Shot noise in chaotic systems: "classical" to quantum crossover

This paper is devoted to study of the classical-to-quantum crossover of the shot noise in chaotic systems. This crossover is determined by the ratio of the particle dwell time in the system, tau(d), to the characteristic time for diffraction t(E) approximately lambda(-1)|lnh, where lambda is the Lyapunov exponent. The shot noise vanishes when t(E)>tau(d), while it reaches a universal value in the opposite limit. Thus, the Lyapunov exponent of chaotic mesoscopic systems may be found by shot noise measurements.     

Microscopic theory for the quantum to classical crossover in chaotic transport

We present a semiclassical theory for the scattering matrix S of a chaotic ballistic cavity at finite Ehrenfest time. Using a phase-space representation coupled with a multibounce expansion, we show how the Liouville conservation of phase-space volume decomposes S as S=S(cl) plus sign in circle S(qm). The short-time, classical contribution S(cl) generates deterministic transmission eigenvalues T=0 or 1, while quantum ergodicity is recovered within the subspace corresponding to the long-time, stochastic contribution S(qm). This provides a microscopic foundation for the two-phase fluid model, in which the cavity acts like a classical and a quantum cavity in parallel, and explains recent numerical data showing the breakdown of universality in quantum chaotic transport in the deep semiclassical limit. We show that the Fano factor of the shot-noise power vanishes in this limit, while weak localization remains universal.     

The proper form of the generator in the weak coupling limit

In the literature one finds several different Markov approximations for a quantum system weakly coupled to a thermal reservoir. We want to point out that, in general, only the rigorous approximation given by E.B. Davies preserves positivity.     

Single particle dynamics in an anharmonic potential with translation-rotation coupling: crossover from weak localisation via chaos to free rotation

The single particle dynamics of a rigid NH₃-molecule in an anharmonic mean crystal potential is analysed. The potential parameters used have been derived earlier from experimental neutron diffraction data on single crystals of Ni(NH₃)₆X₂ (X = I, NO ₃, PF ₆): in all these compounds the ammonia molecules show dynamical orientational disorder. The mean crystal potential which is experienced by the three protons of one ammonia molecule is given by a two-dimensional anharmonic four-well potential, which leads to a coupling of the rotation of the molecule around its threefold axis to the translational motion of the molecular center of mass. Thus the dynamical problem is restricted to three degrees of freedom. The corresponding Hamiltonian equations of motion are solved numerically. Fourier analysis, reconstruction of trajectories in the six dimensional phase space and next-amplitude-maps from the simulated time series reveal either multiple periodic or chaotic solutions, depending on the potential parameters and the energy of the system. The anharmonic potential produces, as a generic property, three different kinds of proton orbits. At low energy, i. e. low temperatures, closed orbits related to hypocycloid functions occur. At intermediate temperatures the orbits are chaotic. High temperature simulations show circular orbits with a week high frequency jitter superimposed. Thus a crossover from weak localization via chaos to nearly free rotation is obtained by a variation of the energy in the simulation.     

Surface of a 3He crystal: crossover from quantum to classical behavior

3He crystals start to show facets on their surface only at about 100 mK, well below the roughening transition temperature. To understand the reason for that, we have performed the first quantitative investigation on the growth dynamics of the basic (110) facet at 60-110 mK. The obtained values of the step free energy suggest an extremely weak coupling of the solid-liquid interface to the crystal lattice which we show to be the result of quantum fluctuations of the interface. The renormalization group approach by Nozières and Gallet, modified to incorporate quantum fluctuations, explains well the temperature dependence of the step energy measured in this work and at ultralow temperatures by Tsepelin et al., where the coupling is known to be strong. We have thus shown that, paradoxically, the role of quantum fluctuations is at higher temperatures much larger than at low temperature.     

Dimensional crossover in quantum networks: from macroscopic to mesoscopic physics

We report on magnetoconductance measurements of metallic networks of various sizes ranging from 10 to 10(6) plaquettes, with an anisotropic aspect ratio. Both Altshuler-Aronov-Spivak h/2e periodic oscillations and Aharonov-Bohm h/e periodic oscillations are observed for all networks. For large samples, the amplitude of both oscillations results from the incoherent superposition of contributions of phase coherent regions. When the transverse size becomes smaller than the phase coherent length Lphi, one enters a new regime which is phase coherent (mesoscopic) along one direction and macroscopic along the other, leading to a new size dependence of the quantum oscillations.     

