Nicholas Cerruti - Academia.edu (original) (raw)
Papers by Nicholas Cerruti
Aps Northwest Section Meeting Abstracts, May 1, 2004
In quantum/wave systems with chaotic classical analogs, a slight perturbation of the system will ... more In quantum/wave systems with chaotic classical analogs, a slight perturbation of the system will cause the evolution of a wave packet to diverge from its original behavior increasingly with time. Examples include acoustic waves propagating through the ocean, electrons diffusing through a metal and qubits interacting with the environment. This divergence can be measured by the fidelity, which is defined as the squared overlap of the two time evolved states. For chaotic systems, two main decay regimes of either Gaussian or exponential behavior have been identified depending on the strength of the perturbation. For perturbation strengths intermediate between the two regimes, the fidelity displays both forms of decay. Combining random matrix and semiclassical theories, a uniform approximation can be derived that covers the full range of perturbation strengths [1]. The time dependence is entirely fixed by the density of states and the so-called transition parameter, which can be related to the classical action diffusion constant. [1] N. R. Cerruti and S. Tomsovic, Phys. Rev. Lett. 88, 054103 (2002); J. Phys. A: Math. Gen. 36, 3451 (2003).
Aps Meeting Abstracts, Mar 1, 2002
The sensitivity of a wave field's evolution to small perturbations is of fundamental interest. A ... more The sensitivity of a wave field's evolution to small perturbations is of fundamental interest. A measure of the sensitivity is the fidelity which is the squared overlap of an initial state propagated forward in time with two slightly different Hamiltonians. The fidelity is important when comparing evolving wave packets that are propagated through a time-varying medium. Well known examples include acoustic waves propagating through the ocean, electrons diffusing through a metal and qubits interacting with the environment. The functional form of the decay with time of the fidelity depends upon the strength of the perturbation and whether the system is regular or chaotic. In regular systems the decay is Gaussian and in chaotic systems its form is either Gaussian for weak perturbations or exponential for strong perturbations. Using first order perturbation theory (classical and quantum) we obtain the rates and form of the decay. We demonstrate these results in the standard map which has the entire range of dynamics from integrable to fully chaotic.
Recently, the sensitivity of wave field propagation due to slight perturbations has attracted a g... more Recently, the sensitivity of wave field propagation due to slight perturbations has attracted a great deal of interest. The divergence of the wave field propagation can be measured by the squared overlap of the two time evolved states. A significant amount of work has been done in simple chaotic systems, such as quantum maps. Here, we examine the sensitivity of acoustic wave propagation in the ocean. The ocean consists of internal waves which produce chaos in the corresponding classical rays. These internal waves are both time and range dependent, with the internal wave structure changing on the order of minutes. Thus, conducting two experiments a few minutes apart will change the medium through which the acoustic waves propagate. We present results which indicate a transition of the functional form of the decay as a function of the delay time between experiments.
Physical Review E, 2000
... Rev. E 60, 3992 ,,1999... Arul Lakshminarayan, Nicholas R. Cerruti, and Steven Tomsovic PACS ... more ... Rev. E 60, 3992 ,,1999... Arul Lakshminarayan, Nicholas R. Cerruti, and Steven Tomsovic PACS number s : 05.45. a, 03.65.Sq, 05.45.Mt, 99.10. g We have located some equation misprints in this paper, and identified one issue that requires clarification. ...
Physical review. E, Statistical, nonlinear, and soft matter physics, 2003
The correlation between overlap intensities and level velocities has been introduced as a sensiti... more The correlation between overlap intensities and level velocities has been introduced as a sensitive measure capable of revealing phase space localization. Previously applied to chaotic quantum systems, here we extend the theory to near-integrable and mixed quantum systems. This measure is useful in the latter cases because it has the ability to highlight certain phase space structures depending upon the perturbation used to parametrically vary the Hamiltonian. A detailed semiclassical theory is presented relating the correlation coefficient to the phase space weighted derivatives of the classical action. In the process, we confront the question of whether the Hannay-Ozorio de Almeida sum rules are simply extendable to mixed phase space systems. In addition, the variant Planck's over 2pi scalings of the correlation coefficient and relevant quantities are derived for nearly integrable systems. Excellent agreement is found between the theory and the results for integrable billiards...
