Time-reversal symmetry breaking by ac field: Effect of commensurability in the frequency domain

It is shown that the variance of the linear dc conductance fluctuations in an open quantum dot under a high-frequency ac pumping depends significantly on the spectral content of the ac field. For a sufficiently strong ac field the dc conductance fluctuations are much stronger for the periodic pumping than in the case of the noise ac field of the same intensity. The reduction factor r in a static magnetic field takes the universal value of 2 only for the white-noise pumping. In general r may deviate from 2 thus signalling on the time-reversal symmetry breaking by the ac field. For the bi-harmonic ac field of the form A(t)=A_{0} [cos(\omega_{1} t)+cos(\omega_{2} t)] we predict the enchancement of effects of T-symmetry breaking at commensurate frequencies \omega_{2}/\omega_{1}=P/Q. In the high-temperature limit there is also the parity effect: the enchancement is only present if either P or Q is even.Comment: 8 pages, 6 figures, submitted for "Electronic Correlations: from meso- to nano-physics", edited by G. Montambaux and T. Martin, Rencontres de Morion

Polymers in Curved Boxes

We apply results derived in other contexts for the spectrum of the Laplace operator in curved geometries to the study of an ideal polymer chain confined to a spherical annulus in arbitrary space dimension D and conclude that the free energy compared to its value for an uncurved box of the same thickness and volume, is lower when $D < 3$, stays the same when $D = 3$, and is higher when \mbox{$D > 3$}. Thus confining an ideal polymer chain to a cylindrical shell, lowers the effective bending elasticity of the walls, and might induce spontaneous symmetry breaking, i.e. bending. (Actually, the above mentioned results show that {\em {any}} shell in $D = 3$ induces this effect, except for a spherical shell). We compute the contribution of this effect to the bending rigidities in the Helfrich free energy expression.Comment: 20 pages RevTeX, epsf; 4 figures; submitted to Macromoledule

Conductance fluctuations in a quantum dot under almost periodic ac pumping

It is shown that the variance of the linear dc conductance fluctuations in an open quantum dot under a high-frequency ac pumping depends significantly on the spectral content of the ac field. For a sufficiently strong ac field $\gamma\tau_{\phi}<< 1$, where $1/\tau_{\phi}$ is the dephasing rate induced by ac noise and $\gamma$ is the electron escape rate, the dc conductance fluctuations are much stronger for the harmonic pumping than in the case of the noise ac field of the same intensity. The reduction factor $r$ in a static magnetic field takes the universal value of 2 only for the white--noise pumping. For the strictly harmonic pumping $A(t)=A_{0}\cos\omega t$ of sufficiently large intensity the variance is almost insensitive to the static magnetic field $r-1= 2\sqrt{\tau_{\phi}\gamma} << 1$. For the quasi-periodic ac field of the form $A(t)=A_{0} [\cos(\omega_{1} t)+\cos(\omega_{2} t)]$ with $\omega_{1,2} >> \gamma$ and $\gamma\tau_{\phi} << 1$ we predict the novel effect of enchancement of conductance fluctuations at commensurate frequencies $\omega_{2}/\omega_{1}=P/Q$.Comment: 4 pages RevTex, 4 eps figures; the final version to appear in Phys.Rev.

Quantized adiabatic quantum pumping due to interference

Recent theoretical calculations, demonstrating that quantized charge transfer due to adiabatically modulated potentials in mesoscopic devices can result purely from the interference of the electron wave functions (without invoking electron-electron interactions) are reviewed: (1) A new formula is derived for the pumped charge Q (per period); It reproduces the Brouwer formula without a bias, and also yields the effect of the modulating potential on the Landauer formula in the presence of a bias. (2) For a turnstile geometry, with time-dependent gate voltages V_L(t) and V_R(t), the magnitude and sign of Q are determined by the relative position and orientation of the closed contour traversed by the system in the {V_L-V_R} plane, relative to the transmission resonances in that plane. Integer values of Q (in units of e) are achieved when a transmission peak falls inside the contour, and are given by the winding number of the contour. (3) When the modulating potential is due to surface acoustic waves, Q exhibits a staircase structure, with integer values, reminiscent of experimental observations.Comment: Invited talk, Localization, Tokyo, August 200

