A) A method for calculating the exact energy levels of integrable quantum systems. B) A process where quantum particles completely lose their wave properties in chaotic fields. C) A phenomenon where eigenstates of a classically chaotic quantum system have enhanced probability density around unstable classical periodic orbits. D) The complete suppression of classical mechanics by quantum interference effects.
A) Stable orbits exhibit quantum interference while unstable orbits do not. B) Unstable orbits can be fully explained as a purely classical phenomenon. C) The instability of the periodic orbit and the essential role of quantum interference. D) Stable orbits only exist in relativistic systems.
A) As a direct result of quantum ergodicity theorems. B) Through the strict application of random matrix theory. C) As a purely classical phenomenon and a manifestation of the Bohr correspondence principle. D) As an exclusive feature of relativistic Dirac equations.
A) Its trajectories are strictly periodic and non-ergodic. B) It always exhibits stable periodic orbits that dominate the phase space. C) It is ergodic, so almost all trajectories eventually explore evenly the entire accessible phase space. D) Its trajectories remain confined to isolated regions of the phase space indefinitely.
A) By concentrating entirely at the boundaries of the phase space. B) Along discrete, highly localized lines corresponding to unstable periodic orbits. C) In a uniform manner up to random fluctuations in the semiclassical limit. D) Without any random fluctuations whatsoever.
A) A significant correction and nonergodic states permitted by quantum ergodicity theorems. B) A strict violation of all quantum ergodicity theorems. C) Proof that chaotic systems are never truly ergodic. D) The complete absence of chaotic behavior in the semiclassical limit.
A) The Bohr correspondence principle in macroscopic limits. B) The validity of the Schrödinger equation in non-relativistic systems. C) The existence of quantum interference in microscopic systems. D) The assumption that eigenstates of a classically chaotic system would be without structure.
A) Perturbation-induced scars and many-body scars. B) Linear wave packet scars and Gaussian fluctuation scars. C) Bouncing-ball states and ghost orbit scars. D) Relativistic Dirac scars and magnetic quantum scars.
A) Deterministic quantum channeling and phase fractures. B) Antiscarring and quantum birthmarks. C) Super-ergodicity and macro-scars. D) Classical resurrection and reverse interference.
A) The Schnirelman ergodicity theorem. B) The Schrödinger wave equation. C) The Bohr correspondence formula. D) The Gutzwiller trace formula.
A) It is determined by a trace over all the periodic orbits only. B) It is determined exclusively by stable periodic orbits. C) It is independent of any classical trajectories. D) It is determined by a trace over all spatial positions.
A) Because periodic orbits always have infinite stability exponents. B) Because altogether periodic orbits occupy a zero-volume portion of the total phase space volume. C) Because quantum interference destroys periodic orbit contributions. D) Because periodic orbits do not exist in fully chaotic systems.
A) E. B. Bogomolny B) Eric J. Heller C) Michael V. Berry D) S. W. McDonald
A) L. Kaplan B) S. W. McDonald C) Alexander Schnirelman D) Eric J. Heller
A) The hydrogen atom B) A graphene-based quantum dot C) An elliptical billiard D) The Bunimovich stadium
A) A thermodynamic phase average B) A relativistic Dirac expansion C) A wave packet analysis D) A random matrix calculation
A) The Bogomolny real-space method B) The Berry phase-space alternative C) The linear theory of scarring D) The Gutzwiller trace expansion
A) By projection of the eigenstates onto certain test states, often Gaussians, having average position and momentum along the periodic orbit. B) By evaluating the microcanonical classical average of random operators. C) By calculating the exact phase space volume of the entire chaotic system. D) By measuring the total energy dispersion across non-relativistic boundaries.
A) Quantum scarring occurs only when chi equals zero. B) Quantum scarring is independent of the stability exponent chi. C) Quantum scarring is significant when chi is less than 2 pi. D) Quantum scarring is significant when chi is greater than 2 pi.
A) It scales as chi squared. B) It scales as chi to the power of minus one. C) It scales exponentially with chi. D) It scales linearly with chi.
A) Non-existent ghost periodic orbits. B) Extremely stable and infinitely long periodic orbits. C) Moderately unstable and relatively short periodic orbits. D) Completely stable and zero-velocity periodic orbits.
A) It cannot account for wave packet propagation. B) It cannot predict scarring in any non-relativistic system. C) It cannot precisely pinpoint which particular states are scarred and how much. D) It fails to incorporate Gaussian test states.
A) Bouncing-ball reflections from straight walls. B) Random superpositions of plane waves. C) Bifurcation points of complex periodic orbits. D) Nonlinear recurrences associated with homoclinic orbits.
A) E. B. Bogomolny B) Michael V. Berry C) S. W. McDonald D) Alexander Schnirelman
A) Steven Zelditch B) E. B. Bogomolny C) Yves Colin de Verdière D) Michael V. Berry
A) If its probability density equals the microcanonical classical average everywhere. B) If the stability exponent chi exceeds 2 pi. C) If the eigenstate completely avoids the classical phase space. D) If its density on classical invariant manifolds near and all along that periodic orbit is systematically enhanced above the classical, statistically expected density.
