Noise at the crossover from Wigner liquid to Wigner glass

Using a simple classical model for interacting electrons in two dimensions with random disorder, we show that a crossover from a Wigner liquid to a Wigner glass occurs as a function of charge density. The noise power increases strongly at the crossover and the characteristics of the 1/f(alpha) noise change. When the temperature is increased, the noise power decreases. We compare these results with recent noise measurements in systems with two-dimensional metal-insulator transitions.     

Classical molecules in two dimensions

The ground-state configurations and spectrum of two parallel two-dimensional classical atoms are obtained as a function of the inter-atomic distance ( ). The classical particles are confined by parabolic potentials and repel each other through a Coulomb potential. As a function of we find several configurational transitions which are of first or second order. For first- (second-) order transitions the first (second) derivative of the energy with respect to is discontinuous, the radial position of the particles changes discontinuously (continuously) and the frequency of the eigenmodes exhibit a jump (softening of a mode). In the limit of an infinite number of electrons the Wigner bilayer system is recovered which moves through five different stable crystalline phases as a function of . For unequal strength of parabolic confinement we find that the number of configurational transitions increases.     

Quantum coherent versus classical coherent light

The paper shows that the Wigner distribution function of quantum optical coherent states, or of a superposition of such states, can be produced and measured with a classical optical set-up using classical coherent light fields. This measurement cannot be done directly in quantum optics since the quantum phase space variables correspond to non-commuting operators. As an example, the Wigner distribution function of Schrödinger cat states of light has been measured. It is also shown that the possibility of measuring the Wigner distribution function of quantum coherent states with classical coherent fields is unique in the sense that it cannot be extended to other quantum states, not even to the incoherent limit of the superposition of coherent states.     

Magnetic field induced transitions between quantized hall and insulator states in a dilute 2D electron gas

We report on the observation of a new phenomenon: a sequence of magnetic field induced transitions between well defined quantum Hall effect states, with a Hall resistance quantized as integer fractions of h/e² and a vanishingly small longitudinal resistance, and insulator states with longitudinal resistance exceeding 2×10⁹ Ω. This phenomenon is observed in extremely high mobility Si MOSFETs, in a range of electron concentrations corresponding to a dilute 2D electron gas in or near an activated electronic transport regime. We attribute this effect to a modulation of the metal-insulator transition by the quantum Hall effect or to the formation of a pinned Wigner solid.     

Dynamics of ‘quantumness’ measures in the decohering harmonic oscillator

We studied the behaviour under decoherence of four different measures of the distance between quantum states and classical states for the harmonic oscillator coupled to a linear Markovian bath. Three of these are relative measures, using different definitions of the distance between the given quantum states and the set of all classical states. The fourth measure is an absolute one, the negative volume of the Wigner function of the state. All four measures are found to agree, in general, with each other. When applied to the eigenstates |n〉, all four measures behave non-trivially as a function of time during dynamical decoherence. First, we find that the first set of classical states to which the set of eigenstate evolves is (by all measures used) closest to the initial set. That is, all the states decohere to classicality along the ‘shortest path’. Finding this closest classical set of states helps improve the behaviour of all the relative distance measures. Second, at each point in time before becoming classical, all measures have a state n^? with maximal quantum-classical distance; the value n^? decreases as a function of time. Finally, we explore the dynamics of these non-classicality measures for more general states.     

Wigner crystallization in Na3Cu2O4 and Na8Cu5O10 chain compounds

We report the synthesis of novel edge-sharing chain systems Na(3)Cu(2)O(4) and Na(8)Cu(5)O(10), which form insulating states with commensurate charge order. We identify these systems as one-dimensional Wigner lattices, where the charge order is determined by long-range Coulomb interaction and the number of holes in the d shell of Cu. Our interpretation is supported by x-ray structure data as well as by an analysis of magnetic susceptibility and specific heat data. Remarkably, due to large second neighbor Cu-Cu hopping, these systems allow for a distinction between the (classical) Wigner lattice and the 4k(F) charge-density wave of quantum mechanical origin.     

