S. Tomsovic - Academia.edu (original) (raw)
Papers by S. Tomsovic
In a recent letter [Phys. Rev. Lett. 100, 164101 (2008)] and within the context of quantized chao... more In a recent letter [Phys. Rev. Lett. 100, 164101 (2008)] and within the context of quantized chaotic billiards, random plane wave and semiclassical theoretical approaches were applied to an example of a relatively new class of statistical measures, i.e. measures involving both complete spatial integration and energy summation as essential ingredients. A quintessential example comes from the desire to understand the short-range approximation to the first order ground state contribution of the residual Coulomb interaction. Billiards, fully chaotic or otherwise, provide an ideal class of systems on which to focus as they have proven to be successful in modeling the single particle properties of a Landau-Fermi liquid in typical mesoscopic systems, i.e. closed or nearly closed quantum dots. It happens that both theoretical approaches give fully consistent results for measure averages, but that somewhat surprisingly for fully chaotic systems the semiclassical theory gives a much improved approximation for the fluctuations. Comparison of the theories highlights a couple of key shortcomings inherent in the random plane wave approach. This paper contains a complete account of the theoretical approaches, elucidates the two shortcomings of the oft-relied-upon random plane wave approach, and treats non-fully chaotic systems as well.
We propose a novel approach to the analysis of experimental data obtained in relativistic nucleus... more We propose a novel approach to the analysis of experimental data obtained in relativistic nucleusnucleus collisions which borrows from methods developed within the context of Random Matrix Theory. It is applied to the detection of correlations in momentum distributions of emitted particles. We find good agreement between the results obtained in this way and a standard analysis based on the two-pair correlation function often used in high energy physics. The method introduced here is free from unwanted background contributions. 24.60.Ky,25.75.Gz,24.60.Lz There is currently an enormous effort underway to detect signals of possible transitions between different phases of a composite system produced in high energy nucleus-nucleus collisions (cf [1, 2]). It is anticipated that in central collisions, at energies that are and will be soon available at SPS(CERN), RHIC(BNL) and LHC(CERN), the nuclear density may exceed the density of stable nuclei by an order of magnitude. Under such extreme conditions, according to a generally held beliefs, the final product of a heavy ion collision would be a composite system that consists of free nucleons, quarks and a quarkgluon plasma. Various methods have been proposed to identify possible manifestations of such a quark-gluon plasma. Often though, results based on such methods are sensitive to assumptions made concerning the background measurements and mechanisms included in the corresponding model. In addition, the identification of the quark-gluon plasma is made more difficult due to a large multiplicity of secondary particles created at these collisions. The formulation of a reliable criterion for the selection of meaningful signals is, indeed, an important objective in relativistic heavy ion collisions physics.
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 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 B, 2001
... REVIEW B, VOLUME 63, 125339 Semiclassical density functional theory: Strutinsky energy correc... more ... REVIEW B, VOLUME 63, 125339 Semiclassical density functional theory: Strutinsky energy corrections in quantum dots Denis Ullmo,1 ... 2 Department of Physics, Washington State University, Pullman, Washington 99164-2814 3 Department of Physics, Duke University, Box ...
Symmetries in Physics, 1992
ABSTRACT We study the problem of quantum electronic transport in a mesoscopic disordered system a... more ABSTRACT We study the problem of quantum electronic transport in a mesoscopic disordered system arranged in a two-probe configuration, using the transfer-matrix scattering formalism. We calculate the statistical average of quantities of physical interest starting from single-scattering units and working our way to the n-unit system by successive multiplication of the single-transfer matrices. In the weak-scattering limit discussed in the text, results are described by a diffusion equation in transfer-matrix space. Second moments of the departure of the single-transfer matrices from the unit matrix give rise to generalized diffusion coefficients: once these are specified, results are universal, in the sense that higher-order moments are irrelevant. The isotropy assumption (N-channel generalization of a random-phase assumption) made in some of our previous publications is not needed: we show that, as a consequence, the present results are physically more reasonable than those involving the isotropy assumption. We study the reflection and transmission amplitudes and coefficients for individual pairs of channels in the ballistic regime and the total-reflection coefficient in the ballistic and metallic regimes (the latter in the approximation of ``equivalent channels''). The failure of isotropy in the localized regime is shown in one example. The present model, and not the one involving isotropy, is appropriate for the description of nonlocal quantum effects in multiprobe measurements, as well as persistent currents in normal metal rings.