Persistent spin current in a quantum wire with weak Dresselhaus spin——orbit coupling

The spin current in a parabolically confined semiconductor heterojunction quantum wire with Dresselhaus spin--orbit coupling is theoretically studied by using the perturbation method. The formulae of the elements for linear and angular spin current densities are derived by using the recent definition for spin current based on spin continuity equation. It is found that the spin current in this Dresselhaus spin--orbit coupling quantum wire is antisymmetrical, which is different from that in Rashba model due to the difference in symmetry between these two models. Some numerical examples for the result are also demonstrated and discussed.     

Electron-phonon coupling and a polaron in the t-J model: from the weak to the strong coupling regime

We present numeric results for ground state and angle resolved photoemission spectra (ARPES) for a single hole in the t-J model coupled to optical phonons. The systematic-error-free diagrammatic Monte Carlo method is employed where the Feynman graphs for the Matsubara Green function in imaginary time are summed up completely with respect to phonon variables, while magnetic variables are subjected to the noncrossing approximation. We obtain that at electron-phonon coupling constants relevant for high T(c) cuprates the polaron undergoes a self-trapping crossover to the strong-coupling limit and theoretical ARPES demonstrate features observed in experiment: A broad peak in the bottom of the spectra has momentum dependence which coincides with that of a hole in the pure t-J model.     

A quantum transition from localized to extended states in a classically chaotic system

We study the quantum dynamics of a particle in a one dimensional triangular well under a monochromatic perturbation. Though the classical dynamics is described by the Standard Map, the quantum motion is not always localized. At a certain threshold field intensity, a transition takes place, from a, regime of power-localized quasi-energy eigenstates to one of extended states.     

Dynamics of delayed-coupled chaotic logistic maps: Influence of network topology,connectivity and delay times

We review our recent work on the synchronization of a network of delay-coupled maps, focusing on the interplay of the network topology and the delay times that take into account the finite velocity of propagation of interactions. We assume that the elements of the network are identical (N logistic maps in the regime where the individual maps, without coupling, evolve in a chaotic orbit) and that the coupling strengths are uniform throughout the network. We show that if the delay times are sufficiently heterogeneous, for adequate coupling strength the network synchronizes in a spatially homogeneous steady state, which is unstable for the individual maps without coupling. This synchronization behavior is referred to as ‘suppression of chaos by random delays’ and is in contrast with the synchronization when all the interaction delay times are homogeneous, because with homogeneous delays the network synchronizes in a state where the elements display in-phase time-periodic or chaotic oscillations. We analyze the influence of the network topology considering four different types of networks: two regular (a ring-type and a ring-type with a central node) and two random (free-scale Barabasi-Albert and small-world Newman-Watts). We find that when the delay times are sufficiently heterogeneous the synchronization behavior is largely independent of the network topology but depends on the network’s connectivity, i.e., on the average number of neighbors per node.      

The crossover from classical to quantum behavior in Duffing oscillator based on quantum state diffusion

The classical Duffing oscillator is a dissipative chaotic system, and so there is not a definite Hamiltonian. We quantize the Duffing oscillator on the basis of quantum state diffusion (QSD) which is a formulation for open quantum systems and a useful tool for analyzing nonlinear problems and classical limits. We can define a ‘Lyapunov exponent’, which corresponds to the classical one in the proper limit, and investigate the behavior of the system by varying the Planck constant effectively. We show that there exists a critical stage, where the behavior of the system crosses over from classical to quantum one.     

