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Izrailev FM, Luna-Acosta GA, Mendez-Bermudez JA. Scarring in Rough Rectangular Billiards. ENTROPY (BASEL, SWITZERLAND) 2023; 25:189. [PMID: 36832556 PMCID: PMC9954974 DOI: 10.3390/e25020189] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/22/2022] [Revised: 01/11/2023] [Accepted: 01/11/2023] [Indexed: 06/18/2023]
Abstract
We study the mechanism of scarring of eigenstates in rectangular billiards with slightly corrugated surfaces and show that it is very different from that known in Sinai and Bunimovich billiards. We demonstrate that there are two sets of scar states. One set is related to the bouncing ball trajectories in the configuration space of the corresponding classical billiard. A second set of scar-like states emerges in the momentum space, which originated from the plane-wave states of the unperturbed flat billiard. In the case of billiards with one rough surface, the numerical data demonstrate the repulsion of eigenstates from this surface. When two horizontal rough surfaces are considered, the repulsion effect is either enhanced or canceled depending on whether the rough profiles are symmetric or antisymmetric. The effect of repulsion is quite strong and influences the structure of all eigenstates, indicating that the symmetric properties of the rough profiles are important for the problem of scattering of electromagnetic (or electron) waves through quasi-one-dimensional waveguides. Our approach is based on the reduction of the model of one particle in the billiard with corrugated surfaces to a model of two artificial particles in the billiard with flat surfaces, however, with an effective interaction between these particles. As a result, the analysis is conducted in terms of a two-particle basis, and the roughness of the billiard boundaries is absorbed by a quite complicated potential.
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Affiliation(s)
- Felix M. Izrailev
- Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico
- Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824-1321, USA
| | - German A. Luna-Acosta
- Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico
| | - J. A. Mendez-Bermudez
- Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico
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2
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Porter MD, Reichl LE. Chaos in the honeycomb optical-lattice unit cell. Phys Rev E 2016; 93:012204. [PMID: 26871070 DOI: 10.1103/physreve.93.012204] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2015] [Indexed: 11/07/2022]
Abstract
Natural and artificial honeycomb lattices are of great interest because the band structure of these lattices, if properly constructed, contains a Dirac point. Such lattices occur naturally in the form of graphene and carbon nanotubes. They have been created in the laboratory in the form of semiconductor 2DEGs, optical lattices, and photonic crystals. We show that, over a wide energy range, gases (of electrons, atoms, or photons) that propagate through these lattices are Lorentz gases and the corresponding classical dynamics is chaotic. Thus honeycomb lattices are also of interest for understanding eigenstate thermalization and the conductor-insulator transition due to dynamic Anderson localization.
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Affiliation(s)
- Max D Porter
- Center for Complex Quantum Systems and Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
| | - L E Reichl
- Center for Complex Quantum Systems and Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
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Bao R, Huang L, Lai YC, Grebogi C. Conductance fluctuations in chaotic bilayer graphene quantum dots. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012918. [PMID: 26274258 DOI: 10.1103/physreve.92.012918] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2015] [Indexed: 06/04/2023]
Abstract
Previous studies of quantum chaotic scattering established a connection between classical dynamics and quantum transport properties: Integrable or mixed classical dynamics can lead to sharp conductance fluctuations but chaos is capable of smoothing out the conductance variations. Relativistic quantum transport through single-layer graphene systems, for which the quasiparticles are massless Dirac fermions, exhibits, due to scarring, this classical-quantum correspondence, but sharp conductance fluctuations persist to a certain extent even when the classical system is fully chaotic. There is an open issue regarding the effect of finite mass on relativistic quantum transport. To address this issue, we study quantum transport in chaotic bilayer graphene quantum dots for which the quasiparticles have a finite mass. An interesting phenomenon is that, when traveling along the classical ballistic orbit, the quasiparticle tends to hop back and forth between the two layers, exhibiting a Zitterbewegung-like effect. We find signatures of abrupt conductance variations, indicating that the mass has little effect on relativistic quantum transport. In solid-state electronic devices based on Dirac materials, sharp conductance fluctuations are thus expected, regardless of whether the quasiparticle is massless or massive and whether there is chaos in the classical limit.
