Measuring the energy level repulsion in quantum dots

Energy level repulsion is one of the remnants of classical chaos in quantum mechanics. Measurements of the distribution of nearest neighbor spacings in quantum dots reveal, in contrast to other classically chaotic systems, deviations from the predictions made by random matrix theory. Here, we survey possible contributions to these deviations from experimental peculiarities present in measurements on quantum dots, and discuss the methods to eliminate or reduce such distortions.     

New representation of quantum chaos

A non-integrable system has an irregular spectrum for stationary bound energy levels. It is shown that the irregular sequence of level spacings gives an unambiguous representation of chaos in quantum systems.     

Level statistics of near-yrast states in rapidly rotating nuclei

The nearest neighbour level spacing distribution and the Δ₃ statistic of level fluctuations associated with very high spin states (I ≳ 30) in rare-earth deformed nuclei are analysed by means of a cranked shell model. The many particle-many hole configurations created in the rotating Nilsson potential are mixed by the surface-delta two-body residual interaction. The levels in the near-yrast region show a Poisson-like level spacing distribution. As the intrinsic excitation energy U increases, the level statistics shows a gradual transition from order to chaos, reaching at U ≳ 2 MeV the Wigner distribution typical-of the Gaussian orthogonal ensemble of random matrices. This transition is caused by the residual two-body interaction. On the other hand, the level spacings between the yrast and the first excited state show a peculiar behaviour, displaying a Wigner-like distribution instead of the Poisson-like distribution seen for the other near-yrast rotational states. The lowest spacings reflect the properties of the single-particle orbits in the mean-field, and are only weakly affected by the residual two-body interaction.     

Classical chaos and quantum level density of an anharmonic oscillator

The Liapunov exponents of two-dimension anharmonic oscillator systems are studied through numerical calculations. The result shows that the systems consist of regular and irregular regions in phase space in the classical limit. The corresponding quantum systems are investigated. The distribitionP(s) of spacings between adjacent energy levels indicates a corresponding transition from Poisson-like distribution to Wigner-like distribution.P(s) is dependent on the total irregular fraction of phase space.     

Spectral Statistics of the Rectangular Billiard with a Flux Line

The density of states of a rectangular billiard with an Aharonov–Bohm flux line in its center was calculated in the semiclassical approximation and was used for the calculation of the form factor in the diagonal approximation. The distribution of nearest level spacings and the form factor were calculated also numerically. For some values of the flux these were found to be close to the ones of the semi-Poisson statistics. The difference between the numerical results and the semiclassical ones were found to be much larger than for chaotic and for integrable systems within similar approximations. Possible reasons for these discrepancies are discussed.     

Giant Nonlinear Absorption by an Ensemble of Metallic Grains

We have investigated the nonlinear low-frequency microwave absorption of an ensemble of small metallic grains. Earlier Zhou et al. [Phys. Rev. Lett. 77, 1958 (1996)] have proved that linear absorption by such a system is due to a mesoscopic relaxation mechanism for which important contribution is from the grains with small level spacings between the ground state and the first excited state. Here we have shown further that such grains are anomalously sensitive to the field amplitude and the distribution of level spacings. Since such a behavior depends on external magnetic field, we expect the appearance of a giant nonlinear magnetoresistance, as well as a very strong temperature dependence of the nonlinear microwave conductivity.     

Spatial extent of random laser modes

We have experimentally studied the distribution of the spatial extent of modes and the crossover from essentially single-mode to distinctly multimode behavior inside a porous gallium phosphide random laser. This system serves as a paragon for random lasers due to its exemplary high index contrast. In the multimode regime, we observed mode competition. We have measured the distribution of spectral mode spacings in our emission spectra and found level repulsion that is well described by the Gaussian orthogonal ensemble of random-matrix theory.     

Spacing and width of Coulomb blockade peaks in a silicon quantum dot

We present an experimental study of the fluctuations of Coulomb blockade peak positions of a quantum dot. The dot is defined by patterning the two-dimensional electron gas of a silicon MOSFET structure using stacked gates. The ratio of charging energy to single-particle energy is considerably larger than in comparable GaAs/AlGaAs quantum dots. The statistical distribution of the conductance peak spacings in the Coulomb blockade regime was found to be unimodal and does not follow the Wigner surmise. The fluctuations of the spacings are much larger than the typical single-particle level spacing and thus clearly contradict the expectation of random matrix theory. Measurements of the natural line width of a set of several adjacent conductance peaks suggest that all of the peaks in the set are dominated by electrons being transported through a single-broad energy level.     

