Identifying the closeness of eigenstates in quantum many-body systems

We propose a quantity called modulus fidelity to measure the closeness of two quantum pure states. We use it to investigate the closeness of eigenstates in one-dimensional hard-core bosons. When the system is integrable, eigenstates close to their neighbor or not, which leads to a large fluctuation in the distribution of modulus fidelity. When the system becomes chaos, the fluctuation is reduced dramatically, which indicates all eigenstates become close to each other. It is also found that two kind of closeness, i.e., closeness of eigenstates and closeness of eigenvalues, are not correlated at integrability but correlated at chaos. We also propose that the closeness of eigenstates is the underlying mechanism of eigenstate thermalization hypothesis(ETH) which explains the thermalization in quantum many-body systems.     

Eigenstate statistics and optical properties of one-dimensional disordered photonic crystals

Optical eigenstates in one-dimensional disordered photonic crystals were studied. The threshold disorder level was established below which the probability of appearance of an eigenstate at the photonic bandgap center is negligible. The threshold is reached when the relative fluctuation in the optical lengths of the structure periods becomes equal to the square root of one-third of the relative bandgap width. The dependence of the ensemble-averaged structure transmission coefficient on the fluctuation of the period optical length has a break corresponding to the threshold fluctuation.     

参数化玻色湮灭算符高次幂的本征态及其量子起伏规律

以参数化方式「ｙ」＝（ｑ＾ｙ－１）／（ｑ－１）定义ｑ玻色湮灭算符ａｑ，生成相应的ｑ相干态，找出能产生并保持这类ｑ相干态的体系的哈密顿量。研究了α＾ｋｑ的正交归一本征态的数学结构和量子起伏性质，发现这些本征态中只有偶ｑ相干态存在通常的压缩效应，并且当ｑ〈１时，场的两个正交分量在各态中的量子起估可以同时有小于相干态的最小不确定度，有ｑ压缩效应。     

Hamiltonian dynamics,nanosystems, and nonequilibrium statistical mechanics

An overview is given of recent advances in nonequilibrium statistical mechanics on the basis of the theory of Hamiltonian dynamical systems and in the perspective provided by the nanosciences. It is shown how the properties of relaxation toward a state of equilibrium can be derived from Liouville's equation for Hamiltonian dynamical systems. The relaxation rates can be conceived in terms of the so-called Pollicott–Ruelle resonances. In spatially extended systems, the transport coefficients can also be obtained from the Pollicott–Ruelle resonances. The Liouvillian eigenstates associated with these resonances are in general singular and present fractal properties. The singular character of the nonequilibrium states is shown to be at the origin of the positive entropy production of nonequilibrium thermodynamics. Furthermore, large-deviation dynamical relationships are obtained, which relate the transport properties to the characteristic quantities of the microscopic dynamics such as the Lyapunov exponents, the Kolmogorov–Sinai entropy per unit time, and the fractal dimensions. We show that these large-deviation dynamical relationships belong to the same family of formulas as the fluctuation theorem, as well as a new formula relating the entropy production to the difference between an entropy per unit time of Kolmogorov–Sinai type and a time-reversed entropy per unit time. The connections to the nonequilibrium work theorem and the transient fluctuation theorem are also discussed. Applications to nanosystems are described.     

Asymmetric propagation of electromagnetic waves through a planar chiral structure

We report that normal incidence transmission of circularly polarized waves through the lossy anisotropic planar chiral structure is asymmetric in the opposite direction. The new effect is fundamentally distinct from conventional gyrotropy of bulk chiral media and the Faraday effect, where the eigenstates are a pair of counterrotating elliptical states, while the eigenstates of the lossy anisotropic planar chiral structure are two corotating elliptical polarizations.     

Duality between the weak and strong interaction limits for randomly interacting fermions

We establish the existence of a duality transformation for generic models of interacting fermions with two-body interactions. The eigenstates at weak and strong interaction U possess similar statistical properties when expressed in the U=0 and U= infinity eigenstates bases, respectively. This implies the existence of a duality point U(d) where the eigenstates have the same spreading in both bases. U(d) is surrounded by an interval of finite width which is characterized by a non-Lorentzian spreading of the strength function in both bases. Scaling arguments predict the survival of this intermediate regime as the number of particles is increased.     