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.
Physics Reports, 1993
Using two coupled quanic oscillators for illustration, the quantum mechanics of simple systems wh... more Using two coupled quanic oscillators for illustration, the quantum mechanics of simple systems whose classical analogs have varying degrees of non-integrability is investigated. By taking advantage of discrete symmetries and dynamical quasidegeneracies it is shown that Percival's semiclassical classification scheme, i.e., eigenstates may be separated into a regular and an irregular group, basically works. This allows us to probe deeply into the workings of semiclassical quantizatlon in mixed phase space systems. Some observations of intermediate status states are made. The standard modeling of quantum fluctuation properties exhibited by the irregular states and levels by random matrix ensembles is then put on a physical footing. Generalized ensembles are constructed incorporating such classical information as fluxes crossing partial barriers and relative fractions of phase space volume occupied by interesting subregions. The ensembles apply equally well to both spectral and eigenstate properties. They typically show non-universal, but nevertheless characteristic level fluctuations. In addition, they predict "semiclassical localization" of eigenfunctions and "quantum suppression of chaos" which are quantitatively borne out in the quantum systems.
Physical Review Letters, 1990
ABSTRACT
Physical Review Letters, 2008
An exact analytical description of extreme intensity statistics in complex random states is deriv... more An exact analytical description of extreme intensity statistics in complex random states is derived. These states have the statistical properties of the Gaussian and Circular Unitary Ensemble eigenstates of random matrix theory. Although the components are correlated by the normalization constraint, it is still possible to derive compact formulae for all values of the dimensionality N . The maximum intensity result slowly approaches the Gumbel distribution even though the variables are bounded, whereas the minimum intensity result rapidly approaches the Weibull distribution. Since random matrix theory is conjectured to be applicable to chaotic quantum systems, we calculate the extreme eigenfunction statistics for the standard map with parameters at which its classical map is fully chaotic. The statistical behaviors are consistent with the finite-N formulae. PACS numbers: 05.45.Mt,02.50.-r,05.40.-a
In a recent letter [Phys. Rev. Lett. 100, 164101 (2008)] and within the context of quantized chao... more In a recent letter [Phys. Rev. Lett. 100, 164101 (2008)] and within the context of quantized chaotic billiards, random plane wave and semiclassical theoretical approaches were applied to an example of a relatively new class of statistical measures, i.e. measures involving both complete spatial integration and energy summation as essential ingredients. A quintessential example comes from the desire to understand the short-range approximation to the first order ground state contribution of the residual Coulomb interaction. Billiards, fully chaotic or otherwise, provide an ideal class of systems on which to focus as they have proven to be successful in modeling the single particle properties of a Landau-Fermi liquid in typical mesoscopic systems, i.e. closed or nearly closed quantum dots. It happens that both theoretical approaches give fully consistent results for measure averages, but that somewhat surprisingly for fully chaotic systems the semiclassical theory gives a much improved approximation for the fluctuations. Comparison of the theories highlights a couple of key shortcomings inherent in the random plane wave approach. This paper contains a complete account of the theoretical approaches, elucidates the two shortcomings of the oft-relied-upon random plane wave approach, and treats non-fully chaotic systems as well.
We propose a novel approach to the analysis of experimental data obtained in relativistic nucleus... more We propose a novel approach to the analysis of experimental data obtained in relativistic nucleusnucleus collisions which borrows from methods developed within the context of Random Matrix Theory. It is applied to the detection of correlations in momentum distributions of emitted particles. We find good agreement between the results obtained in this way and a standard analysis based on the two-pair correlation function often used in high energy physics. The method introduced here is free from unwanted background contributions. 24.60.Ky,25.75.Gz,24.60.Lz There is currently an enormous effort underway to detect signals of possible transitions between different phases of a composite system produced in high energy nucleus-nucleus collisions (cf [1, 2]). It is anticipated that in central collisions, at energies that are and will be soon available at SPS(CERN), RHIC(BNL) and LHC(CERN), the nuclear density may exceed the density of stable nuclei by an order of magnitude. Under such extreme conditions, according to a generally held beliefs, the final product of a heavy ion collision would be a composite system that consists of free nucleons, quarks and a quarkgluon plasma. Various methods have been proposed to identify possible manifestations of such a quark-gluon plasma. Often though, results based on such methods are sensitive to assumptions made concerning the background measurements and mechanisms included in the corresponding model. In addition, the identification of the quark-gluon plasma is made more difficult due to a large multiplicity of secondary particles created at these collisions. The formulation of a reliable criterion for the selection of meaningful signals is, indeed, an important objective in relativistic heavy ion collisions physics.