High electrical conductivity in nonlinear model lattice crystals mediated by thermal excitation of solectrons

The quantum statistics of electrons interacting with nonlinear excitations of a classical heated nonlinear lattice of atoms is studied. By using tight-binding approximation, Wigner momentum distributions and computer simulations we show the existence of quite fast and nearly loss-free motions of charges along crystallographic axes and estimate the range of values of transport coefficients. Using minimization of free energy we estimate the density of mobile bound states between electrons and lattice solitons (so-called solectrons). We calculate the momenta of Wigner velocity distributions and from Kubo relations the diffusivity and the electrical conductivity using the relaxation time approximation. We show that thermally excited solectrons in nonlinear media may lead to a significant transport enhancement. Our estimates and computer simulations demonstrate the existence of a temperature window, where solectrons are relatively stable and contribute strongly to transport. The electrical conductivity may be enhanced up to two orders of magnitude.     

Finite-temperature Wigner solid and other phases of ripplonic polarons on a helium film

Electrons on liquid helium can form different phases depending on density, and temperature. Also the electron-ripplon coupling strength influences the phase diagram, through the formation of so-called “ripplonic polarons”, that change how electrons are localized, and that shifts the transition between the Wigner solid and the liquid phase. We use an all-coupling, finite-temperature variational method to study the formation of a ripplopolaron Wigner solid on a liquid helium film for different regimes of the electron-ripplon coupling strength. In addition to the three known phases of the ripplopolaron system (electron Wigner solid, polaron Wigner solid, and electron fluid), we define and identify a fourth distinct phase, the ripplopolaron liquid. We analyse the transitions between these four phases and calculate the corresponding phase diagrams. This reveals a reentrant melting of the electron solid as a function of temperature. The calculated regions of existence of the Wigner solid are in agreement with recent experimental data.     

从离散Wigner函数的角度探讨量子相干性度量

量子相干性是量子信息处理的基本要素,在量子计算中扮演着重要的角色.为了便于讨论量子相干性在量子计算中的作用,本文从离散Wigner函数角度对量子相干性进行了探讨.首先对奇素数维量子系统的离散Wigner函数进行了分析,分离出表征相干性的部分,提出了一种可能的基于离散Wigner函数的量子相干性度量方法,并对其进行了量子相干性度量规范的分析;同时也比较了该度量与l_1范数相干性度量之间的关系.重要的是,这种度量方法能够明确给出量子相干性程度与衡量量子态量子计算加速能力的负性和之间不等式关系,由此可以解析地解释量子相干性仅是量子计算加速的必要条件.     

Study of shallow impurity states in compound semiconductors using high resolution photoluminescence spectroscopy

In this paper we review briefly the use of high resolution photoluminescence to study the behavior of shallow impurity states in compound semiconductors. As an illustration we focus our review on GaAs. The binding energies of the ground state and of several low-lying excited states of the impurity centers are determined by studying the radiative transitions associated with excitons bound to neutral donors or acceptors. The difference between the binding energies of different donors in GaAs is rather small. Thus to resolve transitions associated with different chemical donors a magnetic field is used. This has the effect of sharpening the transitions as well as increasing the separation between them. One can identify donors in samples with total impurity concentrations as high as 5X10¹⁵/cm³. The binding energies of different chemical acceptors in GaAs are much higher. Thus the radiative transitions associated with excitons bound to neutral acceptors can be resolved in zero magnetic field. Energy levels of shallow donors and acceptors in GaAs are reviewed.     

二维Sinai台球系统的量子混沌研究

研究了二维Sinai台球系统的经典与量子的对应关系,运用定态展开法和Gutzwiller的周期轨道理论对Sinai台球系统的态密度经傅里叶变换得到的量子长度谱进行分析,并把量子长度谱中峰的位置与其所对应的经典体系的周期轨道长度做对比,发现两者之间存在很好的对应关系.观察到了一些量子态局域在短周期轨道附近形成量子scarred态或量子superscarred态.还研究了同心与非同心Sinai台球系统的能级最近邻间距分布,发现同心Sinai台球系统是近可积的,非同心Sinai台球系统在θ=3π/8下,随两中心间距离的增加,能级最近邻间距分布将由近可积向维格那分布过渡.     

