Reprint of : Semiclassical theory of persistent current fluctuations in ballistic chaotic rings

The persistent current in a mesoscopic ring has a Gaussian distribution with small non-Gaussian corrections. Here we report a semiclassical calculation of the leading non-Gaussian correction, which is described by the three-point correlation function. The semiclassical approach is applicable to systems in which the electron dynamics is ballistic and chaotic, and includes the dependence on the Ehrenfest time. At small but finite Ehrenfest times, the non-Gaussian fluctuations are enhanced with respect to the limit of zero Ehrenfest time.     

Semiclassical theory of persistent current fluctuations in ballistic chaotic rings

The persistent current in a mesoscopic ring has a Gaussian distribution with small non-Gaussian corrections. Here we report a semiclassical calculation of the leading non-Gaussian correction, which is described by the three-point correlation function. The semiclassical approach is applicable to systems in which the electron dynamics is ballistic and chaotic, and includes the dependence on the Ehrenfest time. At small but finite Ehrenfest times, the non-Gaussian fluctuations are enhanced with respect to the limit of zero Ehrenfest time.     

开放量子台球体系散射的赝路径半经典近似

本文讨论正方形量子台球的输运性质,考虑电子以费米能量穿过台球区域,在台球出口和入口处对入射和出射波函数采用基尔霍夫散射.采用微扰论的Dyson方程得到半经典格林函数,并把赝路径半经典近似作微扰展开得到体系的传输矩阵元.比较了传输矩阵元的傅立叶变换谱的峰位置与腔内自由电子经典轨道长度,发现在精度允许范围内它们符合的很好.     

开放量子台球体系散射的赝路径半经典近似

本文讨论正方形量子台球的输运性质，考虑电子以费米能量穿过台球区域，在台球出口和入口处对入射和出射波函数采用基尔霍夫散射．采用微扰论的Dyson方程得到半经典格林函数，并把赝路径半经典近似作微扰展开得到体系的传输矩阵元．比较了传输矩阵元的傅立叶变换谱的峰位置与腔内自由电子经典轨道长度，发现在精度允许范围内它们符合的很好．     

Symmetry breaking in quantum chaotic systems

We show, using semiclassical methods, that as a symmetry is broken, the transition between universality classes for the spectral correlations of quantum chaotic systems is governed by the same parametrization as in the theory of random matrices. The theory is quantitatively verified for the kicked rotor quantum map. We also provide an explicit substantiation of the random matrix hypothesis, namely that in the symmetry-adapted basis the symmetry-violating operator is random.     

Quantum virial coefficients of molecular nitrogen

We report virial coefficients up to third order in density for molecular nitrogen, investigating 103 temperatures in the range (15 K, 3000 K). All calculations are based on an ab initio-based potential taken from the literature. Path-integral Monte Carlo (PIMC) is applied to account for nuclear quantum effects, and these results are compared to a more approximate but faster semiclassical treatment. Additionally, we examine a PIMC approach that employs semiclassical beads for the path-integral images, but find that it offers marginal advantage. A recently developed orientation sampling algorithm is used in conjunction with Mayer sampling to compute precise virial coefficients. We find that, within the precision of our calculations of the second-order coefficient (B₂), semiclassical methods are adequate for temperatures greater than 250 K, and are needed to correct classical behaviour for temperatures as high as 800 K. For the third-order coefficient (B₃), the semiclassical methods are adequate above 150 K, and are required up to the highest temperature examined (3000 K) in order to correct the classical treatment within the precision of the calculations. However, three-body contributions to the potential are much more significant than nuclear quantum effects for the evaluation of B₃.     

The effects of macroscopic inhomogeneities on the magnetotransport properties of the electron gas in two dimensions

In experiments on electron transport, the macroscopic inhomogeneities in the sample play a fundamental role. In this paper and a subsequent one, we introduce and develop a general formalism that captures the principal features of sample inhomogeneities (density gradients, contact misalignments) in the magnetoresistance data taken from low-mobility heterostructures. We present detailed assessments and experimental investigations of the different regimes of physical interest, notably the regime of semiclassical transport at weak magnetic fields, the plateau–plateau transitions as well as the plateau–insulator transition that generally occurs at much stronger values of the external field only.It is shown that the semiclassical regime at weak fields plays an integral role in the general understanding of the experiments on the quantum Hall regime. The results of this paper clearly indicate that the plateau–plateau transitions, unlike the plateau–insulator transition, are fundamentally affected by the presence of sample inhomogeneities. We propose a universal scaling result for the magnetoresistance parameters. This result facilitates, amongst many other things, a detailed understanding of the difficulties associated with the experimental methodology of H.P. Wei et al. in extracting the quantum critical behavior of the electron gas from the transport measurements conducted on the plateau–plateau transitions.     

Quantum geometrodynamics: whence,whither?

Quantum geometrodynamics is canonical quantum gravity with the three-metric as the configuration variable. Its central equation is the Wheeler–DeWitt equation. Here I give an overview of the status of this approach. The issues discussed include the problem of time, the relation to the covariant theory, the semiclassical approximation as well as applications to black holes and cosmology. I conclude that quantum geometrodynamics is still a viable approach and provides insights into both the conceptual and technical aspects of quantum gravity.