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1999
We study the response of the quasienergy levels in the context of quantized chaotic systems throu... more We study the response of the quasienergy levels in the context of quantized chaotic systems through the level velocity variance and relate them to classical diffusion coefficients using detailed semiclassical analysis. The systematic deviations from random matrix theory, assuming independence of eigenvectors from eigenvalues, are shown to be connected to classical higher-order time correlations of the chaotic system. We study the standard map as a specific example, and thus the well-known oscillatory behavior of the diffusion coefficient with respect to the parameter is reflected exactly in the oscillations of the variance of the level velocities. We study the case of mixed phase-space dynamics as well and note a transition in the scaling properties of the variance that occurs along with the classical transition to chaos.
Oceans 2003. Celebrating the Past ... Teaming Toward the Future (IEEE Cat. No.03CH37492), 2003
Summary form only given. Brown and Colosi (JASA 103(4), 2232 (1998)) introduced an efficient nume... more Summary form only given. Brown and Colosi (JASA 103(4), 2232 (1998)) introduced an efficient numerical scheme for the internal wave perturbations in the deep ocean sound speed model that reproduces the Garrett-Munk spectrum. This scheme allows for the addition of an infinite number of vertical modes with decreasing wavelengths to the potential. Since wave propagation can only detect features of
Physical Review B, 2001
We develop a semiclassical theory of Coulomb blockade peak heights in chaotic quantum dots. Using... more We develop a semiclassical theory of Coulomb blockade peak heights in chaotic quantum dots. Using Berry's conjecture, we calculate peak height distributions and correlation functions. We demonstrate that corrections to the corresponding results of the standard statistical theory are nonuniversal, and can be expressed in terms of the classical periodic orbits of the dot that are well coupled to the leads. The main effect is an oscillatory dependence of the peak heights on any parameter which is varied; it is substantial for both symmetric and asymmetric lead placement. Surprisingly, these dynamical effects do not influence the full distribution of peak heights, but are clearly seen in the correlation function or power spectrum. For nonzero temperature, the correlation function obtained theoretically is consistent with that measured experimentally.
Physical Review E, 2000
The correlation between level velocities and eigenfunction intensities provides a new way of expl... more The correlation between level velocities and eigenfunction intensities provides a new way of exploring phase space localization in quantized non-integrable systems. It can also serve as a measure of deviations from ergodicity due to quantum effects for typical observables. This paper relies on two well known paradigms of quantum chaos, the bakers map and the standard map, to study correlations in simple, yet chaotic, dynamical systems. The behaviors are dominated by the presence of several classical structures. These primarily include short periodic orbits and their homoclinic excursions. The dependences of the correlations deriving from perturbations allow for eigenfunction features violating ergodicity to be selectively highlighted. A semiclassical theory based on periodic orbit sums leads to certain classical correlations that are super-exponentially cut off beyond a logarithmic time scale. The theory is seen to be quite successful in reproducing many of the quantum localization features.
Physical Review E, 2000
In a previous Letter [Phys. Rev. Lett. 77, 4158 (1996)], a new correlation measure was introduced... more In a previous Letter [Phys. Rev. Lett. 77, 4158 (1996)], a new correlation measure was introduced that sensitively probes phase space localization properties of eigenstates. It is based on a system's response to varying an external parameter. The measure correlates level velocities with overlap intensities between the eigenstates and some localized state of interest. Random matrix theory predicts the absence of such correlations in chaotic systems whereas in the stadium billiard, a paradigm of chaos, strong correlations were observed. Here, we develop further the theoretical basis of that work, extend the stadium results to the full phase space, study thē h-dependence, and demonstrate the agreement between this measure and a semiclassical theory based on homoclinic orbits.
Physical Review Letters, 2002
The sensitivity of a wave field's evolution to small perturbations is of fundamental interest. Fo... more The sensitivity of a wave field's evolution to small perturbations is of fundamental interest. For chaotic systems, there are two distinct regimes of either exponential or Gaussian overlap decay in time. We develop a semiclassical approach for understanding both regimes, and give a simple expression for the crossover time between the regimes. The wave field's evolution is considerably more stable than the exponential instability of chaotic trajectories seem to suggest. The resolution of this paradox lies in the collective behavior of the appropriate set of trajectories. Results are given for the standard map.