Dynamics of 2-D one electron quantum dots in time-dependent magnetic field: Influence of size

We explore the dynamics of harmonically confined single electron quantum dots as a function of dot size under time-dependent magnetic field. The system of interest is a 2-D system in the presence of a perpendicular magnetic field. We show that for given strengths of the confinement potential and effective mass; periodic, as well as exponential variation in the strength of the magnetic field could invite interesting features in the dynamics of the system. Also, the pattern of time evolution of eigenstates of the unperturbed system reveals significant size-dependence. The fluctuation in the magnetic field strength from its initial value is found to modulate the dynamical aspects in a prominent way.     

Delocalization and Heisenberg's uncertainty relation

In the one-dimensional Anderson model the eigenstates are localized for arbitrarily small amounts of disorder. In contrast, the Aubry-André model with its quasiperiodic potential shows a transition from extended to localized states. The difference between the two models becomes particularly apparent in phase space where Heisenberg's uncertainty relation imposes a finite resolution. Our analysis points to the relevance of the coupling between momentum eigenstates at weak potential strength for the delocalization of a quantum particle. Received 3 May 2002 / Received in final form 2 October 2002 Published online 29 November 2002     

Dynamics of 2-D one electron quantum dots in periodically fluctuating confinement potential: Influence of size and anharmonicity

We explore the dynamics of harmonically confined single electron quantum dots as a function of dot size under periodically fluctuating confinement potential. The system of interest is a 2-D system in the presence of a perpendicular magnetic field. We show that for given strengths of the magnetic field and effective mass, a periodic variation in the strength of the confinement potential could invite interesting features in the dynamics of the system. Also, the pattern of time evolution of eigenstates of the unperturbed system reveals significant size-dependence. The fluctuation in the confinement potential from its initial value is found to modulate the dynamical aspects in a prominent way. The presence of cubic anharmonicity in the confining field brings in new features in the dot dynamics.     

Generalized Rotating-Wave Approximation for the Quantum Rabi Model with Optomechanical Interaction

The spectrum of energy and eigenstates of an hybrid cavity optomechanical system, where a cavity field mode interacts with a mechanical mode of a vibrating end mirror via radiation pressure and with a two level atom via electric dipole interaction are investigated. In the spirit of approximations developed for the quantum Rabi model beyond rotating-wave approximation (RWA), the so-called generalized RWA (GRWA) to diagonalize the tripartite Hamiltonian for arbitrary large couplings is implemented. Notably, the GRWA approach still allows to rewrite the hybrid Hamiltonian in a bipartite form, like a Rabi model with dressed atom-field states (polaritons) coupled to mechanical modes through reparametrized coupling strength and Rabi frequency. A more accurate energy spectrum for a wide range of values of the atom-photon and photon–phonon couplings, when compared to the RWA results is found. The fidelity between the numerical eigenstates and its approximated counterparts is also calculated. The degree of polariton-phonon entanglement of the eigenstates presents a non-monotonic behavior as the atom-photon coupling varies, in contrast to the characteristic monotonic increase in the RWA treatment.     

Cooper pairing in the presence of antiferromagnetism

With a BCS interaction, the free energy for usual BCS pairing of electrons but in the presence of antiferromagnetism is shown to be lower than for a different pairing scheme where pairs are formed from electron eigenstates of the antiferromagnet. In both pairing schemes, super-conductivity in the presence of antiferromagnetism is always a mixture of spin-singlet-even-parity-orbital and spin-triplet-odd-parity-orbital electron pairs.     

激发核系统中最大Lyapunov指数、密度涨落以及多重碎裂之间的关系

基于量子分子动力学模型,系统地研究了从48Ca到298114一系列核素在不同温度下的最大Lyapunov指数、密度涨落以及体系多重碎裂之间的关系.发现最大Lyapunov指数随温度变化有一峰值出现(该峰值所对应的温度为"临界温度"),在该临界温度时体系的密度涨落达到最大,碎块的质量分布能够给出较好的PowerLaw指数.通过对最大Lyapunov指数与密度涨落随时间变化行为的研究,发现密度涨落的时间尺度要大于混沌的时间尺度,意味着混沌的概念可以用来研究体系的多重碎裂过程.最后还给出了有限体系相变的临界温度随体系大小变化的规律. Within a quantum molecular dynamics model we calculate the largest Lyapunov exponent (LLE), the density fluctuation, and the mass distribution of fragments for a series of nuclear systems at different initial temperatures. It is found that the LLE peaks at the temperature ("critical temperature") where the density fluctuation reaches a maximal value and the mass distribution fragments is fitted best by the Fisher s power law from which the critical exponents for mass and charge distribution are obtain...     