Quantum chaos of bogoliubov waves for a bose-einstein condensate in stadium billiards

We investigate the possibility of quantum (or wave) chaos for the Bogoliubov excitations of a Bose-Einstein condensate in billiards. Because of the mean field interaction in the condensate, the Bogoliubov excitations are very different from the single particle excitations in a noninteracting system. Nevertheless, we predict that the statistical distribution of level spacings is unchanged by mapping the non-Hermitian Bogoliubov operator to a real symmetric matrix. We numerically test our prediction by using a phase shift method for calculating the excitation energies.     

Donor ordering and the statistics of quantum dot level spacings and widths from full 3D self-consistent electronic structure

Using full 3D self-consistent electronic structure calculations of small (electron numberN 100) lateral quantum dots formed on GaAs–AlGaAs HEMT devices we calculate the statistics of level spacings Δε_pand tunneling coefficients Γ_pbetween leads and confined states of the dot. We employ random and ordered donor layer charge distributions, the latter generated through Monte Carlo variable range hopping simulations, as well as a homogeneous (jellium) ionic charge distribution, and examine the effects on these statistics.It has recently been argued that the statistics of the level spacings and widths follow from random matrix theory when the Hamiltonian is described by the Gaussian orthogonal ensemble (GOE) for zero magnetic fieldB, and by the Gaussian unitary ensemble (GUE) forBsufficiently large to break time reversal symmetry. Specifically it is argued that when the dot wave functions are expanded in an arbitrary basis the expansion coefficients, according to the postulate of Porter and Thomas, are uniformly distributed in Hilbert space.In our calculation we obtain statistics of level spacings and widths by generating many configurations of disordered and ordered donor charge. This corresponds to the experimental situation of thermal cycling of the device. We find that a pronounced transition occurs in the level spacing statistics between the completely disordered donor layer ensemble, which seems to be well described by random matrix theory, and the ordered ensemble which is dominated by secular variations in the coefficients. In particular, a shell structure in the levels, which results from approximate parabolicity in the self-consistent confining potential, is observed. This, and the effects of symmetry under inversion and azimuthal symmetry, are speculated to undermine level repulsion and result in Poisson statistics for the levels here at the band edge.Finally we find that distortions in the dot shape are markedly less significant in varying the widths (and level spacings) than calculations based on a hard wall potential for the dot predict. This suggests that the notion of invariant atomic structure for sufficiently small dots is not invalidated by the randomness inherent in donor positions and shape distortion but, on the contrary, a systematic study of dot structure is possible.     

Guiding, focusing, and cooling of atoms in a strong dipole potential

01 ^* (doughnut) modes for atomic beam manipulation. A slow atomic beam is guided over up to 0.3 m and focused down to 6.5 μm radius. The doughnut mode is used as a strong mesoscopic dipole potential with vibrational level spacings up to the photon recoil energy. Polarization gradient cooling in this system generates a bimodal momentum distribution with a narrow component momentum width of 4 ?k. Received: 26 June 1998     

Neutron resonances in 185Re and 187Re

In a search for intermediate structure, neutron time-of-flight spectra corresponding to 1 and 4 MeV capture γ-ray thresholds were measured for the target isotopes ^{185, 187}Re. The data were analyzed from the point of view of level spacings as well as intermediate structure. A method was developed for estimating the neutron widths of the resonances even in those cases where the neutron widths are comparable to the γ-widths. On the basis of this analysis it was decided which resonances were most likely to be due to p-wave capture. While some unusual behavior was observed, there is no conclusive evidence for intermediate structure. The statistics of level spacings agree with the long range ordering described in the theory of Dyson and Mehta, and are inconsistent with an uncorrelated Wigner distribution. Energies, estimated neutron widths and p-wave probabilities (if over 10 %) for 488 resonances in ¹⁸⁵Re and 335 resonances in ¹⁸⁷Re are tabulated for the energy range 24 eV to 2 keV.     

Does an irregular sequence of level spacings provide a new representation of quantum chaos?

The recent claim by Hirooka et al. that an irregular sequence of energy level spacings gives an unambiguous representation of quantum chaos is examined. It is shown that observation of an irregular sequence of spacings does not necessarily imply that the dynamics is chaotic.     