量子系统哈密顿量的必要条件

在此前的量子理论中,哈密顿量被要求是厄米算符,这既保证了其本征值谱为实又保证了动力学演化过程几率守恒。近年来,一些非厄米哈密顿量被发现同样满足这两条要求。然而,这两条要求都是哈密顿量可描述量子系统动力学的充分条件而非必要条件。文章中我们从量子化条件和动力学演化方程出发,考察一般形式的哈密顿量,表述为产生算符和湮灭算符之正规积的形式,欲为恰当的哈密顿量所应满足的必要条件。对于形如$\\hat{H}=\\hat{p}^2+\\mathrm{i} \\hat{x}^3$和$\\hat{H}=\\hat{p}^2-\\hat{x}^4$这样的近年来得到广泛关注的非厄米哈密顿量,容易验证它们满足必要性条件。必要性条件可以用来及时排除那些不恰当的非厄米哈密顿量形式。     

Interference swapping in scattering from a nonlocal quantum target

We describe a new and distinctive interferometry in which a probe particle scatters off a superposition of locations of a single free target particle. Probe particles scattering off a single free "mirror" (in one dimension) or a single free "slit" (in two dimensions) can "swap" interference with the superposed target states. The condition for interference is loss of orthogonality of the target states and reduces, in simple examples, to transfer of orthogonality from target to probe states. We analyze experimental parameters and conditions necessary for interference to be observed.     

Statistics of S-matrix poles in few-channel chaotic scattering: Crossover from isolated to overlapping resonances

We derive an explicit expression for the distribution of resonance widths in a chaotic quantum system coupled to continua via M equivalent open channels. It describes a crossover from the χ ² distribution (regime of isolated resonances) to a broad, power-law-like distribution typical for the regime of overlapping resonances. The first moment is found to reproduce exactly the Moldauer-Simonius relation between the mean resonance width and the transmission coefficient. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 12, 970–973 (25 June 1996) Petersburg Nuclear Physics Institute, 188350, Gatchina, St. Petersburg District, Russia Published in English in the original Russian journal. Edited by Steve Torstveit.     

Bilayer quantum hall systems at nu(T)=1: coulomb drag and the transition from weak to strong interlayer coupling

Measurements revealing anomalously large frictional drag at the transition between the weakly and strongly coupled regimes of a bilayer two-dimensional electron system at total Landau level filling factor nu(T)=1 are reported. This result suggests the existence of fluctuations, either static or dynamic, near the phase boundary separating the quantized Hall state at small layer separations from the compressible state at larger separations. Interestingly, the anomalies in drag seem to persist to larger layer separations than does interlayer phase coherence as detected in tunneling.     

Light scattering studies of crossover to a liquid crystal tricritical point

We have used light scattering to study nematic elastic constantsK ₂ andK ₃ in the alkyl-cyanobiphenyl (n CB) system. As the average alkyl chain lengthn increases, the temperature range of the nematic phase decreases and the system approaches a tricritical point. Our data are analyzed to determine the parallel and perpendicular correlation lengths and critical exponents for smectic short-range order. We find a continuous decrease in the critical exponentsv andv as the tricritical point, which occurs at 9.1 CB, is approached. There is also a significant decrease in the magnitude of the parallel correlation length at a fixed reduced temperature.     

Noise enhanced phase synchronization and coherence resonance in sets of chaotic oscillators with weak global coupling

The effect of noise on phase synchronization in small sets and larger populations of weakly coupled chaotic oscillators is explored. Both independent and correlated noise are found to enhance phase synchronization of two coupled chaotic oscillators below the synchronization threshold; this is in contrast to the behavior of two coupled periodic oscillators. This constructive effect of noise results from the interplay between noise and the locking features of unstable periodic orbits. We show that in a population of nonidentical chaotic oscillators, correlated noise enhances synchronization in the weak coupling region. The interplay between noise and weak coupling induces a collective motion in which the coherence is maximal at an optimal noise intensity. Both the noise-enhanced phase synchronization and the coherence resonance numerically observed in coupled chaotic R?ssler oscillators are verified experimentally with an array of chaotic electrochemical oscillators.     

Effects of intrasubband coupling on the scattering phases and density of states in a quantum wire

The properties of scattering phases and density of states in a quantum wire with an attractive scatterer are analyzed. We consider two bound states which couple to a scattering channel and give rise to two Fano resonances. It is shown that varying the parameters of the scatterer (such as its strength and position) produces significantly different effects on the phase behavior and density of states, depending on the subband they occur. These effects stem mainly from the difference between the coupling matrix elements of the two resonant levels with the propagating channel mode.