Short time decay of the Loschmidt echo

The Loschmidt echo measures the sensitivity to perturbations of quantum evolutions. We study its short time decay in classically chaotic systems. Using perturbation theory and throwing out all correlation imposed by the initial state and the perturbation, we show that the characteristic time of this regime is well described by the inverse of the width of the local density of states. This result is illustrated and discussed in a numerical study in a 2-dimensional chaotic billiard system perturbed by various contour deformations and using different types of initial conditions. Moreover, the influence to the short time decay of sub-Planck structures developed by time evolution is also investigated.Comment: 7 pages, 7 figures, published versio

Sensitivity to perturbations in a quantum chaotic billiard

The Loschmidt echo (LE) measures the ability of a system to return to the initial state after a forward quantum evolution followed by a backward perturbed one. It has been conjectured that the echo of a classically chaotic system decays exponentially, with a decay rate given by the minimum between the width $\Gamma$ of the local density of states and the Lyapunov exponent. As the perturbation strength is increased one obtains a cross-over between both regimes. These predictions are based on situations where the Fermi Golden Rule (FGR) is valid. By considering a paradigmatic fully chaotic system, the Bunimovich stadium billiard, with a perturbation in a regime for which the FGR manifestly does not work, we find a cross over from $\Gamma$ to Lyapunov decay. We find that, challenging the analytic interpretation, these conjetures are valid even beyond the expected range.Comment: Significantly revised version. To appear in Physical Review E Rapid Communication

Limits of the dynamical approach to non-linear response of mesoscopic systems

We have considered the nonlinear response of mesoscopic systems of non-interacting electrons to the time-dependent external field. In this consideration the inelastic processes have been neglected and the electron thermalization occurs due to the electron exchange with the reservoirs. We have demonstrated that the diagrammatic technique based on the method of analytical continuation or on the Keldysh formalism is capable to describe the heating automatically. The corresponding diagrams contain a novel element, {\it the loose diffuson}. We have shown the equivalence of such a diagrammatic technique to the solution to the kinetic equation for the electron energy distribution function. We have identified two classes of problems with different behavior under ac pumping. In one class of problems (persistent current fluctuations, Kubo conductance) the observable depends on the electron energy distribution renormalized by heating. In another class of problems (Landauer conductance) the observable is insensitive to heating and depends on the temperature of electron reservoirs. As examples of such problems we have considered in detail the persistent current fluctuations under ac pumping and two types of conductance measurements (Landauer conductance and Kubo conductance) that behave differently under ac pumping.Comment: 21 pages, RevTex, 10 eps.figures; final version to appear in Phys.Rev.

Counting statistics for arbitrary cycles in quantum pumps

Statistics of charge transport in an adiabatic pump are determined by the dynamics of the scattering matrix S(t). We show that, up to an integer offset, the statistics depend only on the corresponding path N(t)=S^\dagger\sigma_3 S in the coset space (the sphere for a single channel). For a general loop S(t) we solve for the noise-minimizing pumping strategy. The average current is given by the area enclosed by N(t) in the coset space; its minimal noise by the area of a minimal surface (soap film) spanned by N(t) in the space of all matrices. We formulate conditions for quantization of the pumped charge.Comment: 4 pages, 2 figure

Charge pumping in a quantum wire driven by a series of local time-periodic potentials

We develop a method to calculate electronic transport properties through a mesoscopic scattering region in the presence of a series of time-periodic potentials. Using the method, the quantum charge pumping driven by time-periodic potentials is studied. Jumps in the pumped current are observed at the peak positions of the Wigner delay time. Our main results in both the weak pumping and strong pumping regimes are consistent with experimental results. More interestingly, we also observed the nonzero pumping at the phase difference phi=0 and addressed its relevance to the experimental result.Comment: 5 page

Adiabatic transport in nanostructures

A confined system of non-interacting electrons, subject to the combined effect of a time-dependent potential and different external chemical-potentials, is considered. The current flowing through such a system is obtained for arbitrary strengths of the modulating potential, using the adiabatic approximation in an iterative manner. A new formula is derived for the charge pumped through an un-biased system (all external chemical potentials are kept at the same value); It reproduces the Brouwer formula for a two-terminal nanostructure. The formalism presented yields the effect of the chemical potential bias on the pumped charge on one hand, and the modification of the Landauer formula (which gives the current in response to a constant chemical-potential difference) brought about by the modulating potential on the other. Corrections to the adiabatic approximation are derived and discussed.Comment: 8 pages, 2 figure