Transport properties of open chaotic ballistic systems and their statistics can be expressed in terms of the scattering matrix connecting incoming and outgoing wavefunctions. Here we calculate the dependence of correlation functions of arbitrarily many pairs of scattering matrices at different energies on the Ehrenfest time using trajectory based semiclassical methods. This enables us to verify the prediction from effective random matrix theory that one part of the correlation function obtains an exponential damping depending on the Ehrenfest time, while also allowing us to obtain the additional contribution which arises from bands of always correlated trajectories. The resulting Ehrenfest-time dependence, responsible e.g. for secondary gaps in the density of states of Andreev billiards, can also be seen to have strong effects on other transport quantities like the distribution of delay times.
Quantum interference corrections in ballistic conductors require a minimal time: the Ehrenfest time. In this letter, we investigate the fate of the interference corrections to quantum transport in bulk ballistic conductors if the Ehrenfest time and the dephasing time are comparable.
If the Ehrenfest time tau_E of a ballistic cavity is not negligible in comparison to its dwell time tau_D, the weak localization correction to the cavity's transmission is suppressed proportional to exp(-tau_E/tau_D). At the same time, quantum interference enhances the probability of reflection into the mode of incidence by a factor two. This `enhanced backscattering' does not depend on the Ehrenfest time. We show that, in addition to the diagonal enhanced backscattering, there are off-diagonal contributions to coherent backscattering that become relevant if the Ehrenfest time is not negligibl…
We present a trajectory-based semiclassical calculation of the Ehrenfest-time dependence of the weak localization correction and the universal conductance fluctuations of a ballistic quantum dot with ideal point contacts. While the weak localization correction is proportional to exp(-tau_E/tau_D), where tau_E and tau_D are the dot's Ehrenfest time and dwell time, respectively, the variance of the conductance is found to be independent of tau_E. The latter is in agreement with numerical simulations of the quantum kicked rotator [Tworzydlo et al., Phys. Rev. B 69, 165318 (2004) and Jacquod and S…
In ballistic conductors, there is a low-time threshold for the appearance of quantum effects in transport coefficients. This low-time threshold is the Ehrenfest time. Most previous studies of the Ehrenfest-time dependence of quantum transport assumed ergodic electron dynamics, so that they could be applied to ballistic quantum dots only. In this article we present a theory of the Ehrenfest-time dependence of three signatures of quantum transport - the Fano factor for the shot noise power, the weak localization correction to the conductance, and the conductance fluctuations - for arbitrary ball…
We describe the quantum mechanical spreading of a Gaussian wave packet by means of the semiclassical WKB approximation of Berry and Balazs. We find that the time scale $τ$ on which this approximation breaks down in a chaotic system is larger than the Ehrenfest times considered previously. In one dimension $τ=\fr{7}{6}λ^{-1}\ln(A/\hbar)$, with $λ$ the Lyapunov exponent and $A$ a typical classical action.
We calculate the Ehrenfest-time dependence of the leading quantum correction to the spectral form factor of a ballistic chaotic cavity using periodic orbit theory. For the case of broken time-reversal symmetry, our result differs from that previously obtained using field-theoretic methods [Tian and Larkin, Phys. Rev. B 70, 035305 (2004)]. The discrepancy shows that short-time regularization procedures dramatically affect physics near the Ehrenfest-time.
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 predicts that the weak localization correction to the conductance of a ballistic chaotic cavity is suppressed if the Ehrenfest time exceeds the dwell time in the cavity [I. L. Aleiner and A. I. Larkin, Phys. Rev. B {\bf 54}, 14424 (1996)]. We report numerical simulations of weak localization in the open quantum kicked rotator that confirm this prediction. Our results disagree with the `effective random matrix theory' of transport through ballistic chaotic cavities.
