Quantum multifractality as a probe of phase space in the Dicke model.

We study the multifractal behavior of coherent states projected in the energy eigenbasis of the spin-boson Dicke Hamiltonian, a paradigmatic model describing the collective interaction between a single bosonic mode and a set of two-level systems. By examining the linear approximation and parabolic correction to the mass exponents, we find ergodic and multifractal coherent states and show that they reflect details of the structure of the classical phase space, including chaos, regularity, and features of localization. The analysis of multifractality stands as a sensitive tool to detect changes and structures in phase space, complementary to classical tools to investigate it. We also address the difficulties involved in the multifractal analyses of systems with unbounded Hilbert spaces.

Quantum localization measures in phase space.

Measuring the degree of localization of quantum states in phase space is essential for the description of the dynamics and equilibration of quantum systems, but this topic is far from being understood. There is no unique way to measure localization, and individual measures can reflect different aspects of the same quantum state. Here we present a general scheme to define localization in measure spaces, which is based on what we call Rényi occupations, from which any measure of localization can be derived. We apply this scheme to the four-dimensional unbounded phase space of the interacting spin-boson Dicke model. In particular, we make a detailed comparison of two localization measures based on the Husimi function in the regime where the model is chaotic, namely, one that projects the Husimi function over the finite phase space of the spin and another that uses the Husimi function defined over classical energy shells. We elucidate the origin of their differences, showing that in unbounded spaces the definition of maximal delocalization requires a bounded reference subspace, with different selections leading to contextual answers.

Dynamical signatures of quantum chaos and relaxation time scales in a spin-boson system.

Quantum systems whose classical counterparts are chaotic typically have highly correlated eigenvalues and level statistics that coincide with those from ensembles of full random matrices. A dynamical manifestation of these correlations comes in the form of the so-called correlation hole, which is a dip below the saturation point of the survival probability's time evolution. In this work, we study the correlation hole in the spin-boson (Dicke) model, which presents a chaotic regime and can be realized in experiments with ultracold atoms and ion traps. We derive an analytical expression that describes the entire evolution of the survival probability and allows us to determine the time scales of its relaxation to equilibrium. This expression shows remarkable agreement with our numerical results. While the initial decay and the time to reach the minimum of the correlation hole depend on the initial state, the dynamics beyond the hole up to equilibration is universal. We find that the relaxation time of the survival probability for the Dicke model increases linearly with system size.

Classical chaos in atom-field systems.

The relation between the onset of chaos and critical phenomena, like quantum phase transitions (QPTs) and excited-state quantum phase transitions (ESQPTs), is analyzed for atom-field systems. While it has been speculated that the onset of hard chaos is associated with ESQPTs based in the resonant case, the off-resonant cases, and a close look at the vicinity of the QPTs in resonance, show clearly that both phenomena, ESQPTs and chaos, respond to different mechanisms. The results are supported in a detailed numerical study of the dynamics of the semiclassical Hamiltonian of the Dicke model. The appearance of chaos is quantified calculating the largest Lyapunov exponent for a wide sample of initial conditions in the whole available phase space for a given energy. The percentage of the available phase space with chaotic trajectories is evaluated as a function of energy and coupling between the qubit and bosonic part, allowing us to obtain maps in the space of coupling and energy, where ergodic properties are observed in the model. Different sets of Hamiltonian parameters are considered, including resonant and off-resonant cases.

Delocalization and quantum chaos in atom-field systems.

Employing efficient diagonalization techniques, we perform a detailed quantitative study of the regular and chaotic regions in phase space in the simplest nonintegrable atom-field system, the Dicke model. A close correlation between the classical Lyapunov exponents and the quantum Participation Ratio of coherent states on the eigenenergy basis is exhibited for different points in the phase space. It is also shown that the Participation Ratio scales linearly with the number of atoms in chaotic regions and with its square root in the regular ones.

Short-term adaptation to a simple motor task: a physiological process preserved in multiple sclerosis.

Short-term adaptation indicates the attenuation of the functional MRI (fMRI) response during repeated task execution. It is considered to be a physiological process, but it is unknown whether short-term adaptation changes significantly in patients with brain disorders, such as multiple sclerosis (MS). In order to investigate short-term adaptation during a repeated right-hand tapping task in both controls and in patients with MS, we analyzed the fMRI data collected in a large cohort of controls and MS patients who were recruited into a multi-centre European fMRI study. Four fMRI runs were acquired for each of the 55 controls and 56 MS patients at baseline and 33 controls and 26 MS patients at 1-year follow-up. The externally cued (1 Hz) right hand tapping movement was limited to 3 cm amplitude by using at all sites (7 at baseline and 6 at follow-up) identically manufactured wooden frames. No significant differences in cerebral activation were found between sites. Furthermore, our results showed linear response adaptation (i.e. reduced activation) from run 1 to run 4 (over a 25 minute period) in the primary motor area (contralateral more than ipsilateral), in the supplementary motor area and in the primary sensory cortex, sensory-motor cortex and cerebellum, bilaterally. This linear activation decay was the same in both control and patient groups, did not change between baseline and 1-year follow-up and was not influenced by the modest disease progression observed over 1 year. These findings confirm that the short-term adaptation to a simple motor task is a physiological process which is preserved in MS.

