Effects of symmetry breaking on spectra of chaotic Hamiltonian systems

Symmetry Breaking in Sticky Collisions between Ultracold Molecules

Ultracold molecules undergo "sticky collisions" that result in loss even for chemically nonreactive molecules. Sticking times can be enhanced by orders of magnitude by interactions that lead to nonconservation of nuclear spin or total angular momentum. We present a quantitative theory of the required strength of such symmetry-breaking interactions based on classical simulation of collision complexes. We find static electric fields as small as 10  V/cm can lead to nonconservation of angular momentum, while we find nuclear spin is conserved during collisions. We also compute loss of collision complexes due to spontaneous emission and absorption of black-body radiation, which are found to be slow.

Molecules and the Eigenstate Thermalization Hypothesis

We review a theory that predicts the onset of thermalization in a quantum mechanical coupled non-linear oscillator system, which models the vibrational degrees of freedom of a molecule. A system of N non-linear oscillators perturbed by cubic anharmonic interactions exhibits a many-body localization (MBL) transition in the vibrational state space (VSS) of the molecule. This transition can occur at rather high energy in a sizable molecule because the density of states coupled by cubic anharmonic terms scales as N³, in marked contrast to the total density of states, which scales as exp(aN), where a is a constant. The emergence of a MBL transition in the VSS is seen by analysis of a random matrix ensemble that captures the locality of coupling in the VSS, referred to as local random matrix theory (LRMT). Upon introducing higher order anharmonicity, the location of the MBL transition of even a sizable molecule, such as an organic molecule with tens of atoms, still lies at an energy that may exceed the energy to surmount a barrier to reaction, such as a barrier to conformational change. Illustrative calculations are provided, and some recent work on the influence of thermalization on thermal conduction in molecular junctions is also discussed.

Strength distributions and symmetry breaking in coupled microwave billiards

Flat microwave cavities can be used to experimentally simulate quantum mechanical systems. By coupling two such cavities, we study the equivalent to symmetry breaking in quantum mechanics. As the coupling is tunable, we can measure resonance strength distributions as a function of the symmetry breaking. We analyze the data by employing a qualitative model based on random matrix theory and show that the results derived from the strength distribution are consistent with those previously obtained from spectral statistics.

Quantum chaotic patterns in the E (b1 + b2) Jahn-Teller model

We study statistical properties of excited levels of the E (b(1) + b(2) Jahn-Teller model. The multitude of avoided crossings of energy levels is generally claimed to be a testimony of quantum chaos. We found that apart from two limiting cases (E e and Holstein model) the distribution of nearest-neighbor spacings is rather stable as to the change of parameters and different from the Wigner one. This limiting distribution assumably shows approximately radical S scaling at small and resembles the semi-Poisson law P(S) = 4S exp(-2S) at S > or = 1. The latter is believed to be universal and characteristic, e.g., at the transition between metal and insulator phases.

Energy localization in two chaotically coupled systems

We set up and analyze a random matrix model to study energy localization and its time behavior in two chaotically coupled systems. This investigation is prompted by a recent experimental and theoretical study of Weaver and Lobkis on coupled elastomechanical systems. Our random matrix model properly describes the main features of the findings by Weaver and Lobkis. Due to its general character, our model is also applicable to similar systems in other areas of physics--for example, to chaotically coupled quantum dots.

Phenomenological model for symmetry breaking in a chaotic system

We assume that the energy spectrum of a chaotic system undergoing symmetry-breaking transitions can be represented as a superposition of independent level sequences, one increasing at the expense of the others. The relation between the fractional level densities of the sequences and the symmetry-breaking interaction is deduced by comparing the asymptotic expression of the level-number variance with the corresponding expression obtained using the perturbation theory. This relation is supported by a comparison with previous numerical calculations. The predictions of the model for the nearest-neighbor-spacing distribution and the spectral rigidity are in agreement with the results of an acoustic resonance experiment.

Bayesian analysis of level-spacing distributions for chaotic systems with broken symmetry

Bayesian inference is applied to the nearest-neighbor and next-nearest-neighbor spacing distributions of levels of coupled superconducting microwave billiards. The weakly coupled resonators are equivalent to a quantum system with a partially broken symmetry. The coupling parameters are obtained with help from Bayes's theorem. This procedure does not require the introduction of a set of bins. The results are more accurate than those obtained from other bin-independent procedures.

Decoding the dynamical information embedded in highly mixed quantum states

The standard description of the vibrational and rotational motion of polyatomic molecules, as expressed by the distortable rotor/harmonic oscillator approximation, provides an adequate description of the molecular quantum states only in regions of low total state density. When the total state density is large, exceeding 100 states/cm(-1), the vibrational dynamics are "dissipative" and the fundamental process of intramolecular vibrational energy redistribution is operative. The presence of intramolecular vibrational energy redistribution leads to molecular quantum states of a qualitatively different nature. With respect to a normal-mode vibrational basis, these quantum states are "highly mixed" in their vibrational character and represent nuclear motion that is a combination of all the normal-mode motions. This review describes frequency domain spectroscopy techniques designed to probe the vibrational, rotational, and structural composition of these eigenstates. Recent work that investigates spectroscopy between highly mixed states is also reviewed.

Analyzing symmetry breaking within a chaotic quantum system via bayesian inference

Bayesian inference is applied to the level fluctuations of two coupled microwave billiards in order to extract the coupling strength. The coupled resonators provide a model of a chaotic quantum system containing two coupled symmetry classes of levels. The number variance is used to quantify the level fluctuations as a function of the coupling and to construct the conditional probability distribution of the data. The prior distribution of the coupling parameter is obtained from an invariance argument on the entropy of the posterior distribution.

Impact of isospin breaking on the distribution of transition probabilities

In the present paper we investigate the effect of symmetry breaking in the statistical distributions of reduced transition amplitudes and reduced transition probabilities. These quantities are easier to access experimentally than the components of the eigenvectors and were measured by Adams et al. [Phys. Lett. B 422, 13 (1998)] for the electromagnetic transitions in 26Al. We focus on isospin symmetry breaking described by a matrix model where both the Hamiltonian and the electromagnetic operator break the symmetry. The results show that for partial isospin conservation, the statistical distribution of the reduced transition probability can considerably deviate from the Porter-Thomas distribution.