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