Pure state condition for the semi-classical Wigner function

The Wigner function W(p,q) is a symmetrized Fourier transform of the density matrix ρ(q₁,q₂), representing quantum-mechanical states or their statistical mixture in phase space. Identification of these two alternatives in the case of density matrices depends on the projection identity ρ² = ρ; its Wigner correspondence is the pure state condition. This criterion is applied to the Wigner functions obtained from standard semiclassical wave functions, determining as pure states those whose classical invariant tori satisfy the generalized Bohr-Sommerfeld conditions. Superpositions of eigenstates are then examined and it is found that the Wigner function corresponding to Gaussian random wave functions are smoothed out in the manner of mixed-state Wigner functions. Attention is also given to the pure-state condition in the case where an angular coordinate is used.     

On the quantum-mechanical Fokker-Planck and Kramers-Chandrasekhar equation

In the classical theory of Brownian motion we can consider the Langevin equation as an infinitesimal transformation between the coordinates and momenta of a Brownian particle, given probabilistically, since the impulse appearing is characterized by a Gaussian random process. This probabilistic infinitesimal transformation generates a streaming on the distribution function, expressed by the classical Fokker-Planck and Kramers-Chandrasekhar equations. If the laws obeyed by the Brownian particle are quantum mechanical, we can reinterpret the Langevin equation as an operator relation expressing an infinitesimal transformation of these operators. Since the impulses are independent of the coordinates and momenta we can think of them as c numbers described by a Gaussian random process. The so resulting infinitesimal operator transformation induces a streaming on the density matrix. We may associate, according to Weyl functions with operators. The function associated with the density matrix is the Wigner function. Expressing, then, these operator relations in terms of these functions we can express the streaming as a continuity equation of the Wigner function. We find that in this parametrization the extra terms which appear are the same as in the classical theory, augmenting the usual Wigner equation.     

Rigged Hilbert spaces and time asymmetry: The case of the upside-down simple harmonic oscillator

The upside-down simple harmonic oscillator system is studied in the contexts of quantum mechanics and classical statistical mechanics. It is shown that in order to study in a simple manner the creation and decay of a physical system by way of Gamow vectors we must formulate the theory in a time-asymmetric fashion, namely using two different rigged Hilbert spaces to describe states evolving toward the past and the future. The spaces defined in the contexts of quantum and classical statistical mechanics are shown to be directly related by the Wigner function.     

Schwinger Bose实现下自旋相干态Wigner函数的特性分析

在Schwinger Bose实现下,引入纠缠态表象及Wigner算符在该表象下的表示,得到自旋相干态的Wigner函数,数值计算画出相空间中Wigner函数的分布图,并加以分析,发现在SchwingerBose实现下自旋相干态确实体现出纠缠特性。     

Direct observation of geometrical phase transitions in mesoscopic superconductors by scanning tunneling microscopy

Using scanning tunneling microscopy, we mapped the distribution of the local density of states in a single crystal superconductor heterostructure with an array of submicron normal metal islands. We observe the coexistence of strongly interacting multiquanta vortex lattice with interstitial Abrikosov vortices. The newly formed composite magnetic flux structure undergoes a series of phase transitions between different topological configuration states. The vortex configuration states are strongly dependent on the number of flux quanta and the nanoscale confinement architecture of the mesoscopic superconductor. Here, we present images of vortex phase transitions due to confinement effects when the number of magnetic flux quanta in the system changes. The vortex dynamics in these systems could serve as a model for behavior of confined many-body systems when the number of particles changes.     

量子扩散通道中Wigner算符的演化规律

众所周知,量子态的演化可用与其相应的Wigner函数演化来代替.因为量子态的Wigner函数和量子态的密度矩阵一样,都包含了概率分布和相位等信息,因此对量子态的Wigner函数进行研究,可以更加快速有效地获取量子态在演化过程的重要信息.本文从经典扩散方程出发,利用密度算符的P表示,导出了量子态密度算符的扩散方程.进一步通过引入量子算符的Weyl编序记号,给出了其对应的Weyl量子化方案.另外,借助于密度算符的另一相空间表示-Wigner函数,建立了Wigner算符在扩散通道中演化方程,并给出了其Wigner算符解的形式.本文推导出了Wigner算符在量子扩散通道中的演化规律,即演化过程中任意时刻Wigner算符的形式.在此结论的基础上,讨论了相干态经过量子扩散通道的演化情况.