These considerations reveal that the concepts of spacetime and time itself are not primary but secondary ideas in the structure of physical theory. These concepts are valid in the classical approximation. However, they have neither meaning nor application under circumstances when quantum-geometrodynamical effects become important. ...There is no spacetime, there is no time, there is no before, there is no after. The question what happens “next” is without meaning [1].

Dedicated to the memory of John Archibald Wheeler.     

Statistical description of eigenfunctions in chaotic and weakly disordered systems beyond universality

We present a semiclassical approach to eigenfunction statistics in chaotic and weakly disordered quantum systems which goes beyond random matrix theory, supersymmetry techniques, and existing semiclassical methods. The approach is based on a generalization of Berry's random wave model, combined with a consistent semiclassical representation of spatial two-point correlations. We derive closed expressions for arbitrary wave-function averages in terms of universal coefficients and sums over classical paths, which contain, besides the supersymmetry results, novel oscillatory contributions. Their physical relevance is demonstrated in the context of Coulomb blockade physics.     

Semiclassical theory of chaotic quantum transport

We present a refined semiclassical approach to the Landauer conductance and Kubo conductivity of clean chaotic mesoscopic systems. We demonstrate for systems with uniformly hyperbolic dynamics that including off-diagonal contributions to double sums over classical paths gives a weak-localization correction in quantitative agreement with results from random matrix theory. We further discuss the magnetic-field dependence. This semiclassical treatment accounts for current conservation.     

Shot noise in semiclassical chaotic cavities

We construct a trajectory-based semiclassical theory of shot noise in clean chaotic cavities. In the universal regime of vanishing Ehrenfest time tau(E), we reproduce the random matrix theory result and show that the Fano factor is exponentially suppressed as tau(E) increases. We demonstrate how our theory preserves the unitarity of the scattering matrix even in the regime of finite tau(E). We discuss the range of validity of our semiclassical approach and point out subtleties relevant to the recent semiclassical treatment of shot noise in the universal regime by Braun et al. (cond-mat/0511292).     

Resonant tunneling through Andreev levels

We use a semiclassical approach for analyzing the tunneling transport through a normal conductor in contact with superconducting mirrors. Our analysis of the electron–hole propagation along semiclassical trajectories shows that resonant transmission through Andreev levels is possible resulting in an excess, low-energy quasiparticle contribution to the conductance. The excess conductance oscillates with the phase difference between the superconductors having maxima at odd multiples of π for temperatures much below the Thouless temperature.     

Probing quantum dissipative chaos using purity

In this Letter, the purity of quantum states is applied to probe chaotic dissipative dynamics. To achieve this goal, a comparative analysis of regular and chaotic regimes of nonlinear dissipative oscillator (NDO) are performed on the base of excitation number and the purity of oscillatory states. While the chaotic regime is identified in our semiclassical approach by means of strange attractors in Poincaré section and with the Lyapunov exponent, the state in the quantum regime is treated via the Wigner function. Specifically, interesting quantum purity effects that accompany the chaotic dynamics are elucidated in this Letter for NDO system driven by either: (i) a time-modulated field, or (ii) a sequence of pulses with Gaussian time-dependent envelopes.     

无限深势阱中单粒子的泡利处理

Pauli在处理无限深势阱中的单粒子时,要求粒子具有经典力学的能量动量关系E=p²/2m,而且混用了定波和定态的概念,这说明Pauli更多地用到的是半经典量子论而不是量子力学,他所得到的动量分布函数是半经典理论的结果,只有在大量子数极限下才与量子力学的结果趋于一致.     

Collective excitations of a periodic Bose condensate in the Wannier representation

We study the dispersion relation of the excitations of a dilute Bose-Einstein condensate confined in a periodic optical potential and its Bloch oscillations in an accelerated frame. The problem is reduced to one-dimensionality through a renormalization of the s-wave scattering length and the solution of the Bogolubov-de Gennes equations is formulated in terms of the appropriate Wannier functions. Some exact properties of a periodic one-dimensional condensate are easily demonstrated: (i) the lowest band at positive energy refers to phase modulations of the condensate and has a linear dispersion relation near the Brillouin zone centre; (ii) the higher bands arise from the superposition of localized excitations with definite phase relationships; and (iii) the wavenumber-dependent current under a constant force in the semiclassical transport regime vanishes at the zone boundaries. Early results by Slater [Phys. Rev. 87, 807 (1952)] on a soluble problem in electron energy bands are used to specify the conditions under which the Wannier functions may be approximated by on-site tight-binding orbitals of harmonic-oscillator form. In this approximation the connections between the low-lying excitations in a lattice and those in a harmonic well are easily visualized. Analytic results are obtained in the tight-binding scheme and are illustrated with simple numerical calculations for the dispersion relation and semiclassical transport in the lowest energy band, at values of the system parameters which are relevant to experiment. Received 3 December 1999 and Received in final form 22 March 2000     

Quantization of chaotic systems

Starting from the semiclassical dynamical zeta function for chaotic Hamiltonian systems we use a combination of the cycle expansion method and a functional equation to obtain highly excited semiclassical eigenvalues. The power of this method is demonstrated for the anisotropic Kepler problem, a strongly chaotic system with good symbolic dynamics. An application of the transfer matrix approach of Bogomolny is presented leading to a significant reduction of the classical input and to comparable accuracy for the calculated eigenvalues.