Quantum effects are expected to disappear in the short-wavelength, semiclassical limit. As a matter of fact, recent investigations of transport through quantum chaotic systems have demonstrated the exponential suppression of the weak localization corrections to the conductance and of the Fano factor for shot-noise when the Ehrenfest time exceeds the electronic dwell time. On the other hand, conductance fluctuations, an effect of quantum coherence, retain their universal value in the limit of the ratio of Ehrenfest time over dwell time to infinity, when the system is ideally coupled to external…
A semiclassical theory is developed for the appearance of an excitation gap in a ballistic chaotic cavity connected by a point contact to a superconductor. Diffraction at the point contact is a singular perturbation in the limit $\hbar\to 0$, which opens up a gap $E_{\rm gap}$ in the excitation spectrum. The time scale $\hbar/E_{\rm gap}\proptoα^{-1}\ln\hbar$ (with $α$ the Lyapunov exponent) is the Ehrenfest time, the characteristic time scale of quantum chaos.
We add simple tunnelling effects and ray-splitting into the recent trajectory-based semiclassical theory of quantum chaotic transport. We use this to derive the weak-localization correction to conductance and the shot-noise for a quantum chaotic cavity (billiard) coupled to $n$ leads via tunnel-barriers. We derive results for arbitrary tunnelling rates and arbitrary (positive) Ehrenfest time, $τ_{\rm E}$. For all Ehrenfest times, we show that the shot-noise is enhanced by the tunnelling, while the weak-localization is suppressed. In the opaque barrier limit (small tunnelling rates with large l…
We study a crossover from classical to quantum picture in the electron energy statistics in a system with broken time-reversal symmetry. The perturbative and nonperturbative parts of the two level correlation function, $R(ω)$ are analyzed. We find that in the intermediate region, $Δ\llω\sim t_E^{-1}\ll t_{erg}^{-1}$, where $t_E$ and $t_{erg}$ are the Ehrenfest and ergodic times, respectively, $R(ω)$ consists of a series of oscillations with the periods depending on $t_E$, deviating from the universal Wigner-Dyson statistics. These Ehrenfest oscillations have the period dependence as $t_E^{-1}$…
We investigate the influence of spin-orbit interaction on ballistic transport through chaotic cavities by using semiclassical methods. Our approach is based on the Landauer formalism and the Fisher-Lee relations, appropriately generalized to spin-orbit interaction, and a semiclassical representation of Green functions. We calculate conductance coefficients by exploiting ergodicity and mixing of suitably combined classical spin-orbit dynamics, and making use of the Sieber-Richter method and its most recent extensions. That way we obtain weak anti-localization and confirm previous results obtain…
We review properties of open chaotic mesoscopic systems with a finite Ehrenfest time tau_E. The Ehrenfest time separates a short-time regime of the quantum dynamics, where wave packets closely follow the deterministic classical motion, from a long-time regime of fully-developed wave chaos. For a vanishing Ehrenfest time the quantum systems display a degree of universality which is well described by random-matrix theory. In the semiclassical limit, tau_E becomes parametrically larger than the scattering time off the boundaries and the dwell time in the system. This results in the emergence of a…
We re-examine the problem of the "Loschmidt echo", which measures the sensitivity to perturbation of quantum chaotic dynamics. The overlap squared $M(t)$ of two wave packets evolving under slightly different Hamiltonians is shown to have the double-exponential initial decay $\propto \exp(-{\rm constant}\times e^{2λ_0 t})$ in the main part of phase space. The coefficient $λ_0$ is the self-averaging Lyapunov exponent. The average decay $\bar{M}\propto e^{-λ_1 t}$ is single exponential with a different coefficient $λ_1$. The volume of phase space that contributes to $\bar{M}$ vanishes in the clas…
In a quantum charge pump, the periodic variation of two parameters that affect the phase of the electronic wavefunction causes the flow of a direct current. The operating mechanism of a quantum pump is based on quantum interference, the phases of interfering amplitudes being modulated by the external parameters. In a ballistic quantum dot, there is a minimum time before which quantum interference can not occur: the Ehrenfest time. Here we calculate the current pumped through a ballistic quantum dot when the Ehrenfest time is comparable to the mean dwell time. Remarkably, we find that the pumpe…