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Affiliation(s)
- Rui Bao
- Institute of Computational Physics and Complex Systems, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Liang Huang
- Institute of Computational Physics and Complex Systems, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Ying-Cheng Lai
- School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA
- Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
- Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
| | - Celso Grebogi
- Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
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Méndez-Bermúdez JA, de Oliveira JA, Leonel ED. Two-dimensional nonlinear map characterized by tunable Lévy flights. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042138. [PMID: 25375469 DOI: 10.1103/physreve.90.042138] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2014] [Indexed: 06/04/2023]
Abstract
After recognizing that point particles moving inside the extended version of the rippled billiard perform Lévy flights characterized by a Lévy-type distribution P(l)∼l(-(1+α)) with α=1, we derive a generalized two-dimensional nonlinear map Mα able to produce Lévy flights described by P(l) with 0<α<2. Due to this property, we call Mα the Lévy map. Then, by applying Chirikov's overlapping resonance criteria, we are able to identify the onset of global chaos as a function of the parameters of the map. With this, we state the conditions under which the Lévy map could be used as a Lévy pseudorandom number generator and furthermore confirm its applicability by computing scattering properties of disordered wires.
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Affiliation(s)
- J A Méndez-Bermúdez
- Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico
| | - Juliano A de Oliveira
- UNESP - Univ Estadual Paulista, Campus São João da Boa Vista, São João da Boa Vista, São Paulo 13874-149, Brazil
| | - Edson D Leonel
- Departamento de Física, UNESP - Univ Estadual Paulista, Avenida 24A, 1515 Bela Vista, Rio Claro, São Paulo 13506-900, Brazil
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5
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Rendón M, Makarov NM, Izrailev FM. Ballistic, diffusive, and localized transport in surface-disordered systems: two-mode waveguide. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:051124. [PMID: 21728507 DOI: 10.1103/physreve.83.051124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2010] [Revised: 02/12/2011] [Indexed: 05/31/2023]
Abstract
This paper presents an analytical study of the coexistence of different transport regimes in quasi-one-dimensional surface-disordered waveguides (or electron conductors). To elucidate main features of surface scattering, the case of two open modes (channels) is considered in great detail. Main attention is paid to the transmission in dependence on various parameters of the model with two types of rough-surface profiles (symmetric and antisymmetric). It is shown that depending on the symmetry, basic mechanisms of scattering can be either enhanced or suppressed. As a consequence, different transport regimes can be realized. Specifically, in the two-mode waveguide with symmetric rough boundaries, there are ballistic, localized and coexistence transport regimes. In the waveguide with antisymmetric roughness of lateral walls, another regime of the diffusive transport can arise. Our study allows to reveal the interplay between all relevant scattering mechanisms, in particular, the role of the so-called square-gradient scattering which is typically neglected in literature, however, can give a strong impact to the transmission.
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Affiliation(s)
- M Rendón
- Facultad de Ciencias de la Electrónica, Universidad Autónoma de Puebla, Puebla, México.
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Barra F, Maurel A, Pagneux V, Zuñiga J. Number of propagating modes of a diffusive periodic waveguide in the semiclassical limit. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:066210. [PMID: 20866504 DOI: 10.1103/physreve.81.066210] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2010] [Indexed: 05/29/2023]
Abstract
We study the number of propagating Bloch modes N(B) of an infinite periodic billiard chain. The asymptotic semiclassical behavior of this quantity depends on the phase-space dynamics of the unit cell, growing linearly with the wave number k in systems with a non-null measure of ballistic trajectories and going like ∼square root of k in diffusive systems. We have calculated numerically N(B) for a waveguide with cosine-shaped walls exhibiting strongly diffusive dynamics. The semiclassical prediction for diffusive systems is verified to good accuracy and a connection between this result and the universality of the parametric variation of energy levels is presented.