The Journal of the Acoustical Society of America, 2009
ABSTRACT Prior research examined the dependence on simulated burial depth of the low-frequency sc... more ABSTRACT Prior research examined the dependence on simulated burial depth of the low-frequency scattering by small targets illuminated by evanescent waves [P. L. Marston, A. L. Espana, C. F. Osterhoudt, and D. B. Thiessen, J. Acoust. Soc. Am. 122, 3034 (2007)]. The backscattering amplitude from targets with localized coupling displayed a spatial decay rate approximately twice that of the evanescent wave. An extended reciprocity relation was proposed which accounts for the more general case of a bistatic observation in the water column above the sea floor. In the bistatic case the spatial decay rate may differ from the case of backscattering. The present research concerns the testing of generalized reciprocity for small circular cylinders using two-dimensional finite elements. The calculated spatial decay rate for low-frequency bistatic scattering follows the generalized reciprocity condition when the predicted decay rate (for the specified observation scattering angle) exceeds the spatial decay rate of the incident evanescent wave. This computational result includes agreement with the double decay-rate case of backscattering. The calculations indicate that bistatic observation can significantly reduce the spatial decay rate of the signal dependence on burial depth. [Work supported by ONR.].
The Journal of the Acoustical Society of America, 2003
Acoustic wave fields propagating long ranges through the ocean are refracted by the inhomogeneiti... more Acoustic wave fields propagating long ranges through the ocean are refracted by the inhomogeneities in the ocean's sound speed profile. Intuitively, for a given acoustic source frequency, the inhomogeneities become ineffective at refracting the field beyond a certain fine scale determined by the acoustic wavelength. On the other hand, ray methods are sensitive to infinitely fine features. Thus, it is possible to complicate arbitrarily the ray dynamics, and yet have the wave field propagate unchanged. This feature raises doubts about the ray/wave correspondence. Given the importance of various analyses relying on ray methods, a proper model should, at a minimum, exclude all of the fine structure that does not significantly alter the propagated wave field when the correspondence to the ray dynamics is integral. We develop a simple, efficient, smoothing technique to be applied to the inhomogeneities -a low pass filtering performed in the spatial domain -and give a characterization of its necessary extent as a function of acoustic source frequency. We indicate how the smoothing improves the ray/wave correspondence, and show that the so-called "ray chaos" problem remains above a very low frequency (∼ 15 − 25 Hz).
The Journal of the Acoustical Society of America, 2004
Journal of Physics A: Mathematical and General, 2003
The Journal of Chemical Physics, 2002
Numerous experimental and theoretical studies have established that intramolecular vibrational en... more Numerous experimental and theoretical studies have established that intramolecular vibrational energy redistribution (IVR) in isolated molecules has a hierarchical tier structure. The tier structure implies strong correlations between the energy level motions of a quantum system and its intensityweighted spectrum. A measure, which explicitly accounts for this correlation, was first introduced by one of us as a sensitive probe of phase space localization. It correlates eigenlevel velocities with the overlap intensities between the eigenstates and some localized state of interest. A semiclassical theory for the correlation is developed for systems that are classically integrable and complements earlier work focusing exclusively on the chaotic case. Application to a model two dimensional effective spectroscopic Hamiltonian shows that the correlation measure can provide information about the terms in the molecular Hamiltonian which play an important role in an energy range of interest and the character of the dynamics. Moreover, the correlation function is capable of highlighting relevant phase space structures including the local resonance features associated with a specific bright state. In addition to being ideally suited for multidimensional systems with a large density of states, the measure can also be used to gain insights into phase space transport and localization. It is argued that the overlap intensity-level velocity correlation function provides a novel way of studying vibrational energy redistribution in isolated molecules. The correlation function is ideally suited to analyzing the parametric spectra of molecules in external fields.
Physical Review Letters, 1999
We develop a semiclassical theory of Coulomb blockade peak heights in quantum dots and show that ... more We develop a semiclassical theory of Coulomb blockade peak heights in quantum dots and show that the dynamics in the dot leads to a large modulation of the peak height. The corrections to the standard statistical theory of peak height distributions, power spectra, and correlation functions are nonuniversal and can be expressed in terms of the classical periodic orbits of the dot that are well coupled to the leads. The resulting correlation function oscillates as a function of the peak number in a way defined by such orbits. In addition, the correlation of adjacent conductance peaks is enhanced. Both of these effects are in agreement with recent experiments.