由非绝热相关获得的形式量子数及其在高激发振动态的经典解释

我们利用非绝热相关方法 ,通过关闭所有的振动模式间的耦合项并追溯到零级本征态 ,以得到体系的形式量子数 ,将形式量子数对高激发振动态的能级谱图进行归属 ,并重构本征能级图谱 ,使本征能级以有序的方式排列。这有助于对高激发振动态的能级进行分类和归属。形式量子数是体现高激发振动态的重要特征 ,是高激发振动态的近似运动守恒量。我们将多维陪集相空间的经典方法应用于高激发态的研究 ,发现形式量子数对应的李雅普诺夫指数为零或最小 ,并且它对应于较大的相空间密度     

Dual-polarization microchip laser at 1.53 microm

Two-frequency operation of a composite Er,Yb:glass-LiTaO3 monolithic microlaser is demonstrated at 1.53 microm. The thermo-optic effect of the intracavity birefringent crystal makes it possible to control the wavelengths of the two orthogonal linearly polarized eigenstates. It provides a tunable beat note from 0 to 60 GHz. Direct evaluation of the Lamb-type coupling constant C between the two eigenstates is obtained from a single intensity noise spectrum measurement, yielding values from 0.33 to 0.86, depending on transverse and axial distributions of the eigenstates. Applications to radar and telecommunication systems are discussed.     

Unification of perturbation theory, random matrix theory, and semiclassical considerations in the study of parametrically dependent eigenstates

We consider a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where x is a constant parameter. Specifically, we discuss a gas particle inside a cavity, where x controls a deformation of the boundary or the position of a "piston." The quantum eigenstates of the system are |n(x)>. We describe how the parametric kernel P(nmid R:m) = ||(2) evolves as a function of deltax = x-x(0). We explore both the perturbative and the nonperturbative regimes, and discuss the capabilities and the limitations of semiclassical as well as random waves and random-matrix-theory considerations.     

Does phase cycling work for nuclei experiencing strong quadrupolar couplings?

The question of whether the phase cycling can still be used to select coherence transfer pathways in spin systems experiencing a tilting of its eigenstates away from the Zeeman eigenstates due to strong couplings was investigated theoretically. Based on the analysis presented it is concluded that conventional phase cycling is still a valid approach for selecting a coherence transfer pathway signal, although changes in pathway efficiencies can occur as the mechanisms for excitation and detection of coherences are affected by the tilting of the eigenstates.     

Pairing in the Hubbard model: the Cu O cluster versus the Cu-O plane

We study the Cu₅O₄ cluster by exact diagonalization of a three-band Hubbard model and show that bound electron or hole pairs are obtained at appropriate fillings, and produce superconducting flux quantization. The results extend earlier cluster studies and illustrate a canonical transformation approach to pairing that we have developed recently for the full plane. The quasiparticles that in the many-body problem behave like Cooper pairs are W =0 pairs, that is, two-hole eigenstates of the Hubbard Hamiltonian with vanishing on-site repulsion. The cluster allows W =0 pairs of d symmetry, due to a spin fluctuation, and ssymmetry, due to a charge fluctuation. Flux quantization is shown to be a manifestation of symmetry properties that hold for clusters of arbitrary size. Received 23 July 1999     

Device-independent certification of entangled measurements

We present a device-independent protocol to test if a given black-box measurement device is entangled, that is, has entangled eigenstates. Our scheme involves three parties and is inspired by entanglement swapping; the test uses the Clauser-Horne-Shimony-Holt Bell inequality, checked between each pair of parties. In the case where all particles are qubits, we characterize quantitatively the deviation of the measurement device from a perfect Bell-state measurement.