We consider the semiclassical ballistic sigma-model as an effective theory describing the quantum mechanics of classically chaotic systems. Specifically, we elaborate on close analogies to the recently developed semiclassical theory of quantum interference in chaotic systems and show how semiclassical 'diagrams' involving near action degenerate sets of periodic orbits emerge in the field theoretical description. We further discuss how the universality phenomenon (i.e. the fact that individual chaotic systems behave according to the prescriptions of random matrix theory) can be understood from …
Electron-electron interactions are responsible for a correction to the conductance of a diffusive metal, the "Altshuler-Aronov correction" $δG_{AA}$. Here we study the counterpart of this correction for a ballistic conductor, in which the electron motion is governed by chaotic classical dynamics. In the ballistic conductance, the Ehrenfest time $τ_{E}$ enters as an additional time scale that determines the magnitude of quantum interference effects. The Ehrenfest time effectively poses a short-time threshold for the trajectories contributing to the interaction correction. As a consequence, $δG_…
This paper is withdrawn. While almost all findings reported here remain valid, some of our comments on the fate of weak localization corrections to the conductance in the deep semiclassical limit are now obsolete. Contrarily to what was suggested here, we find an exponential suppression of weak localization at finite Ehrenfest time. For more details, see cond-mat/0512662 .
The Ehrenfest time dependence of the suppression of the weak localization correction to the conductance of a {\em clean} chaotic cavity is calculated. Unlike in earlier work, no impurity scattering is invoked to imitate diffraction effects. The calculation extends the semiclassical theory of K. Richter and M. Sieber [Phys. Rev. Lett. {\bf 89}, 206801 (2002)] to include the effect of a finite Ehrenfest time.
The quantum kicked rotor (QKR) is known to exhibit dynamical localization in the space of its angular momentum. The present paper is devoted to the systematic first--principal (without a regularizer) diagrammatic calculations of the weak--localization corrections for QKR. Our particular emphasis is on the Ehrenfest time regime -- the phenomena characteristic for the classical--to--quantum crossover of classically chaotic systems.
In Aharonov-Bohm (AB) cavities forming doubly connected ballistic structures, h/e AB oscillations that result from the interference among the complicated trapped paths in the cavity can be described by the framework of the semiclassical theory. We derive formulas of the correlation function C(Δϕ) of the nonaveraged magnetoconductance for chaotic and regular AB cavities. The different higher harmonics behaviors for C(Δϕ) are related to the differing distribution of classical dwelling times. The AB oscillation in ballistic regimes provides an experimental probe of quantum signatures of classical…
Quantum cavities or dots have markedly different properties depending on whether their classical counterparts are chaotic or not. Connecting a superconductor to such a cavity leads to notable proximity effects, particularly the appearance, predicted by random matrix theory, of a hard gap in the excitation spectrum of quantum chaotic systems. Andreev billiards are interesting examples of such structures built with superconductors connected to a ballistic normal metal billiard since each time an electron hits the superconducting part it is retroreflected as a hole (and vice-versa). Using a semic…
We consider quantum decay and photofragmentation processes in open chaotic systems in the semiclassical limit. We devise a semiclassical approach which allows us to consistently calculate quantum corrections to the classical decay to high order in an expansion in the inverse Heisenberg time. We present results for systems with and without time reversal symmetry and also for the symplectic case, as well as extending recent results to non-localized initial states. We further analyze related photodissociation and photoionization phenomena and semiclassically compute cross-section correlations, in…
We construct a trajectory-based semiclassical theory of shot noise in clean chaotic cavities. In the universal regime of vanishing Ehrenfest time $\tE$, we reproduce the random matrix theory result, and show that the Fano factor is exponentially suppressed as $\tE$ increases. We demonstrate how our theory preserves the unitarity of the scattering matrix even in the regime of finite $\tE$. 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].
