Elementary solution to the time-independent quantum navigation problem

A quantum navigation problem concerns the identification of a time-optimal Hamiltonian that realizes a required quantum process or task, under the influence of a prevailing ‘background’ Hamiltonian that cannot be manipulated. When the task is to transform one quantum state into another, finding the solution in closed form to the problem is nontrivial even in the case of timeindependent Hamiltonians. An elementary solution, based on trigonometric analysis, is found here when the Hilbert space dimension is two. Difficulties arising from generalizations to higher-dimensional systems are discussed

Random Hamiltonian in thermal equilibrium

A framework for the investigation of disordered quantum systems in thermal equilibrium is proposed. The approach is based on a dynamical model--which consists of a combination of a double-bracket gradient flow and a uniform Brownian fluctuation--that `equilibrates' the Hamiltonian into a canonical distribution. The resulting equilibrium state is used to calculate quenched and annealed averages of quantum observables.Comment: 8 pages, 4 figures. To appear in DICE 2008 conference proceeding

A Riemannian approach to randers geodesics

In certain circumstances tools of Riemannian geometry are sufficient to address questions arising in the more general Finslerian context. We show that one such instance presents itself in the characterisation of geodesics in Randers spaces of constant flag curvature. To achieve a simple, Riemannian derivation of this special family of curves, we exploit the connection between Randers spaces and the Zermelo problem of time-optimal navigation in the presence of background fields. The characterisation of geodesics is then proven by generalising an intuitive argument developed recently for the solution of the quantum Zermelo problem

Hamiltonian statistical mechanics

A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward those of the reference Hamiltonian. The nonlinear double-bracket equation governing the flow is such that the eigenvalues of the initial Hamiltonian remain unperturbed. The space of Hamiltonians is foliated by compact invariant subspaces, which permits the construction of statistical distributions over the Hamiltonians. In two dimensions, an explicit dynamical model is introduced, wherein the density function on the space of Hamiltonians approaches an equilibrium state characterised by the canonical ensemble. This is used to compute quenched and annealed averages of quantum observables.Comment: 8 pages, 2 figures, references adde

Muscle Activity During the Star Excursion Balance Test in Healthy Adults

Purpose: To determine electromyographic (EMG) activity of the hip and the trunk muscles during the Star Excursion Balance Test (SEBT) performance in 8 reach directions

Hip and Trunk Muscle Activity During the Star Excursion Balance Test in Healthy Adults

CONTEXT: Dynamic balance is a measure of core stability. Deficits in the dynamic balance have been related to injuries in the athletic populations. The Star Excursion Balance Test (SEBT) is suggested to measure and improve dynamic balance when used as a rehabilitative tool. OBJECTIVE: To determine the electromyographic activity of the hip and the trunk muscles during the SEBT. DESIGN: Descriptive. SETTING: University campus. PARTICIPANTS: Twenty-two healthy adults (11 males and 11 females; 23.3 [3.8] y, 170.3 [7.6] cm, 67.8 [10.3] kg, and 15.1% [5.0%] body fat). INTERVENTION: Surface electromyographic data were collected on 22 healthy adults of the erector spinae, external oblique, and rectus abdominis bilaterally, and gluteus medius and gluteus maximus muscle of the stance leg. A 2-way repeated measures analysis of variance was used to determine the interaction between the percentage maximal voluntary isometric contraction (%MVIC) and the reach directions. The %MVIC for each muscle was compared across the 8 reach directions using the Sidak post hoc test with α at .05. MAIN OUTCOME MEASURES: %MVIC. RESULTS: Significant differences were observed for all the 8 muscles. Highest electromyographic activity was found for the tested muscles in the following reach directions-ipsilateral external oblique (44.5% [38.4%]): anterolateral; contralateral external oblique (52.3% [40.8%]): medial; ipsilateral rectus abdominis (8% [6.6%]): anterior; contralateral rectus abdominis (8% [5.3%]): anteromedial; ipsilateral erector spinae (46.4% [20.2%]): posterolateral; contralateral erector spinae (33.5% [11.3%]): posteromedial; gluteus maximus (27.4% [11.7%]): posterior; and gluteus medius (54.6% [26.1%]): medial direction. CONCLUSIONS: Trunk and hip muscle activation was direction dependent during the SEBT. This information can be used during rehabilitation of the hip and the trunk muscles

A new theoretical framework jointly explains behavioral and neural variability across subjects performing flexible decision-making

The ability to flexibly select and accumulate relevant information to form decisions, while ignoring irrelevant information, is a fundamental component of higher cognition. Yet its neural mechanisms remain unclear. Here we demonstrate that, under assumptions supported by both monkey and rat data, the space of possible network mechanisms to implement this ability is spanned by the combination of three different components, each with specific behavioral and anatomical implications. We further show that existing electrophysiological and modeling data are compatible with the full variety of possible combinations of these components, suggesting that different individuals could use different component combinations. To study variations across subjects, we developed a rat task requiring context-dependent evidence accumulation, and trained many subjects on it. Our task delivers sensory evidence through pulses that have random but precisely known timing, providing high statistical power to characterize each individual’s neural and behavioral responses. Consistent with theoretical predictions, neural and behavioral analysis revealed remarkable heterogeneity across rats, despite uniformly good task performance. The theory further predicts a specific link between behavioral and neural signatures, which was robustly supported in the data. Our results provide a new experimentally-supported theoretical framework to analyze biological and artificial systems performing flexible decision-making tasks, and open the door to the study of individual variability in neural computations underlying higher cognition