Aps Northwest Section Meeting Abstracts, May 1, 2004
In quantum/wave systems with chaotic classical analogs, a slight perturbation of the system will ... more In quantum/wave systems with chaotic classical analogs, a slight perturbation of the system will cause the evolution of a wave packet to diverge from its original behavior increasingly with time. Examples include acoustic waves propagating through the ocean, electrons diffusing through a metal and qubits interacting with the environment. This divergence can be measured by the fidelity, which is defined as the squared overlap of the two time evolved states. For chaotic systems, two main decay regimes of either Gaussian or exponential behavior have been identified depending on the strength of the perturbation. For perturbation strengths intermediate between the two regimes, the fidelity displays both forms of decay. Combining random matrix and semiclassical theories, a uniform approximation can be derived that covers the full range of perturbation strengths [1]. The time dependence is entirely fixed by the density of states and the so-called transition parameter, which can be related to the classical action diffusion constant. [1] N. R. Cerruti and S. Tomsovic, Phys. Rev. Lett. 88, 054103 (2002); J. Phys. A: Math. Gen. 36, 3451 (2003).
Aps Meeting Abstracts, Mar 1, 2002
The sensitivity of a wave field's evolution to small perturbations is of fundamental interest. A ... more The sensitivity of a wave field's evolution to small perturbations is of fundamental interest. A measure of the sensitivity is the fidelity which is the squared overlap of an initial state propagated forward in time with two slightly different Hamiltonians. The fidelity is important when comparing evolving wave packets that are propagated through a time-varying medium. Well known examples include acoustic waves propagating through the ocean, electrons diffusing through a metal and qubits interacting with the environment. The functional form of the decay with time of the fidelity depends upon the strength of the perturbation and whether the system is regular or chaotic. In regular systems the decay is Gaussian and in chaotic systems its form is either Gaussian for weak perturbations or exponential for strong perturbations. Using first order perturbation theory (classical and quantum) we obtain the rates and form of the decay. We demonstrate these results in the standard map which has the entire range of dynamics from integrable to fully chaotic.
Recently, the sensitivity of wave field propagation due to slight perturbations has attracted a g... more Recently, the sensitivity of wave field propagation due to slight perturbations has attracted a great deal of interest. The divergence of the wave field propagation can be measured by the squared overlap of the two time evolved states. A significant amount of work has been done in simple chaotic systems, such as quantum maps. Here, we examine the sensitivity of acoustic wave propagation in the ocean. The ocean consists of internal waves which produce chaos in the corresponding classical rays. These internal waves are both time and range dependent, with the internal wave structure changing on the order of minutes. Thus, conducting two experiments a few minutes apart will change the medium through which the acoustic waves propagate. We present results which indicate a transition of the functional form of the decay as a function of the delay time between experiments.
Physical Review E, 2000
... Rev. E 60, 3992 ,,1999... Arul Lakshminarayan, Nicholas R. Cerruti, and Steven Tomsovic PACS ... more ... Rev. E 60, 3992 ,,1999... Arul Lakshminarayan, Nicholas R. Cerruti, and Steven Tomsovic PACS number s : 05.45. a, 03.65.Sq, 05.45.Mt, 99.10. g We have located some equation misprints in this paper, and identified one issue that requires clarification. ...
Physical review. E, Statistical, nonlinear, and soft matter physics, 2003
The correlation between overlap intensities and level velocities has been introduced as a sensiti... more The correlation between overlap intensities and level velocities has been introduced as a sensitive measure capable of revealing phase space localization. Previously applied to chaotic quantum systems, here we extend the theory to near-integrable and mixed quantum systems. This measure is useful in the latter cases because it has the ability to highlight certain phase space structures depending upon the perturbation used to parametrically vary the Hamiltonian. A detailed semiclassical theory is presented relating the correlation coefficient to the phase space weighted derivatives of the classical action. In the process, we confront the question of whether the Hannay-Ozorio de Almeida sum rules are simply extendable to mixed phase space systems. In addition, the variant Planck's over 2pi scalings of the correlation coefficient and relevant quantities are derived for nearly integrable systems. Excellent agreement is found between the theory and the results for integrable billiards...