啁啾Moire光栅波分复用/解复用器件的理论分析

根据耦合模理论,用传输矩阵法计算了啁啾Moire光栅的透射谱特性,分析表明其透射谱具有多个通带及好的通道隔离度.通过调整光栅各参量可获得通道间隔满足国际电信联盟标准的啁啾Moire光栅.     

超小金属微粒超导电性的能级统计

用平均场理论的自洽方程计算了随机矩阵理论中三种系综(Gauss Orthogonal Ensemble;Gauss Unitary Ensemble;Gauss Symplectic Ensemble)所对应的电子能级的奇/偶电子数分布对临界电子能级间距的影响,得到了在不同的自旋-轨道耦合和磁场中奇/偶电子数分布的临界电子能级间距的定量关系以及奇电子数的Δ((0)随平均能间距o>的变化. 关键词：     

Nearest Neighbor Distances on a Circle: Multidimensional Case

We study the distances, called spacings, between pairs of neighboring energy levels for the quantum harmonic oscillator. Specifically, we consider all energy levels falling between E and E+1, and study how the spacings between these levels change for various choices of E, particularly when E goes to infinity. Primarily, we study the case in which the spring constant is a badly approximable vector. We first give the proof by Boshernitzan-Dyson that the number of distinct spacings has a uniform bound independent of E. Then, if the spring constant has components forming a basis of an algebraic number field, we show that, when normalized up to a unit, the spacings are from a finite set. Moreover, in the specific case that the field has one fundamental unit, the probability distribution of these spacings behaves quasiperiodically in logE. We conclude by studying the spacings in the case that the spring constant is not badly approximable, providing examples for which the number of distinct spacings is unbounded.     

Full configuration interaction studies of phonon and photon transition rates in semiconductor quantum dots

Quantum chemical methods originally developed for studying atomic and molecular systems can be applied successfully to the study of few-body electron-hole systems in semiconductor nanostructures. A new computational approach is presented for studying the energetics and dynamics of interacting electrons and holes in a semiconductor quantum dot. The electron-hole system is described by a two-band effective mass Hamiltonian. The Hamiltonian is diagonalized in a configuration state function basis constructed as antisymmetric products of the electron one-particle functions and antisymmetric products of the hole one-particle functions. The symmetry adapted basis set used for the expansion of the one-particle functions consists of anisotropic Gaussian basis functions. The transition probability between electron-hole states consisting of different numbers of carrier pairs is calculated at the full configuration interaction level. The results show that the electron-hole correlation affects the radiative recombination rates significantly. A method for calculating the phonon relaxation rates between excited states and the ground state of quantum dots is described. The phonon relaxation calculations show that the relaxation rate is strongly dependent on the energy level spacings between the states.     

New Collocation Integrator for Solving Dynamic Problems. I. Theoretical Background

Russian Physics Journal - A new collocation integrator with Lobatto spacings is proposed for numerical solving mixed systems of firstand second-order differential equations for dynamic problems....     

Chaos in intrinsic motion of nuclei and its role in dissipative collective dynamics

We shall discuss the role of chaotic intrinsic motion in dissipative dynamics of the collective coordinates for nuclear systems. Using the formalism of linear response theory, it will be shown that the dissipation in adiabatic collective motion depends on the degree of chaos in the intrinsic dynamics of a system. This gives rise to a shape dependent dissipation rate for collective coordinates when the intrinsic motion is described by the independent particle model in a nucleus. The shape dependent chaos parameter measuring the degree of chaos in the intrinsic dynamics of the nuclear system will be obtained using the interpolating Brody distribution of nearest neighbour spacings in the single particle energy spectrum. A similar shape dependence is also found to be essential for phenomenological dissipation rates used in fission dynamics calculations.     

Rate-dependent slip of Newtonian liquid at smooth surfaces

Newtonian fluids were placed between molecularly smooth surfaces whose spacing was vibrated at spacings where the fluid responded as a continuum. Hydrodynamic forces agreed with predictions from the no-slip boundary condition only provided that flow rate (peak velocity normalized by spacing) was low, but implied partial slip when it exceeded a critical level, different in different systems, correlated with contact angle (surface wettability). With increasing flow rate and partially wetted surfaces, hydrodynamic forces became up to 2-4 orders of magnitude less than expected by assuming the no-slip boundary condition that is commonly stated in textbooks.