding the two bosons (as oppose to fermions, and even distinguishable particles) at the initial trap region, there is a higher chance (higher than fermions) of finding them on two opposite sides of the trap as if the repulsion between bosons is higher than the repulsion between fermions. The results are demonstrated by numerical simulations and are calculated analytically in the short-time approximation. Furthermore, experimental validation is suggested.     

Full counting statistics of renormalized dynamics in open quantum transport system

The internal dynamics of a double quantum dot system is renormalized due to coupling respectively with transport electrodes and a dissipative heat bath. Their essential differences are identified unambiguously in the context of full counting statistics. The electrode coupling caused level detuning renormalization gives rise to a fast-to-slow transport mechanism, which is not resolved at all in the average current, but revealed uniquely by pronounced super-Poissonian shot noise and skewness. The heat bath coupling introduces an interdot coupling renormalization, which results in asymmetric Fano factor and an intriguing change of line shape in the skewness.     

The interpolation approach to nonextensive quantum statistics

Recently it has been shown by the present author [H. Hasegawa, Phys. Rev. E 80 (2009) 011126] that the interpolation approximation (IA) to the generalized Bose-Einstein and Fermi-Dirac distributions yields good results in agreement with the exact ones within the O(q−1) and in high- and low-temperature limits, where (q−1) expresses the nonextensivity: the case of q=1 corresponding to the conventional quantal distributions. This paper reports applications of the IA to four nonextensive quantum subjects: (i) the black-body radiation, (ii) the Bose-Einstein condensation, (iii) the BCS superconductivity and (iv) itinerant-electron (metallic) ferromagnetism. Effects of the nonextensivity on physical quantities in these nonextensive quantum systems have been investigated. Comparisons between the calculated results and available observed data are made for the subjects (ii) and (iii). It has been pointed out that the factorization approximation (FA) which has been so far applied to many nonextensive systems, overestimates the nonextensivity and that it leads to inappropriate results for fermion systems like the subjects (iii) and (iv).     

Optical theorem in curved space-time quantum field theory

A structural analysis is given of the optical theorem in theS-matrix approach to mutually interacting quantum fields in classical Robertson-Walker universes. As a case study, theφψ ²-interaction of conformally coupled massive (φ) and massless (φ) Klein-Gordon particles is studied. Based on the outgoing massless particles as indicator configuration, the physical interpretation is reduced to the corresponding added-up probabilities. Several examples are discussed in an in-in scheme which has the advantage that only a few non-Minkowskian in-in Feynman diagrams are involved.     

Energy-level statistics of model quantum systems: Universality and scaling in a lattice-point problem

We investigate the statistics of the numberN(R, S) of lattice pointsnZ ², in an annular domain (R, w)=(R+w)A\RA, whereR, w>0. HereA is a fixed convex set with smooth boundary andw is chosen so that the area of (R, w) isS. The statistics comes fromR being taken as random (with a smooth density) in some interval [c ₁ T,c ₂,T],c ₂>c ₁>0. We find that in the limitT the variance and distribution of N=N(R; S)–S depend strongly on howS grows withT. There is a saturation regimeS/T, asT, in which the fluctuations in N coming from the two boundaries of are independent. Then there is a scaling regime,S/Tz, 0<z<, in which the distribution depends onz in an almost periodic way going to a Gaussian asz0. The variance in this limit approachesz for genericA, but can be larger for degenerate cases. The former behavior is what one would expect from the Poisson limit of a distribution for annuli of finite area.     

Geometric quantization and quantum field theory in curved space-time

The Kostant-Souriau geometric quantization theory is applied to the problem of constructing a generally covariant quantum field theory. The occupation number formalism for a scalar field is introduced as a semiclassical approximation which is valid in low curvature regions of space-time and which depends on making a particular choice of polarization in the classical phase space of a single massive particle. The application of the formalism to particle creation problems is outlined.     

最大占据数为任意整数的统计

用拉格朗日乘子法推导了各个量子态上粒子最大占据数是任意整数的统计分布。     

Causal stochastic interpretation of quantum statistics

The differences between Einstein and Bohr on the interpretation of quantum mechanics revolved around the question of completeness of the Copenhagen Interpretation. This fundamental problem is examined here in the light of recent neutron interference experiments which allow for novel experimental situations. Exploiting the possibility of neutron spin flip in these experiments, the inadequacy of the Copenhagen interpretation to fully understand the experimental results is brought out. Instead a causal interpretation of quantum mechanics is advocated, in which the neutron, as a particle, does always have a definite space time trajectory but also involves a wave which creates a potential affecting the particle neutron. The reestablishment of definite particle trajectories in the microscopic domain obliges us to reexamine the statistical treatment of ‘identical’ particles, as well as the problem of negative energies and probabilities in relativistic quantum mechanics.     

Probing the effective nuclear-spin magnetic field in a single quantum dot via full counting statistics

We study theoretically the full counting statistics of electron transport through a quantum dot weakly coupled to two ferromagnetic leads, in which an effective nuclear-spin magnetic field originating from the configuration of nuclear spins is considered. We demonstrate that the quantum coherence between the two singly-occupied eigenstates and the spin polarization of two ferromagnetic leads play an important role in the formation of super-Poissonian noise. In particular, the orientation and magnitude of the effective field have a significant influence on the variations of the values of high-order cumulants, and the variations of the skewness and kurtosis values are more sensitive to the orientation and magnitude of the effective field than the shot noise. Thus, the high-order cumulants of transport current can be used to qualitatively extract information on the orientation and magnitude of the effective nuclear-spin magnetic field in a single quantum dot.     

爱因斯坦转盘上的热平衡及其时空对偶性

分别用狭义和广义相对论解出了爱因斯坦转盘上的热平衡流体系统内固有温度对柱坐标的依赖关系T0(ρ).结果表明,运动温度的收缩只与子系统的速度有关而与加速度无关.考虑到引力场中坐标温度的均恒性,爱因斯坦转盘与早期宇宙的时空对偶性直接给出宇宙介质固有温度反比于标度因子R(t)的结论. 关键词： 热平衡 弯曲时空 坐标温度 早期宇宙     

A comparative study of local quantum Fisher information and local quantum uncertainty in Heisenberg XY model

Recently, it has been shown that the quantum Fisher information via local observables and via local measurements (i.e., local quantum Fisher information (LQFI)) is a central concept in quantum estimation and quantum metrology and captures the quantumness of correlations in multi-component quantum system (Kim et al. (2018) [28]). This new discord-like measure is very similar to the quantum correlations measure called local quantum uncertainty (LQU). In the present study, we have revealed that LQU is bounded by LQFI in the phase estimation protocol. Also, a comparative study between these two quantum correlations quantifiers is addressed for the quantum Heisenberg XY model. Two distinct situations are considered. The first one concerns the anisotropic XY model and the second situation concerns isotropic XY model submitted to an external magnetic field. Our results confirm that LQFI reveals more quantum correlations than LQU.     

史瓦西时空中自由粒子的运动方程

直接求解史瓦西时空中自由粒子的测地线方程,得出粒子运动方程的一般常见形式.此方法与一般教材中根据史瓦西度规的静态球对称性以及四速归一条件得出的运动方程完全相同.此方法物理意义更清晰、明确,同时对理解弯曲时空中的测地线方程具有重要意义.