An effective random matrix theory description is developed for the universal gap fluctuations and the ensemble averaged density of states of chaotic Andreev billiards for finite Ehrenfest time. It yields a very good agreement with the numerical calculation for Sinai-Andreev billiards. A systematic linear decrease of the mean field gap with increasing Ehrenfest time $τ_E$ is observed but its derivative with respect to $τ_E$ is in between two competing theoretical predictions and close to that of the recent numerical calculations for Andreev map. The exponential tail of the density of states is …
States supported by chaotic open quantum systems fall into two categories: a majority showing instantaneous ballistic decay, and a set of quantum resonances of classically vanishing support in phase space. We present a theory describing these structures within a unified semiclassical framework. Emphasis is put on the quantum diffraction mechanism which introduces an element of probability and is crucial for the formation of resonances. Our main result are boundary conditions on the semiclassical propagation along system trajectories. Depending on whether the trajectory propagation time is shor…
The persistent current of ballistic chaotic billiards is considered with the help of the Gutzwiller trace formula. We derive the semiclassical formula of a typical persistent current $I^{typ}$ for a single billiard and an average persistent current $<I>$ for an ensemble of billiards at finite temperature. These formulas are used to show that the persistent current for chaotic billiards is much smaller than that for integrable ones. The persistent currents in the ballistic regime therefore become an experimental tool to search for the quantum signature of classical chaotic and regular dynamics.
We study the effect of left-right symmetry on the distribution of the parametric derivative of the dimensionless conductance T with respect to an external parameter X, dT/dX, of ballistic chaotic cavities with two leads, each supporting N propagating modes. We show that T and dT/dX are uncorrelated for any N. For N=1 we calculate the distribution of dT/dX in the presence and absence of time-reversal invariance. In both cases, it has a logarithmic singularity at zero derivative and algebraic tails with an exponent different from the one of the asymmetric case. We also obtain explicit analytical…
The scattering matrix S of a ballistic chaotic cavity is the direct sum of a `classical' and a `quantum' part, which describe the scattering of channels with typical dwell time smaller and larger than the Ehrenfest time, respectively. According to the `effective random matrix theory' of Silvestrov, Goorden, and Beenakker [Phys. Rev. Lett. 90, 116801 (2003)], statistical averages involving the quantum-mechanical scattering matrix are given by random matrix theory. While this effective random matrix theory is known not to be applicable for quantum interference corrections to transport, which app…
We present a comprehensive account of directed transport in one-dimensional Hamiltonian systems with spatial and temporal periodicity. They can be considered as Hamiltonian ratchets in the sense that ensembles of particles can show directed ballistic transport in the absence of an average force. We discuss general conditions for such directed transport, like a mixed classical phase space, and elucidate a sum rule that relates the contributions of different phase-space components to transport with each other. We show that regular ratchet transport can be directed against an external potential g…
We study the magneto-transport in Aharonov-Bohm (AB) billiards forming doubly connected structures. In these systems, non-averaged conductance oscillates as a function of magnetic flux with period h/e. We derive formulas of the correlation function C of the magneto-conductance for chaotic and regular AB billiards by use of the semiclassical theory. The different higher harmonics behaviors for C are related to the differing distribution of classical dwelling times. The AB oscillation in ballistic regimes provides an experimental probe of quantum signatures of classical chaotic and regular dynam…
We extend previous studies on transport through ballistic chaotic cavities with spatial left-right (LR) reflection symmetry to include the presence of direct processes. We first analyze fully LR-symmetric systems in the presence of direct processes and compare the distribution w(T) of the transmission coefficient T with that for an asymmetric cavity with the same "optical" S matrix. We then study the problem of "external mixing" of the symmetry caused by an asymmetric coupling of the cavity to the outside. We first consider the case where symmetry breaking arises because two symmetrically posi…
We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth disorder. The conjecture of Gaussian fluctuations of wave functions put forward by Berry and generalized by Hortikar and Srednicki is proven to hold on sufficiently short distances, while it is found to be strongly violated on larger scales. This also resolves the conflict between the above conjecture and the wave function normalization. The method is further used to study ballistic correlations of wave functions in a random magnetic field.