Detection of delayed focal MR changes in the lateral hippocampus in transient global amnesia.

BACKGROUND: There is still limited knowledge on the location and etiology of transient global amnesia (TGA). MR studies including diffusion-weighted imaging (DWI) have been unable to demonstrate consistently the location and underlying pathology of TGA. OBJECTIVE: To investigate patients with TGA using serial DWI performed from the day of symptom onset through days 1 and 2. METHODS: After reporting negative DWI results in a previous study, the authors used a modified study design to investigate patients with TGA using serial DWI performed from the day of symptom onset through days 1 and 2. RESULTS: Of 31 consecutive patients studied, 26 developed a small, punctate DWI lesion in the lateral aspect of the hippocampal formation (pes and fimbria hippocampi) on either side (left, n = 15; right, n = 6) or bilaterally (n = 5). Lesions were rarely noted in the hyperacute phase (n = 2), but all became visible regularly at 48 hours. CONCLUSIONS: The study confirms the involvement of hippocampal parenchyma in the pathophysiology of TGA. The delayed detectability of the lesions may explain the incongruence of previous MR DWI studies in TGA patients.

Clinicotopographical correlation of corticospinal tract stroke: a color-coded diffusion tensor imaging study.

UNLABELLED: Background- Small capsular strokes are difficult to assess with regard to the precise location and the extent of pyramidal tract damage with conventional brain imaging. Color-coded diffusion tensor imaging (CDTI) provides a means to visualize the course of the corticospinal tract within the white matter. In addition to T2-weighted MRI, diffusion-weighted MRI and CDTI were used to analyze the topographical patterns of small lacunar corticospinal tract strokes. METHODS: We examined 15 patients with pyramidal tract strokes in the subacute phase (days 3 to 7). Lesions were identified on diffusion-weighted MRI and superimposed on CDTI images. The anatomic location and pattern of the lesion were visualized on CDTI with regard to the corticospinal tract and subsequently compared with the clinical presentation. In addition, infarct areas were evaluated with quantitative parameters: mean diffusivity and lattice anisotropy index of lesions were determined. RESULTS: We identified 5 different patterns of corticospinal tract stroke falling into 2 clinical subgroups: (1) those with marked deficits and minor improvement (6/15) and (2) those with good recovery (9/15). Group 1 had long lesions centered in the pyramidal tract, involving the basal ganglia (anterior choroidal artery); group 2 lesions were very small and/or located anteriorly and medially (periventricular anterior choroidal artery territory; thalamogeniculate, tuberothalamic, and lateral striate branches). Lesions showed a significant increase of mean diffusivity and decrease of lattice anisotropy. CONCLUSIONS: CDTI allows in vivo differentiation of distinct subcortical stroke subtypes. Improved anatomic definition of lesion localization using CDTI may help in better establishing the prognosis for patients after subcortical stroke.

[Diffusion tensor imaging (DTI) and functional magnetic resonance tomography (fMRI) expand methodological spectrum in psychiatric research]. / Diffusions-Tensor-Bildgebung (DTI) und funktionelle Magnetresonanztomographie (fMRI) erweitern das Methodenspektrum in der psychiatrischen Forschung.

In psychiatric research, there is a growing interest in the microstructural and functional characteristics of brain networks, which often form the basis of current etiological concepts. As a result of novel magnetic resonance imaging techniques, the pathogenic characteristics of neuronal activity and connectivity can be examined in a noninvasive, safe, and repeatable manner. Functional magnetic resonance imaging (fMRI) uses blood oxygenation level-dependent (BOLD) measures for identifying the gray matter contribution to cognition. Diffusion tensor imaging (DTI) reveals the course and structural integrity of white matter projections. Because DTI does not require special motivation and performance, group differences in psychiatry are more easily interpreted in terms of underlying pathology. To date few studies have tried to investigate both, i.e. dynamic and microstructural data in the sense of a modern multi-dimensional investigation approach. The combination of both techniques, however, seems to offer a promising vehicle to further extent our current understanding of mental disorders and to identify populations at risk. In addition to addressing findings in psychiatric research, the present article presents a technical overview of DTI and examines the limitations and potential applications of both techniques.

Acute and chronic changes of the apparent diffusion coefficient in neurological disorders--biophysical mechanisms and possible underlying histopathology.