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 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 B, 2001
... REVIEW B, VOLUME 63, 125339 Semiclassical density functional theory: Strutinsky energy correc... more ... REVIEW B, VOLUME 63, 125339 Semiclassical density functional theory: Strutinsky energy corrections in quantum dots Denis Ullmo,1 ... 2 Department of Physics, Washington State University, Pullman, Washington 99164-2814 3 Department of Physics, Duke University, Box ...
Symmetries in Physics, 1992
ABSTRACT We study the problem of quantum electronic transport in a mesoscopic disordered system a... more ABSTRACT We study the problem of quantum electronic transport in a mesoscopic disordered system arranged in a two-probe configuration, using the transfer-matrix scattering formalism. We calculate the statistical average of quantities of physical interest starting from single-scattering units and working our way to the n-unit system by successive multiplication of the single-transfer matrices. In the weak-scattering limit discussed in the text, results are described by a diffusion equation in transfer-matrix space. Second moments of the departure of the single-transfer matrices from the unit matrix give rise to generalized diffusion coefficients: once these are specified, results are universal, in the sense that higher-order moments are irrelevant. The isotropy assumption (N-channel generalization of a random-phase assumption) made in some of our previous publications is not needed: we show that, as a consequence, the present results are physically more reasonable than those involving the isotropy assumption. We study the reflection and transmission amplitudes and coefficients for individual pairs of channels in the ballistic regime and the total-reflection coefficient in the ballistic and metallic regimes (the latter in the approximation of ``equivalent channels''). The failure of isotropy in the localized regime is shown in one example. The present model, and not the one involving isotropy, is appropriate for the description of nonlocal quantum effects in multiprobe measurements, as well as persistent currents in normal metal rings.
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.
Physics Reports, 1993
Using two coupled quanic oscillators for illustration, the quantum mechanics of simple systems wh... more Using two coupled quanic oscillators for illustration, the quantum mechanics of simple systems whose classical analogs have varying degrees of non-integrability is investigated. By taking advantage of discrete symmetries and dynamical quasidegeneracies it is shown that Percival's semiclassical classification scheme, i.e., eigenstates may be separated into a regular and an irregular group, basically works. This allows us to probe deeply into the workings of semiclassical quantizatlon in mixed phase space systems. Some observations of intermediate status states are made. The standard modeling of quantum fluctuation properties exhibited by the irregular states and levels by random matrix ensembles is then put on a physical footing. Generalized ensembles are constructed incorporating such classical information as fluxes crossing partial barriers and relative fractions of phase space volume occupied by interesting subregions. The ensembles apply equally well to both spectral and eigenstate properties. They typically show non-universal, but nevertheless characteristic level fluctuations. In addition, they predict "semiclassical localization" of eigenfunctions and "quantum suppression of chaos" which are quantitatively borne out in the quantum systems.
Physical Review Letters, 1990
ABSTRACT
Physical Review Letters, 2008
An exact analytical description of extreme intensity statistics in complex random states is deriv... more An exact analytical description of extreme intensity statistics in complex random states is derived. These states have the statistical properties of the Gaussian and Circular Unitary Ensemble eigenstates of random matrix theory. Although the components are correlated by the normalization constraint, it is still possible to derive compact formulae for all values of the dimensionality N . The maximum intensity result slowly approaches the Gumbel distribution even though the variables are bounded, whereas the minimum intensity result rapidly approaches the Weibull distribution. Since random matrix theory is conjectured to be applicable to chaotic quantum systems, we calculate the extreme eigenfunction statistics for the standard map with parameters at which its classical map is fully chaotic. The statistical behaviors are consistent with the finite-N formulae. PACS numbers: 05.45.Mt,02.50.-r,05.40.-a