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Affiliation(s)
- Felipe Barra
- Departamento de Física y CIMAT, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile
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de Oliveira JA, Bizão RA, Leonel ED. Finding critical exponents for two-dimensional Hamiltonian maps. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:046212. [PMID: 20481812 DOI: 10.1103/physreve.81.046212] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/30/2009] [Revised: 01/14/2010] [Indexed: 05/29/2023]
Abstract
The transition from integrability to nonintegrability for a set of two-dimensional Hamiltonian mappings exhibiting mixed phase space is considered. The phase space of such mappings show a large chaotic sea surrounding Kolmogorov-Arnold-Moser islands and limited by a set of invariant tori. The description of the phase transition is made by the use of scaling functions for average quantities of the mapping averaged along the chaotic sea. The critical exponents are obtained via extensive numerical simulations. Given the mappings considered are parametrized by an exponent gamma in one of the dynamical variables, the critical exponents that characterize the scaling functions are obtained for many different values of gamma . Therefore classes of universality are defined.
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Affiliation(s)
- Juliano A de Oliveira
- Departamento de Estatística, Matemática Aplicada e Computação, Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista, Av 24A, 1515 Bela Vista, CEP 13506-700 Rio Claro, SP, Brazil
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8
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Ladeira DG, Leonel ED. Competition between suppression and production of Fermi acceleration. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:036216. [PMID: 20365841 DOI: 10.1103/physreve.81.036216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2009] [Revised: 01/20/2010] [Indexed: 05/29/2023]
Abstract
The behavior of the average velocity for a classical particle in the one-dimensional Fermi accelerator model under sawtooth external force is considered. For elastic collisions, it is known that the average velocity of the particle grows unlimitedly because of the discontinuities of the derivative of the moving wall's position with respect to time. However, and contrary to what was expected to be observed, the introduction of a friction force generated from a slip of a body against a rough surface leads to a boundary separating different regions of the phase space that yields the particle to either experience unlimited energy growth or suppression of Fermi acceleration. The Fermi acceleration is described by using scaling arguments. The formalism presented can be extended to two-dimensional time-dependent billiards as well as to higher-order mappings.
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Affiliation(s)
- Denis Gouvêa Ladeira
- Campus Alto Paraopeba, Universidade Federal de São João Del-Rei, Fazenda do Cadete, CEP 36420-000, Ouro Branco, MG, Brazil
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9
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Izrailev FM, Makarov NM. Anomalous transport in low-dimensional systems with correlated disorder. ACTA ACUST UNITED AC 2005. [DOI: 10.1088/0305-4470/38/49/010] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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10
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Leonel ED, McClintock PVE. Scaling properties for a classical particle in a time-dependent potential well. CHAOS (WOODBURY, N.Y.) 2005; 15:33701. [PMID: 16252990 DOI: 10.1063/1.1941067] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
Some scaling properties for a classical particle interacting with a time-dependent square-well potential are studied. The corresponding dynamics is obtained by use of a two-dimensional nonlinear area-preserving map. We describe dynamics within the chaotic sea by use of a scaling function for the variance of the average energy, thereby demonstrating that the critical exponents are connected by an analytic relationship.
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Affiliation(s)
- Edson D Leonel
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, United Kingdom.
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11
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Dembowski C, Dietz B, Friedrich T, Gräf HD, Heine A, Mejía-Monasterio C, Miski-Oglu M, Richter A, Seligman TH. First experimental evidence for quantum echoes in scattering systems. PHYSICAL REVIEW LETTERS 2004; 93:134102. [PMID: 15524724 DOI: 10.1103/physrevlett.93.134102] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2004] [Indexed: 05/24/2023]
Abstract
A self-pulsing effect termed quantum echoes has been observed in experiments with an open superconducting and a normal conducting microwave billiard whose geometry provides soft chaos, i.e., a mixed phase space portrait with a large stable island. For such systems a periodic response to an incoming pulse has been predicted. Its period has been associated with the degree of development of a horseshoe describing the topology of the classical dynamics. The experiments confirm this picture and reveal the topological information.