Diffusion-weighted imaging (DWI) of the brain has become a valuable tool for the reliable detection and diagnosis of several neurological disorders. Although DWI is in wide use in daily practice, the underlying biophysical mechanisms that contribute to changes in the apparent diffusion coefficient (ADC) are still under discussion. Alterations in the apparent water diffusion rate reflect pathological changes in the brain tissue state, via changes in the diffusion characteristics of the intra- and extra-cellular water compartments including restricted diffusion, water exchange across permeable boundaries, the concept of the extra-cellular tortuosity and the intra- and extra-cellular volume fraction. A reduction of the ADC has been detected in acute neurological diseases, while disease states associated with dominant acute vasogenic edema formation or chronic tissue destruction usually show elevations of the ADC. Compromise of energy metabolism is likely to contribute to a reduction of the ADC while already minor structural disintegration may contribute to elevations of the ADC.

Failure to demonstrate peri-infarct depolarizations by repetitive MR diffusion imaging in acute human stroke.

BACKGROUND AND PURPOSE: Peri-infarct depolarizations (PIDs) have been demonstrated with diffusion-weighted MRI (DWI) in experimental stroke and are regarded as an important mechanism of ischemic injury. We tested the hypothesis that PIDs are of relevance for the early enlargement of human brain infarcts. METHODS: Ten stroke patients were investigated by repetitive imaging of the apparent diffusion coefficient (ADC) in the acute phase (7 patients) or subacute phase (3 patients) of developing cortical infarction. In each patient, 20 ADC maps were obtained from serially measured echo-planar DWI (interval of 45 seconds). Data analysis focused on the potential spatial and temporal ADC changes, including structured qualitative analysis, calculation of subtraction images, serial analysis of regions of interest positioned in the infarct core and border, and calculation of hemispheric lesion areas, depending on various ADC thresholds ranging between 0 and 800 microm(2)/s. RESULTS: Data analysis was unable to disclose any time-dependent changes in ADC that would resemble PID. In ischemic regions, the ADC reduction significantly progressed from the infarct border (555+/-96 microm(2)/s) to the infarct core (431+/-104 microm(2)/s, P:<0.01). CONCLUSIONS: By using an MRI protocol with high temporal resolution and elaborated postprocessing, we were unable to demonstrate a pattern of diffusion changes that would be indicative of PID in human stroke. Experimental infarction and human stroke may differ in the detectability of PID.

Comparison of diffusion anisotropy measurements in combination with the flair-technique.

Fluid-attenuated inversion recovery (FLAIR) technique offers an effective tool to diminish partial-volume averaging effects from cerebrospinal (CSF) signal with in vivo magnetic resonance imaging. CSF-suppressed and unsuppressed direction-dependent diffusion-weighted (DW) images are obtained with a DW spin-echo EPI sequence in a single acquisition scheme. Comparison of unsuppressed and CSF-suppressed apparent diffusion coefficient (ADC) maps yields consistent values for brain tissue in volunteers when no partial-volume effects are expected, but differs considerably at borders of parenchyma to ventricles and sulci. From theory and phantom studies, a corrected anisotropy index is introduced considering differences of statistical fit errors. Anisotropy of white matter is observed in normal brain of volunteers. Anisotropy index maps reveal destruction of fiber tracts in pathologic areas. Results of a preliminary study on 12 patients with intra-axial tumors indicate an improved delineation of tumor boundaries of FLAIR ADC maps against unsuppressed acquisition.

Suicide and violence prevention: parent education in the emergency department.

OBJECTIVE: To determine prospectively whether parental receipt of injury prevention education is associated with new action limiting access to lethal means and if so, what action was taken for which means. METHOD: Prospective follow-up of 103 adults whose children made an emergency department visit for mental health assessment or treatment. Record review assessed whether hospital staff provided injury prevention education. Logistic regression was used to determine the likelihood of new caretaker action limiting access to the following potentially lethal means: firearms, alcohol, prescription medications, and over-the-counter medications. RESULTS: Significant associations were found between exposure to injury prevention education and action to limit access (adjusted odds ratio = 3.6, 95% confidence interval = 1.1-12.1, p = .04). Five of 8 adults whose households contained firearms took new action to limit access after injury prevention education, whereas none of the 7 firearm-owning families who did not receive injury prevention education took new action to limit firearm access. Similar patterns were seen for other means. Adults more often chose to lock up rather than dispose of lethal means. CONCLUSIONS: Injury prevention education should be provided to parents during child/adolescent emergency department mental health-related visits. Potential for violence prevention is real because parents do take new action to limit access to lethal means when means restriction education is provided.

Understanding the adolescent patient.

The chapter has presented a frame of reference with which to approach adolescent patients with skin disease. To be most effective, the physician must understand the complexities of adolescent development and the various biological, social, and psychological circumstances and reactions with which young people must cope. Suggestions are made regarding approaches to the management of the adolescent skin patient, in the wish to maximize the usefulness of the physician--patient relationship as a resource for helping young people to health and happiness.