We consider the $1/N$-expansion of the moments of the proper delay times for a ballistic chaotic cavity supporting $N$ scattering channels. In the random matrix approach, these moments correspond to traces of negative powers of Wishart matrices. For systems with and without broken time reversal symmetry (Dyson indices $β=1$ and $β=2$) we obtain a recursion relation, which efficiently generates the coefficients of the $1/N$-expansion of the moments. The integrality of these coefficients and their possible diagrammatic interpretation is discussed.
We study shot noise for generic quantum dots coupled to two leads and allow for an arbitrary strength of diffractive impurity scattering inside the dots. The ballistic quantum dots possess a mixed classical phase space, where regular and chaotic regions coexist. In absence of disorder, the noise is systematically suppressed below the universal value of fully chaotic systems, by an amount which varies with the positions of the leads. This suppression is due to the deterministic nature of transport through regular regions and along short chaotic trajectories, and disappears by increasing the sca…
The magneto-resistance of antidot lattices shows pronounced peaks, which became a hallmark of ballistic electron transport. While most studies agree that they reflect the interplay of regular and chaotic motion in the quasi-classical dynamics, the exact mechanism has been surprisingly controversial. Inspired by recent experiments on graphene antidot lattices showing that the effect survives strong impurity scattering, we give a new explanation of the peaks linked to a fundamental relation between collision times and accessible phase space volumes, accounting for their robustness. Due to the fu…
By considering correlations between classical orbits we derive semiclassical expressions for the decay of the quantum fidelity amplitude for classically chaotic quantum systems, as well as for its squared modulus, the fidelity or Loschmidt echo. Our semiclassical results for the fidelity amplitude agree with random matrix theory (RMT) and supersymmetry predictions in the universal Fermi golden rule regime. The calculated quantum corrections can be viewed as arising from a static random perturbation acting on nearly self-retracing interfering paths, and hence will be suppressed for time-varying…
We calculate the Landauer conductance through chaotic ballistic devices in the semiclassical limit, to all orders in the inverse number of scattering channels without and with a magnetic field. Families of pairs of entrance-to-exit trajectories contribute, similarly to the pairs of periodic orbits making up the small-time expansion of the spectral form factor of chaotic dynamics. As a clue to the exact result we find that close self-encounters slightly hinder the escape of trajectories into leads.
We investigate the behavior of weak localization, conductance fluctuations, and shot noise of a chaotic scatterer in the semiclassical limit. Time resolved numerical results, obtained by truncating the time-evolution of a kicked quantum map after a certain number of iterations, are compared to semiclassical theory. Considering how the appearance of quantum effects is delayed as a function of the Ehrenfest time gives a new method to compare theory and numerical simulations. We find that both weak localization and shot noise agree with semiclassical theory, which predicts exponential suppression…
We investigate shot noise for quantum dots whose classical phase space consists of both regular and chaotic regions. The noise is systematically suppressed below the universal value of fully chaotic systems, by an amount which varies with the positions of the leads. We analyze the dynamical origin of this effect by a novel way to incorporate diffractive impurity scattering. The dependence of the shot noise on the scattering rate shows that the suppression arises due to the deterministic nature of transport through regular regions and along short chaotic trajectories. Shot noise can be used to …
We study matrix element fluctuations of the two-body screened Coulomb interaction and of the one-body surface charge potential in ballistic quantum dots, comparing behavior in actual chaotic billiards with analytic results previously obtained in a normalized random wave model. We find that the matrix element variances in actual chaotic billiards typically exceed by a factor of 3 or 4 the predictions of the random wave model, for dot sizes commonly used in experiments. We discuss dynamical effects that are responsible for this enhancement. These dynamical effects have an even more striking effe…
We use the open kicked rotator to model the chaotic scattering in a ballistic quantum dot coupled by two point contacts to electron reservoirs. By calculating the system-size-over-wave-length dependence of the shot noise power we study the crossover from wave to particle dynamics. Both a fully quantum mechanical and a semiclassical calculation are presented. We find numerically in both approaches that the noise power is reduced exponentially with the ratio of Ehrenfest time and dwell time, in agreement with analytical predictions.
