Exact Coupling Coefficient Distribution in the Doorway Mechanism

In many--body and other systems, the physics situation often allows one to interpret certain, distinct states by means of a simple picture. In this interpretation, the distinct states are not eigenstates of the full Hamiltonian. Hence, there is an interaction which makes the distinct states act as doorways into background states which are modeled statistically. The crucial quantities are the overlaps between the eigenstates of the full Hamiltonian and the doorway states, that is, the coupling coefficients occuring in the expansion of true eigenstates in the simple model basis. Recently, the distribution of the maximum coupling coefficients was introduced as a new, highly sensitive statistical observable. In the particularly important regime of weak interactions, this distribution is very well approximated by the fidelity distribution, defined as the distribution of the overlap between the doorway states with interaction and without interaction. Using a random matrix model, we calculate the latter distribution exactly for regular and chaotic background states in the cases of preserved and fully broken time--reversal invariance. We also perform numerical simulations and find excellent agreement with our analytical results.Comment: 22 pages, 4 figure

Ballistic Electron Quantum Transport in Presence of a Disordered Background

Effect of a complicated many-body environment is analyzed on the electron random scattering by a 2D mesoscopic open ballistic structure. A new mechanism of decoherence is proposed. The temperature of the environment is supposed to be zero whereas the energy of the incoming particle $E_{in}$ can be close to or somewhat above the Fermi surface in the environment. The single-particle doorway resonance states excited in the structure via external channels are damped not only because of escape through such channels but also due to the ulterior population of the long-lived environmental states. Transmission of an electron with a given incoming $E_{in}$ through the structure turns out to be an incoherent sum of the flow formed by the interfering damped doorway resonances and the retarded flow of the particles re-emitted into the structure by the environment. Though the number of the particles is conserved in each individual event of transmission, there exists a probability that some part of the electron's energy can be absorbed due to environmental many-body effects. In such a case the electron can disappear from the resonance energy interval and elude observation at the fixed transmission energy $E_{in}$ thus resulting in seeming loss of particles, violation of the time reversal symmetry and, as a consequence, suppression of the weak localization. The both decoherence and absorption phenomena are treated within the framework of a unit microscopic model based on the general theory of the resonance scattering. All the effects discussed are controlled by the only parameter: the spreading width of the doorway resonances, that uniquely determines the decoherence rateComment: 7 pages, 1 figure. The published version. A figure has been added; the list of references has been improved. Some explanatory remarks have been include

Group Mutual Exclusion in Linear Time and Space

We present two algorithms for the Group Mutual Exclusion (GME) Problem that satisfy the properties of Mutual Exclusion, Starvation Freedom, Bounded Exit, Concurrent Entry and First Come First Served. Both our algorithms use only simple read and write instructions, have O(N) Shared Space complexity and O(N) Remote Memory Reference (RMR) complexity in the Cache Coherency (CC) model. Our first algorithm is developed by generalizing the well-known Lamport's Bakery Algorithm for the classical mutual exclusion problem, while preserving its simplicity and elegance. However, it uses unbounded shared registers. Our second algorithm uses only bounded registers and is developed by generalizing Taubenfeld's Black and White Bakery Algorithm to solve the classical mutual exclusion problem using only bounded shared registers. We show that contrary to common perception our algorithms are the first to achieve these properties with these combination of complexities.Comment: A total of 21 pages including 5 figures and 3 appendices. The bounded shared registers algorithm in the old version has a subtle error (that has no easy fix) necessitating replacement. A correct, but fundamentally different, bounded shared registers algorithm, which has the same properties claimed in the old version is presented in this new version. Also, this version has an additional autho

Accelerating Reinforcement Learning by Composing Solutions of Automatically Identified Subtasks

This paper discusses a system that accelerates reinforcement learning by using transfer from related tasks. Without such transfer, even if two tasks are very similar at some abstract level, an extensive re-learning effort is required. The system achieves much of its power by transferring parts of previously learned solutions rather than a single complete solution. The system exploits strong features in the multi-dimensional function produced by reinforcement learning in solving a particular task. These features are stable and easy to recognize early in the learning process. They generate a partitioning of the state space and thus the function. The partition is represented as a graph. This is used to index and compose functions stored in a case base to form a close approximation to the solution of the new task. Experiments demonstrate that function composition often produces more than an order of magnitude increase in learning rate compared to a basic reinforcement learning algorithm

