Localization of Eigenfunctions in the Stadium Billiard

We present a systematic survey of scarring and symmetry effects in the stadium billiard. The localization of individual eigenfunctions in Husimi phase space is studied first, and it is demonstrated that on average there is more localization than can be accounted for on the basis of random-matrix theory, even after removal of bouncing-ball states and visible scars. A major point of the paper is that symmetry considerations, including parity and time-reversal symmetries, enter to influence the total amount of localization. The properties of the local density of states spectrum are also investigated, as a function of phase space location. Aside from the bouncing-ball region of phase space, excess localization of the spectrum is found on short periodic orbits and along certain symmetry-related lines; the origin of all these sources of localization is discussed quantitatively and comparison is made with analytical predictions. Scarring is observed to be present in all the energy ranges considered. In light of these results the excess localization in individual eigenstates is interpreted as being primarily due to symmetry effects; another source of excess localization, scarring by multiple unstable periodic orbits, is smaller by a factor of $\sqrt{\hbar}$.Comment: 31 pages, including 10 figure

A new class of semiclassical wave function uniformizations

We present a new semiclassical technique which relies on replacing complicated classical manifold structure with simpler manifolds, which are then evaluated by the usual semiclassical rules. Under circumstances where the original manifold structure gives poor or useless results semiclassically the replacement manifolds can yield remarkable accuracy. We give several working examples to illustrate the theory presented here.Comment: 12 pages (incl. 12 figures

Parallel transport in an entangled ring

This paper defines a notion of parallel transport in a lattice of quantum particles, such that the transformation associated with each link of the lattice is determined by the quantum state of the two particles joined by that link. We focus particularly on a one-dimensional lattice--a ring--of entangled rebits, which are binary quantum objects confined to a real state space. We consider states of the ring that maximize the correlation between nearest neighbors, and show that some correlation must be sacrificed in order to have non-trivial parallel transport around the ring. An analogy is made with lattice gauge theory, in which non-trivial parallel transport around closed loops is associated with a reduction in the probability of the field configuration. We discuss the possibility of extending our result to qubits and to higher dimensional lattices.Comment: 31 pages, no figures; v2 includes a new example of a qubit rin

Recognition without identification, erroneous familiarity, and déjà vu

Déjà vu is characterized by the recognition of a situation concurrent with the awareness that this recognition is inappropriate. Although forms of déjà vu resolve in favor of the inappropriate recognition and therefore have behavioral consequences, typical déjà vu experiences resolve in favor of the awareness that the sensation of recognition is inappropriate. The resultant lack of behavioral modification associated with typical déjà vu means that clinicians and experimenters rely heavily on self-report when observing the experience. In this review, we focus on recent déjà vu research. We consider issues facing neuropsychological, neuroscientific, and cognitive experimental frameworks attempting to explore and experimentally generate the experience. In doing this, we suggest the need for more experimentation and amore cautious interpretation of research findings, particularly as many techniques being used to explore déjà vu are in the early stages of development.PostprintPeer reviewe

Correlated Gravitational Wave and Neutrino Signals from General-Relativistic Rapidly Rotating Iron Core Collapse

We present results from a new set of 3D general-relativistic hydrodynamic simulations of rotating iron core collapse. We assume octant symmetry and focus on axisymmetric collapse, bounce, the early postbounce evolution, and the associated gravitational wave (GW) and neutrino signals. We employ a finite-temperature nuclear equation of state, parameterized electron capture in the collapse phase, and a multi-species neutrino leakage scheme after bounce. The latter captures the important effects of deleptonization, neutrino cooling and heating and enables approximate predictions for the neutrino luminosities in the early evolution after core bounce. We consider 12-solar-mass and 40-solar-mass presupernova models and systematically study the effects of (i) rotation, (ii) progenitor structure, and (iii) postbounce neutrino leakage on dynamics, GW, and, neutrino signals. We demonstrate, that the GW signal of rapidly rotating core collapse is practically independent of progenitor mass and precollapse structure. Moreover, we show that the effects of neutrino leakage on the GW signal are strong only in nonrotating or slowly rotating models in which GW emission is not dominated by inner core dynamics. In rapidly rotating cores, core bounce of the centrifugally-deformed inner core excites the fundamental quadrupole pulsation mode of the nascent protoneutron star. The ensuing global oscillations (f~700-800 Hz) lead to pronounced oscillations in the GW signal and correlated strong variations in the rising luminosities of antineutrino and heavy-lepton neutrinos. We find these features in cores that collapse to protoneutron stars with spin periods <~ 2.5 ms and rotational energies sufficient to drive hyper-energetic core-collapse supernova explosions. Hence, joint GW + neutrino observations of a core collapse event could deliver strong evidence for or against rapid core rotation. [abridged]Comment: 29 pages, 14 figures. Replaced with version matching published versio

Quantum State Reconstruction of Many Body System Based on Complete Set of Quantum Correlations Reduced by Symmetry

We propose and study a universal approach for the reconstruction of quantum states of many body systems from symmetry analysis. The concept of minimal complete set of quantum correlation functions (MCSQCF) is introduced to describe the state reconstruction. As an experimentally feasible physical object, the MCSQCF is mathematically defined through the minimal complete subspace of observables determined by the symmetry of quantum states under consideration. An example with broken symmetry is analyzed in detail to illustrate the idea.Comment: 10 pages, n figures, Revte

Matrix geometries and Matrix Models

We study a two parameter single trace 3-matrix model with SO(3) global symmetry. The model has two phases, a fuzzy sphere phase and a matrix phase. Configurations in the matrix phase are consistent with fluctuations around a background of commuting matrices whose eigenvalues are confined to the interior of a ball of radius R=2.0. We study the co-existence curve of the model and find evidence that it has two distinct portions one with a discontinuous internal energy yet critical fluctuations of the specific heat but only on the low temperature side of the transition and the other portion has a continuous internal energy with a discontinuous specific heat of finite jump. We study in detail the eigenvalue distributions of different observables.Comment: 20 page

Field evolution of the magnetic structures in Er2_2Ti2_2O7_7 through the critical point

We have measured neutron diffraction patterns in a single crystal sample of the pyrochlore compound Er$_2$Ti$_2$O$_7$ in the antiferromagnetic phase (T=0.3\,K), as a function of the magnetic field, up to 6\,T, applied along the [110] direction. We determine all the characteristics of the magnetic structure throughout the quantum critical point at $H_c$=2\,T. As a main result, all Er moments align along the field at $H_c$ and their values reach a minimum. Using a four-sublattice self-consistent calculation, we show that the evolution of the magnetic structure and the value of the critical field are rather well reproduced using the same anisotropic exchange tensor as that accounting for the local paramagnetic susceptibility. In contrast, an isotropic exchange tensor does not match the moment variations through the critical point. The model also accounts semi-quantitatively for other experimental data previously measured, such as the field dependence of the heat capacity, energy of the dispersionless inelastic modes and transition temperature.Comment: 7 pages; 8 figure

Geometry of the Grosse-Wulkenhaar Model

We define a two-dimensional noncommutative space as a limit of finite-matrix spaces which have space-time dimension three. We show that on such space the Grosse-Wulkenhaar (renormalizable) action has natural interpretation as the action for the scalar field coupled to the curvature. We also discuss a natural generalization to four dimensions.Comment: 16 pages, version accepted in JHE