When coupling a superconductor to a normal conducting region the physical properties of the system are highly affected by the superconductor. We will investigate the effect of one or two superconductors on the conductance of a ballistic chaotic quantum dot to leading order in the total channel number using trajectory based semiclassics. The results show that the effect of one superconductor on the conductance is of the order of the number of channels and that the sign of the correction from the Drude conductance depends on the particular ratios of the numbers of channels of the superconducting…
We investigate the effect of dephasing/decoherence on quantum transport through open chaotic ballistic conductors in the semiclassical limit of small Fermi wavelength to system size ratio, $λ_F/L << 1$. We use the trajectory-based semiclassical theory to study a two-terminal chaotic dot with decoherence originating from: (i) an external closed quantum chaotic environment, (ii) a classical source of noise, (iii) a voltage probe, i.e. an additional current-conserving terminal. We focus on the pure dephasing regime, where the coupling to the external source of dephasing is so weak that it does no…
We calculate the sample-to-sample fluctuations in the excitation gap of a chaotic dynamical system coupled by a narrow lead to a superconductor. Quantum fluctuations on the order of magnitude of the level spacing, predicted by random-matrix theory, apply if $τ_E\ll\hbar/E_T$ (with $τ_E$ the Ehrenfest time and $E_T$ the Thouless energy). For $τ_E\agt\hbar/ E_T$ the fluctuations are much greater than the level spacing. We demonstrate the quasiclassical nature of the gap fluctuations in the large-$τ_E$ regime by correlating them to an integral over the classical dwell-time distribution.
We address frequency-dependent quantum transport through mesoscopic conductors in the semiclassical limit. By generalizing the trajectory-based semiclassical theory of dc quantum transport to the ac case, we derive the average screened conductance as well as ac weak-localization corrections for chaotic conductors. Thereby we confirm respective random matrix results and generalize them by accounting for Ehrenfest time effects. We consider the case of a cavity connected through many leads to a macroscopic circuit which contains ac-sources. In addition to the reservoir the cavity itself is capaci…
We consider the problem of electronic quantum transport through ballistic mesoscopic systems with chaotic dynamics, connected to a three-terminal architecture in which one of the terminals has a tunnel barrier. Using a semiclassical approximation based on matrix integrals, we calculate several transport statistics, such as average and variance of conductance, average shot-noise power, among others, that give access to the extreme quantum regime (small channel numbers in the terminal) for broken and intact time-reversal symmetry, which the traditional random matrix approach does not access. As …
We present a semiclassical theory for the scattering matrix ${\cal S}$ of a chaotic ballistic cavity at finite Ehrenfest time. Using a phase-space representation coupled with a multi-bounce expansion, we show how the Liouville conservation of phase-space volume decomposes ${\cal S}$ as ${\cal S}={\cal S}^{\rm cl} \oplus {\cal S}^{\rm qm}$. The short-time, classical contribution ${\cal S}^{\rm cl}$ generates deterministic transmission eigenvalues T=0 or 1, while quantum ergodicity is recovered within the subspace corresponding to the long-time, stochastic contribution ${\cal S}^{\rm qm}$. This …
We performed path integral simulations of spin evolution controlled by the Rashba spin-orbit interaction in the semiclassical regime for chaotic and regular quantum dots. The spin polarization dynamics have been found to be strikingly different from the D'yakonov-Perel' (DP) spin relaxation in bulk systems. Also an important distinction have been found between long time spin evolutions in classically chaotic and regular systems. In the former case the spin polarization relaxes to zero within relaxation time much larger than the DP relaxation, while in the latter case it evolves to a time indep…
We investigate transport properties of quantized chaotic systems in the short wavelength limit. We focus on non-coherent quantities such as the Drude conductance, its sample-to-sample fluctuations, shot-noise and the transmission spectrum, as well as coherent effects such as weak localization. We show how these properties are influenced by the emergence of the Ehrenfest time scale $\tE$. Expressed in an optimal phase-space basis, the scattering matrix acquires a block-diagonal form as $\tE$ increases, reflecting the splitting of the system into two cavities in parallel, a classical determinist…