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Affiliation(s)
- C Dembowski
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
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12
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Izrailev FM, Méndez-Bermúdez JA, Luna-Acosta GA. Ballistic localization in quasi-one-dimensional waveguides with rough surfaces. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:066201. [PMID: 14754291 DOI: 10.1103/physreve.68.066201] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/11/2003] [Indexed: 05/24/2023]
Abstract
Structure of eigenstates in a periodic quasi-one-dimensional waveguide with a rough surface is studied both analytically and numerically. We have found a large number of "regular" eigenstates for any high energy. They result in a very slow convergence to the classical limit in which the eigenstates are expected to be completely ergodic. As a consequence, localization properties of eigenstates originated from unperturbed transverse channels with low indexes are strongly localized (delocalized) in the momentum (coordinate) representation. These eigenstates were found to have a quite unexpected form that manifests a kind of "repulsion" from the rough surface. Our results indicate that standard statistical approaches for ballistic localization in such waveguides seem to be inappropriate.
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Affiliation(s)
- F M Izrailev
- Instituto de Física, Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico
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Akguc GB, Reichl LE. Direct scattering processes and signatures of chaos in quantum waveguides. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:046202. [PMID: 12786455 DOI: 10.1103/physreve.67.046202] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2002] [Revised: 11/27/2002] [Indexed: 05/24/2023]
Abstract
The effect of direct processes on the statistical properties of deterministic scattering processes in a chaotic waveguide is examined. The single-channel Poisson kernel describes well the distribution of S-matrix eigenphases when evaluated over an energy interval. When direct processes are transformed away, the scattering processes exhibit universal random matrix behavior. The effect of chaos on scattering wave functions, eigenphases, and time delays is discussed.
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Affiliation(s)
- G B Akguc
- Center for Studies in Statistical Mechanics and Complex Systems, The University of Texas at Austin, Austin, Texas 78712, USA
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Méndez-Bermúdez JA, Luna-Acosta GA, Seba P, Pichugin KN. Understanding quantum scattering properties in terms of purely classical dynamics: two-dimensional open chaotic billiards. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:046207. [PMID: 12443299 DOI: 10.1103/physreve.66.046207] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2002] [Revised: 07/02/2002] [Indexed: 05/24/2023]
Abstract
We study classical and quantum scattering properties of particles in the ballistic regime in two-dimensional chaotic billiards that are models of electron- or micro-waveguides. To this end we construct the purely classical counterparts of the scattering probability (SP) matrix |S(n,m)|(2) and Husimi distributions specializing to the case of mixed chaotic motion (incomplete horseshoe). Comparison between classical and quantum quantities allows us to discover the purely classical dynamical origin of certain general as well as particular features that appear in the quantum description of the system. On the other hand, at certain values of energy the tunneling of the wave function into classically forbidden regions produces striking differences between the classical and quantum quantities. A potential application of this phenomenon in the field of microlasers is discussed briefly. We also see the manifestation of whispering gallery orbits as a self-similar structure in the transmission part of the classical SP matrix.
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Affiliation(s)
- J A Méndez-Bermúdez
- Instituto de Física, Universidad Autónoma de Puebla, Apartado Postal J-48, México
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Li W, Reichl LE, Wu B. Quantum chaos in a ripple billiard. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:056220. [PMID: 12059693 DOI: 10.1103/physreve.65.056220] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2001] [Indexed: 05/23/2023]
Abstract
We study the quantum chaos of a ripple billiard that has sinusoidal walls. We show that this type of ripple billiard has a Hamiltonian matrix that can be found exactly in terms of elementary functions. This feature greatly improves computation efficiency; a complete set of eigenstates from the ground state up to the 10,000th level can be calculated simultaneously. Nearest neighbor spacing of energy levels of a chaotic ripple billiard shows a Brody distribution (with a confidence level of 99% by chi(2) test) instead of the Gaussian orthogonal ensemble prediction. For high energy levels we observe scars and interesting patterns that have no resemblance to classical periodic orbits. Momentum localization of scarred eigenstates is also observed. We compare the scar associated localization with quantum dynamical Anderson localization by drawing the wave function distribution on basis state coefficients.