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1999
We study the response of the quasienergy levels in the context of quantized chaotic systems throu... more We study the response of the quasienergy levels in the context of quantized chaotic systems through the level velocity variance and relate them to classical diffusion coefficients using detailed semiclassical analysis. The systematic deviations from random matrix theory, assuming independence of eigenvectors from eigenvalues, are shown to be connected to classical higher-order time correlations of the chaotic system. We study the standard map as a specific example, and thus the well-known oscillatory behavior of the diffusion coefficient with respect to the parameter is reflected exactly in the oscillations of the variance of the level velocities. We study the case of mixed phase-space dynamics as well and note a transition in the scaling properties of the variance that occurs along with the classical transition to chaos.
Oceans 2003. Celebrating the Past ... Teaming Toward the Future (IEEE Cat. No.03CH37492), 2003
Summary form only given. Brown and Colosi (JASA 103(4), 2232 (1998)) introduced an efficient nume... more Summary form only given. Brown and Colosi (JASA 103(4), 2232 (1998)) introduced an efficient numerical scheme for the internal wave perturbations in the deep ocean sound speed model that reproduces the Garrett-Munk spectrum. This scheme allows for the addition of an infinite number of vertical modes with decreasing wavelengths to the potential. Since wave propagation can only detect features of
Physical Review B, 2001
We develop a semiclassical theory of Coulomb blockade peak heights in chaotic quantum dots. Using... more We develop a semiclassical theory of Coulomb blockade peak heights in chaotic quantum dots. Using Berry's conjecture, we calculate peak height distributions and correlation functions. We demonstrate that corrections to the corresponding results of the standard statistical theory are nonuniversal, and can be expressed in terms of the classical periodic orbits of the dot that are well coupled to the leads. The main effect is an oscillatory dependence of the peak heights on any parameter which is varied; it is substantial for both symmetric and asymmetric lead placement. Surprisingly, these dynamical effects do not influence the full distribution of peak heights, but are clearly seen in the correlation function or power spectrum. For nonzero temperature, the correlation function obtained theoretically is consistent with that measured experimentally.
Physical Review E, 2000
The correlation between level velocities and eigenfunction intensities provides a new way of expl... more The correlation between level velocities and eigenfunction intensities provides a new way of exploring phase space localization in quantized non-integrable systems. It can also serve as a measure of deviations from ergodicity due to quantum effects for typical observables. This paper relies on two well known paradigms of quantum chaos, the bakers map and the standard map, to study correlations in simple, yet chaotic, dynamical systems. The behaviors are dominated by the presence of several classical structures. These primarily include short periodic orbits and their homoclinic excursions. The dependences of the correlations deriving from perturbations allow for eigenfunction features violating ergodicity to be selectively highlighted. A semiclassical theory based on periodic orbit sums leads to certain classical correlations that are super-exponentially cut off beyond a logarithmic time scale. The theory is seen to be quite successful in reproducing many of the quantum localization features.
Physical Review E, 2000
In a previous Letter [Phys. Rev. Lett. 77, 4158 (1996)], a new correlation measure was introduced... more In a previous Letter [Phys. Rev. Lett. 77, 4158 (1996)], a new correlation measure was introduced that sensitively probes phase space localization properties of eigenstates. It is based on a system's response to varying an external parameter. The measure correlates level velocities with overlap intensities between the eigenstates and some localized state of interest. Random matrix theory predicts the absence of such correlations in chaotic systems whereas in the stadium billiard, a paradigm of chaos, strong correlations were observed. Here, we develop further the theoretical basis of that work, extend the stadium results to the full phase space, study thē h-dependence, and demonstrate the agreement between this measure and a semiclassical theory based on homoclinic orbits.
Physical Review Letters, 2002
The sensitivity of a wave field's evolution to small perturbations is of fundamental interest. Fo... more The sensitivity of a wave field's evolution to small perturbations is of fundamental interest. For chaotic systems, there are two distinct regimes of either exponential or Gaussian overlap decay in time. We develop a semiclassical approach for understanding both regimes, and give a simple expression for the crossover time between the regimes. The wave field's evolution is considerably more stable than the exponential instability of chaotic trajectories seem to suggest. The resolution of this paradox lies in the collective behavior of the appropriate set of trajectories. Results are given for the standard map.