A) Macroscopic classical mechanical billiards. B) Non-relativistic quantum systems described by the Schrödinger equation. C) Open quantum dots with linear energy-momentum relations. D) Relativistic quantum systems described exclusively by the Dirac equation.
A) Logarithmic B) Exponential C) Quadratic D) Linear
A) The Gutzwiller trace formula B) The Helmholtz equation C) The random matrix theory matrix equation D) The Schrödinger equation
A) Strong conductance fluctuations B) Uniform probability density distribution C) Zero-volume phase space occupation D) Complete suppression of electrical resistance
A) In graphene-based quantum dots B) In hydrogen atoms C) In ultracold atomic gases D) In microwave billiards
A) Superconducting circuits and harmonic oscillators B) Relativistic particle accelerators and plasma chambers C) Quantum wells, optical cavities, and the hydrogen atom D) Macroscopic pendulums and classical fluid tanks
A) An elliptical billiard B) A stadium billiard C) A graphene quantum dot D) A microwave cavity
A) Bouncing-ball states B) Ghost orbits C) Quantum mirages D) Quantum birthmarks
A) Ultracold atomic gases B) Radioactive atomic nuclei C) High-temperature plasmas D) Ionized stellar atmospheres
A) Using microwave cavity resonance detection in optical traps B) Using magnetic resonance imaging in ultracold atomic gases C) Using ultrasonic wave reflection in elliptical billiards D) Using scanning tunneling microscopy in a stadium-shaped, graphene-based quantum dot
A) Homoclinic orbit recurrences B) Complex periodic bifurcation ghosts C) Random plane wave superpositions D) Classical 'bouncing-ball' motion
A) S. W. McDonald, Eric J. Heller, and L. Kaplan B) Alexander Schnirelman, Yves Colin de Verdière, and Steven Zelditch C) E. B. Bogomolny, Michael V. Berry, and Gutzwiller D) Dirac, Schrödinger, and Helmholtz
A) Quantum mirage focus concentrations B) Homoclinic nonlinear recurrences C) Resonant transmission conductance fluctuations D) Statistical fluctuations in the sense of the Berry conjecture
A) Relativistic quantum scars that have vanished in the semiclassical limit. B) Numerical artifacts produced during wave packet propagation. C) Stable periodic orbits that obey the Bohr correspondence principle. D) Scars caused not by actual periodic orbits, but by their remnants found in a nearby system via a tunable external system parameter.
A) Zero-volume phase space orbits B) Almost-periodic orbits C) Infinitely stable periodic orbits D) Relativistic linear orbits
A) Bouncing-ball boundary states B) Complex periodic orbits C) Microcanonical classical averages D) Gaussian test packet states
A) Phase space volume approaching total accessible space B) Stability exponent chi approaching two pi C) Planck's constant approaching zero D) Energy approaching infinity
A) Steven Zelditch B) L. Kaplan C) E. B. Bogomolny D) S. W. McDonald
A) It is quantified solely by the Berry conjecture. B) There is no universal measure on scarring. C) It is universally measured by the Gutzwiller trace formula. D) It is defined strictly by the stability exponent chi squared.
A) It is strictly defined as any state satisfying the Dirac equation. B) There is no generally accepted definition of it. C) It has a rigid definition based on the Bohr correspondence principle. D) It is defined exclusively as random superpositions of plane waves.
A) 1984 B) 1983 C) 2000 D) 1990
A) Constant B) Linear C) Quadratic D) Exponential
A) It converges to the corresponding microcanonical classical average. B) It diverges to infinity around unstable periodic orbits. C) It becomes entirely random without any convergence. D) It matches the exact trace of all periodic orbits.
A) The quantum phase space volume of the scars gradually vanishes in the semiclassical limit. B) They have infinite stability exponents. C) They occupy the entire phase space uniformly. D) They violate the Schrödinger equation entirely.
A) One-dimensional linear chains B) Superconducting quantum circuits C) Disordered two-dimensional nanostructures D) Three-dimensional lattice models
A) Strong external magnetic fields B) Disorder arising from small perturbations C) Complete absence of any potential bumps D) Thermal fluctuations at high temperatures
A) Abelian gauge fields B) Random matrix ensembles C) Dynamical symmetries D) Topological invariants
A) The adiabatic theorem of quantum mechanics B) The quantum fluctuation theorem C) The thermalization hypothesis theorem D) A general stacking theorem
A) Extremely rapid thermalization rates B) Anomalously long escape times C) Zero probability density everywhere D) Instantaneous emission of quantum information
A) Reflection symmetries B) Time-averaged probability densities C) Vertical bouncing-ball orbits D) Black arrows
A) A quantum scar B) Weak ergodicity breaking C) A generic initial state D) A bouncing-ball orbit |