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Affiliation(s)
- Wenjun Li
- Center for Studies in Statistical Mechanics and Complex Systems and Department of Physics, The University of Texas at Austin, Texas 78712, USA
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Luna-Acosta GA, Méndez-Bermúdez JA, Seba P, Pichugin KN. Classical versus quantum structure of the scattering probability matrix: chaotic waveguides. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:046605. [PMID: 12006045 DOI: 10.1103/physreve.65.046605] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2001] [Indexed: 05/23/2023]
Abstract
The purely classical counterpart of the scattering probability matrix (SPM)/S(n,m)/(2) of the quantum scattering matrix S is defined for two-dimensional quantum waveguides for an arbitrary number of propagating modes M. We compare the quantum and classical structures of /S(n,m)/(2) for a waveguide with generic Hamiltonian chaos. It is shown that even for a moderate number of channels, knowledge of the classical structure of the SPM allows us to predict the global structure of the quantum one and, hence, understand important quantum transport properties of waveguides in terms of purely classical dynamics. It is also shown that the SPM, being an intensity measure, can give additional dynamical information to that obtained by the Poincaré maps.
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Affiliation(s)
- G A Luna-Acosta
- Instituto de Física, Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico
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Akguc G, Reichl LE. Effect of evanescent modes and chaos on deterministic scattering in electron waveguides. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:056221. [PMID: 11736068 DOI: 10.1103/physreve.64.056221] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2000] [Revised: 06/29/2001] [Indexed: 05/23/2023]
Abstract
Statistical properties of Wigner delay times and the effect of evanescent modes on the deterministic scattering of an electron matter wave from a classically chaotic two-dimensional electron waveguide are studied for the case of 2, 6, and 16 propagating modes. Deterministic reaction matrix theory for this system is generalized to include the effect of evanescent modes on the scattering process. The statistical properties of the Wigner delay times for the deterministic scattering process are compared to the predictions of random reaction matrix theory.
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Affiliation(s)
- G Akguc
- Center for Studies in Statistical Mechanics and Complex Systems, University of Texas at Austin, 78712, USA
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Luna-Acosta GA, Méndez-Bermúdez JA, Izrailev FM. Periodic chaotic billiards: quantum-classical correspondence in energy space. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:036206. [PMID: 11580421 DOI: 10.1103/physreve.64.036206] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2001] [Indexed: 05/23/2023]
Abstract
We investigate the properties of eigenstates and local density of states (LDOS) for a periodic two-dimensional rippled billiard, focusing on their quantum-classical correspondence in energy representation. To construct the classical counterparts of LDOS and the structure of eigenstates (SES), the effects of the boundary are first incorporated (via a canonical transformation) into an effective potential, rendering the one-particle motion in the 2D rippled billiard equivalent to that of two interacting particles in 1D geometry. We show that classical counterparts of SES and LDOS in the case of strong chaotic motion reveal quite a good correspondence with the quantum quantities. We also show that the main features of the SES and LDOS can be explained in terms of the underlying classical dynamics, in particular, of certain periodic orbits. On the other hand, statistical properties of eigenstates and LDOS turn out to be different from those prescribed by random matrix theory. We discuss the quantum effects responsible for the nonergodic character of the eigenstates and individual LDOS that seem to be generic for this type of billiards with a large number of transverse channels.
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Affiliation(s)
- G A Luna-Acosta
- Instituto de Física, Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico
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Luna-Acosta GA, Krokhin AA, Rodríguez MA, Hernández-Tejeda PH. Classical chaos and ballistic transport in a mesoscopic channel. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:11410-11416. [PMID: 9984930 DOI: 10.1103/physrevb.54.11410] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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