The Journal of the Acoustical Society of America, 2009
ABSTRACT Prior research examined the dependence on simulated burial depth of the low-frequency sc... more ABSTRACT Prior research examined the dependence on simulated burial depth of the low-frequency scattering by small targets illuminated by evanescent waves [P. L. Marston, A. L. Espana, C. F. Osterhoudt, and D. B. Thiessen, J. Acoust. Soc. Am. 122, 3034 (2007)]. The backscattering amplitude from targets with localized coupling displayed a spatial decay rate approximately twice that of the evanescent wave. An extended reciprocity relation was proposed which accounts for the more general case of a bistatic observation in the water column above the sea floor. In the bistatic case the spatial decay rate may differ from the case of backscattering. The present research concerns the testing of generalized reciprocity for small circular cylinders using two-dimensional finite elements. The calculated spatial decay rate for low-frequency bistatic scattering follows the generalized reciprocity condition when the predicted decay rate (for the specified observation scattering angle) exceeds the spatial decay rate of the incident evanescent wave. This computational result includes agreement with the double decay-rate case of backscattering. The calculations indicate that bistatic observation can significantly reduce the spatial decay rate of the signal dependence on burial depth. [Work supported by ONR.].
The Journal of the Acoustical Society of America, 2003
Acoustic wave fields propagating long ranges through the ocean are refracted by the inhomogeneiti... more Acoustic wave fields propagating long ranges through the ocean are refracted by the inhomogeneities in the ocean's sound speed profile. Intuitively, for a given acoustic source frequency, the inhomogeneities become ineffective at refracting the field beyond a certain fine scale determined by the acoustic wavelength. On the other hand, ray methods are sensitive to infinitely fine features. Thus, it is possible to complicate arbitrarily the ray dynamics, and yet have the wave field propagate unchanged. This feature raises doubts about the ray/wave correspondence. Given the importance of various analyses relying on ray methods, a proper model should, at a minimum, exclude all of the fine structure that does not significantly alter the propagated wave field when the correspondence to the ray dynamics is integral. We develop a simple, efficient, smoothing technique to be applied to the inhomogeneities -a low pass filtering performed in the spatial domain -and give a characterization of its necessary extent as a function of acoustic source frequency. We indicate how the smoothing improves the ray/wave correspondence, and show that the so-called "ray chaos" problem remains above a very low frequency (∼ 15 − 25 Hz).
The Journal of the Acoustical Society of America, 2004
Journal of Physics A: Mathematical and General, 2003
The Journal of Chemical Physics, 2002
Numerous experimental and theoretical studies have established that intramolecular vibrational en... more Numerous experimental and theoretical studies have established that intramolecular vibrational energy redistribution (IVR) in isolated molecules has a hierarchical tier structure. The tier structure implies strong correlations between the energy level motions of a quantum system and its intensityweighted spectrum. A measure, which explicitly accounts for this correlation, was first introduced by one of us as a sensitive probe of phase space localization. It correlates eigenlevel velocities with the overlap intensities between the eigenstates and some localized state of interest. A semiclassical theory for the correlation is developed for systems that are classically integrable and complements earlier work focusing exclusively on the chaotic case. Application to a model two dimensional effective spectroscopic Hamiltonian shows that the correlation measure can provide information about the terms in the molecular Hamiltonian which play an important role in an energy range of interest and the character of the dynamics. Moreover, the correlation function is capable of highlighting relevant phase space structures including the local resonance features associated with a specific bright state. In addition to being ideally suited for multidimensional systems with a large density of states, the measure can also be used to gain insights into phase space transport and localization. It is argued that the overlap intensity-level velocity correlation function provides a novel way of studying vibrational energy redistribution in isolated molecules. The correlation function is ideally suited to analyzing the parametric spectra of molecules in external fields.
Physical Review Letters, 1999
We develop a semiclassical theory of Coulomb blockade peak heights in quantum dots and show that ... more We develop a semiclassical theory of Coulomb blockade peak heights in quantum dots and show that the dynamics in the dot leads to a large modulation of the peak height. The corrections to the standard statistical theory of peak height distributions, power spectra, and correlation functions are nonuniversal and can be expressed in terms of the classical periodic orbits of the dot that are well coupled to the leads. The resulting correlation function oscillates as a function of the peak number in a way defined by such orbits. In addition, the correlation of adjacent conductance peaks is enhanced. Both of these effects are in agreement with recent experiments.