A Dynamic Localized Adjustable Force Field Method for Real-time Assistive Non-holonomic Mobile Robotics

Providing an assistive navigation system that augments rather than usurps user control of a powered wheelchair represents a significant technical challenge. This paper evaluates an assistive collision avoidance method for a powered wheelchair that allows the user to navigate safely whilst maintaining their overall governance of the platform motion. The paper shows that by shaping, switching and adjusting localized potential fields we are able to negotiate different obstacles by generating a more intuitively natural trajectory, one that does not deviate significantly from the operator in the loop desired-trajectory. It can also be seen that this method does not suffer from the local minima problem, or narrow corridor and proximity oscillation, which are common problems that occur when using potential fields. Furthermore this localized method enables the robotic platform to pass very close to obstacles, such as when negotiating a narrow passage or doorway

Doorway states in nuclear reactions as a manifestation of the "super-radiant" mechanism

A mechanism is considered for generating doorway states and intermediate structure in low-energy nuclear reactions as a result of collectivization of widths of unstable intrinsic states coupled to common decay channels. At the limit of strong continuum coupling, the segregation of broad (''super-radiating") and narrow (''trapped") states occurs revealing the separation of direct and compound processes. We discuss the conditions for the appearance of intermediate structure in this process and doorways related to certain decay channels.Comment: 16 page

Super-Radiant Dynamics, Doorways, and Resonances in Nuclei and Other Open Mesoscopic Systems

The phenomenon of super-radiance (Dicke effect, coherent spontaneous radiation by a gas of atoms coupled through the common radiation field) is well known in quantum optics. The review discusses similar physics that emerges in open and marginally stable quantum many-body systems. In the presence of open decay channels, the intrinsic states are coupled through the continuum. At sufficiently strong continuum coupling, the spectrum of resonances undergoes the restructuring with segregation of very broad super-radiant states and trapping of remaining long-lived compound states. The appropriate formalism describing this phenomenon is based on the Feshbach projection method and effective non-Hermitian Hamiltonian. A broader generalization is related to the idea of doorway states connecting quantum states of different structure. The method is explained in detail and the examples of applications are given to nuclear, atomic and particle physics. The interrelation of the collective dynamics through continuum and possible intrinsic many-body chaos is studied, including universal mesoscopic conductance fluctuations. The theory serves as a natural framework for general description of a quantum signal transmission through an open mesoscopic system.Comment: 85 pages, 10 figure

Freezing of Gait in Parkinson’s Disease: A Perceptual Cuase for a Motor Impairment?

While freezing of gait (FOG) is typically considered a motor impairment, the fact that it occurs more frequently in confined spaces suggests that perception of space might contribute to FOG. The present study evaluated how doorway size influenced characteristics of gait that might be indicative of freezing. Changes in spatiotemporal aspects of gait were evaluated while walking through three different-sized doorways (narrow (0.675 m wide X 2.1 m high), normal (0.9 m wide X 2.1 m high) and wide (1.8 m wide X 2.1 m high)) in three separate groups: 15 individuals with Parkinson’s disease confirmed to be experiencing FOG at the time of test; 16 non-FOG individuals with Parkinson’s disease and 16 healthy age-matched control participants. Results for step length indicated that the FOG group was most affected by the narrow doorway and was the only group whose step length was dependent on upcoming doorway size as indicated by a significant interaction of group by condition (F(4,88)=2.73, p\u3c0.034). Importantly, the FOG group also displayed increased within-trial variability of step length and step time, which was exaggerated as doorway size decreased (F(4,88)=2.99, p\u3c0.023). A significant interaction between group and condition for base of support measures indicated that the non-FOG participants were also affected by doorway size (similar to Parkinson’s disease FOG) but only in the narrow doorway condition. These results support the notion that some occurrences of freezing may be the result of an underlying perceptual mechanism that interferes with online movement planning