Lissajous curves and semiclassical theory: The two-dimensional harmonic oscillator

The semiclassical treatment of the two-dimensional harmonic oscillator provides an instructive example of the relation between classical motion and the quantum mechanical energy spectrum. We extend previous work on the anisotropic oscillator with incommensurate frequencies and the isotropic oscillator to the case with commensurate frequencies for which the Lissajous curves appear as classical periodic orbits. Because of the three different scenarios depending on the ratio of its frequencies, the two-dimensional harmonic oscillator offers a unique way to explicitly analyze the role of symmetries in classical and quantum mechanics.Comment: 9 pages, 3 figures; to appear in Am. J. Phy

Quantum revival patterns from classical phase-space trajectories

A general semiclassical method in phase space based on the final value representation of the Wigner function is considered that bypasses caustics and the need to root-search for classical trajectories. We demonstrate its potential by applying the method to the Kerr Hamiltonian, for which the exact quantum evolution is punctuated by a sequence of intricate revival patterns. The structure of such revival patterns, lying far beyond the Ehrenfest time, is semiclassically reproduced and revealed as a consequence of constructive and destructive interferences of classical trajectories.Comment: 7 pages, 6 figure

Signatures of a Noise-Induced Quantum Phase Transition in a Mesoscopic Metal Ring

We study a mesoscopic ring with an in-line quantum dot threaded by an Aharonov-Bohm flux. Zero-point fluctuations of the electromagnetic environment capacitively coupled to the ring, with $\omega^s$ spectral density, can suppress tunneling through the dot, resulting in a quantum phase transition from an unpolarized to a polarized phase. We show that robust signatures of such a transition can be found in the response of the persistent current in the ring to the external flux as well as to the bias between the dot and the arm. Particular attention is paid to the experimentally relevant cases of ohmic ($s=1$) and subohmic ($s=1/2$) noise.Comment: 4 pages, 4 figures, realistic parameters estimated, reference update

Electron-magnon coupling and nonlinear tunneling transport in magnetic nanoparticles

We present a theory of single-electron tunneling transport through a ferromagnetic nanoparticle in which particle-hole excitations are coupled to spin collective modes. The model employed to describe the interaction between quasiparticles and collective excitations captures the salient features of a recent microscopic study. Our analysis of nonlinear quantum transport in the regime of weak coupling to the external electrodes is based on a rate-equation formalism for the nonequilibrium occupation probability of the nanoparticle many-body states. For strong electron-boson coupling, we find that the tunneling conductance as a function of bias voltage is characterized by a large and dense set of resonances. Their magnetic field dependence in the large-field regime is linear, with slopes of the same sign. Both features are in agreement with recent tunneling experiments.Comment: 4 pages, 2 figure

Spin-orbital Kondo decoherence by environmental effects in capacitively coupled quantum dot devices

Strong correlation effects in a capacitively coupled double quantum-dot setup were previously shown to provide the possibility of both entangling spin-charge degrees of freedom and realizing efficient spin-filtering operations by static gate-voltage manipulations. Motivated by the use of such a device for quantum computing, we study the influence of electromagnetic noise on a general spin-orbital Kondo model, and investigate the conditions for observing coherent, unitary transport, crucial to warrant efficient spin manipulations. We find a rich phase diagram, where low-energy properties sensitively depend on the impedance of the external environment and geometric parameters of the system. Relevant energy scales related to the Kondo temperature are also computed in a renormalization-group treatment, allowing to assess the robustness of the device against environmental effects.Comment: 13 pages, 13 figures. Minor modifications in V

Quantum percolation in granular metals

Theory of quantum corrections to conductivity of granular metal films is developed for the realistic case of large randomly distributed tunnel conductances. Quantum fluctuations of intergrain voltages (at energies E much below bare charging energy scale E_C) suppress the mean conductance \bar{g}(E) much stronger than its standard deviation \sigma(E). At sufficiently low energies E_* any distribution becomes broad, with \sigma(E_*) ~ \bar{g}(E_*), leading to strong local fluctuations of the tunneling density of states. Percolative nature of metal-insulator transition is established by combination of analytic and numerical analysis of the matrix renormalization group equations.Comment: 6 pages, 5 figures, REVTeX

Phase diffusion and charging effects in Josephson junctions

The supercurrent of a Josephson junction is reduced by phase diffusion. For ultrasmall capacitance junctions the current may be further decreased by Coulomb blockade effects. We calculate the Cooper pair current by means of time-dependent perturbation theory to all orders in the Josephson coupling energy and obtain the current-voltage characteristic in closed form in a range of parameters of experimental interest. The results comprehend phase diffusion of the coherent Josephson current in the classical regime as well as the supercurrent peak due to incoherent Cooper pair tunneling in the strong Coulomb blockade regime.Comment: 4 pages, 3 figures, RevTe

Collective transport in the insulating state of Josephson junction arrays

We investigate collective Cooper-pair transport of one- and two-dimensional Josephson junction arrays in the insulating state. We derive an analytical expression for the current-voltage characteristic revealing thermally activated conductivity at small voltages and threshold voltage depinning. The activation energy and the related depinning voltage represent a dynamic Coulomb barrier for collective charge transfer over the whole system and scale with the system size. We show that both quantities are non-monotonic functions of magnetic field. We propose that formation of the dynamic Coulomb barrier as well as the size scaling of the activation energy and the depinning threshold voltage, are consequences of the mutual phase synchronization. We apply the results for interpretation of experimental data in disordered films near the superconductor-insulator transition.Comment: 4 pages, 2 figures; typos corrected, new figures, an improved fit to experimental dat

Dynamical Coulomb blockade and spin-entangled electrons

We consider the production of mobile and nonlocal pairwise spin-entangled electrons from tunneling of a BCS-superconductor (SC) to two normal Fermi liquid leads. The necessary mechanism to separate the two electrons coming from the same Cooper pair (spin-singlet) is achieved by coupling the SC to leads with a finite resistance. The resulting dynamical Coulomb blockade effect, which we describe phenomenologically in terms of an electromagnetic environment, is shown to be enhanced for tunneling of two spin-entangled electrons into the same lead compared to the process where the pair splits and each electron tunnels into a different lead. On the other hand in the pair-split process, the spatial correlation of a Cooper pair leads to a current suppression as a function of distance between the two tunnel junctions which is weaker for effectively lower dimensional SCs.Comment: 5 pages, 2 figure