We study matrix element fluctuations of the two-body screened Coulomb interaction and of the one-body surface charge potential in ballistic quantum dots. For chaotic dots, we use a normalized random wave model to obtain analytic expansions for matrix element variances and covariances in the limit of large kL (where k is the Fermi wave number and L the linear size of the dot). These leading-order analytical results are compared with exact numerical results. Both two-body and one-body matrix elements are shown to follow strongly non-Gaussian distributions, despite the Gaussian random nature of t…
We study transport through a two-dimensional billiard attached to two infinite leads by numerically calculating the Landauer conductance and the Wigner time delay. In the generic case of a mixed phase space we find a power law distribution of resonance widths and a power law dependence of conductance increments apparently reflecting the classical dwell time exponent, in striking difference to the case of a fully chaotic phase space. Surprisingly, these power laws appear on energy scales {\em below} the mean level spacing, in contrast to semiclassical expectations.
Shot noise in a chaotic cavity (Lyapunov exponent $λ$, level spacing $δ$, linear dimension $L$), coupled by two $N$-mode point contacts to electron reservoirs, is studied as a measure of the crossover from stochastic quantum transport to deterministic classical transport. The transition proceeds through the formation of {\em fully} transmitted or reflected scattering states, which we construct explicitly. The fully transmitted states contribute to the mean current $\bar{I}$, but not to the shot-noise power $S$. We find that these noiseless transmission channels do not exist for $N\alt\sqrt{k_{…
We illustrate how classical chaotic dynamics influences the quantum properties at mesoscopic scales. As a model case we study semiclassically coherent transport through ballistic mesoscopic systems within the Landauer formalism beyond the so-called diagonal approximation, i.e. by incorporating classical action correlations. In this context we review and explain the two main trajectory-based methods developed for calculating quantum corrections: the configuration space approach and the phase space approach that can be regarded as less illustrative but more general than the first one.
By an inductive reasoning, and based on recent results of the joint moments of proper delay times of open chaotic systems for ideal coupling to leads, we obtain a general expression for the distribution of the partial delay times for an arbitrary number of channels and any symmetry. This distribution was not completely known for all symmetry classes. Our theoretical distribution is verified by random matrix theory simulations of ballistic chaotic cavities.
We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth random potential, which allows us to apply the ballistic $σ$-model approach. We analyze conditions of applicability of the $σ$-model, emphasizing the role played by the single-particle mean free path and the Lyapunov exponent due to the random potential. In particular, we present a resolution of the puzzle of repetitions of periodic orbits counted differently by the $σ$-model and by the trace formula.
Quantum corrections to transport through a chaotic ballistic cavity are known to be universal. The universality not only applies to the magnitude of quantum corrections, but also to their dependence on external parameters, such as the Fermi energy or an applied magnetic field. Here we consider such parameter dependence of quantum transport in a ballistic chaotic cavity in the semiclassical limit obtained by sending Planck's constant to zero without changing the classical dynamics of the open cavity. In this limit quantum corrections are shown to have a universal parametric dependence which is …
In the semiclassical limit of open ballistic quantum systems, we demonstrate the emergence of instantaneous decay modes guided by classical escape faster than the Ehrenfest time. The decay time of the associated quasi-bound states is smaller than the classical time of flight. The remaining long-lived quasi-bound states obey random-matrix statistics, renormalized in compliance with the recently proposed fractal Weyl law for open systems [W. T. Lu, S. Sridhar, and M. Zworski, Phys. Rev. Lett. 91, 154101 (2003)]. We validate our theory numerically for a model system, the open kicked rotator.
