The Fundamental Concepts of Classical Equilibrium Statistical Mechanics

A critical examination of some basic conceptual issues in classical statistical mechanics is attempted, with a view to understanding the origins, structure and statuts of that discipline. Due attention is given to the interplay between physical and mathematical aspects, particularly regarding the role of probability theory. The focus is on the equilibrium case, which is currently better understood, serving also as a prelude for a further discussion of non-equilibrium statistical mechanics.Comment: 33 pages, overview, conceptual discussio

Solid immersion lens at the aplanatic condition for enhancing the spectral bandwidth of a waveguide grating coupler

We report a technique to substantially boost the spectral bandwidth of a conventional waveguide grating coupler by using a solid immersion cylindrical lens at the aplanatic condition to create a highly anamorphic beam and reach a much larger numerical aperture, thus enhancing the spectral bandwidth of a free-space propagating optical beam coupled into a single-mode planar integrated optical waveguide (IOW). Our experimental results show that the broadband IOW spectrometer thus created almost doubles (94% enhancement) the coupled spectral bandwidth of a conventional configuration. To exemplify the benefits made possible by the developed approach, we applied the technique to the broadband spectroscopic characterization of a protein submonolayer; our experimental data confirm the enhanced spectral bandwidth (around 380–nm) and illustrate the potentials of the developed technology. Besides the enhanced bandwidth, the broadband coupler of the single-mode IOW spectrometer described here is more robust and user-friendly than those previously reported in the literature and is expected to have an important impact on spectroscopic studies of surface-adsorbed molecular layers and surface phenomena

Heat fluctuations for harmonic oscillators

Heat fluctuations of a harmonic oscillator in contact with a thermostat and driven out of equilibrium by an external deterministic force are studied experimentally and theoretically within the context of Fluctuation Theorems. We consider the case of a periodic forcing of the oscillator, and we calculate the analytic probability density function of heat fluctuations. The limit of large time is discussed and we show that heat fluctuations satisfy the conventional fluctuation theorem, even if a different fluctuation relation exists for this quantity. Experimental results are also given for a transient state.Comment: Submitted to Europhysics Letter

Quasi-ballistic, nonequilibrium electron distribution in inhomogeneous semiconductor structures

We report on a study of quasi-ballistic transport in deep submicron, inhomogeneous semiconductor structures, focusing on the analysis of signatures found in the full nonequilibrium electron distribution. We perform self-consistent numerical calculations of the Poisson-Boltzmann equations for a model n(+)-n(-)-n(+) GaAs structure and realistic, energy-dependent scattering. We show that, in general, the electron distribution displays significant, temperature dependent broadening and pronounced structure in the high-velocity tail of the distribution. The observed characteristics have a strong spatial dependence, related to the energy-dependence of the scattering, and the large inhomogeneous electric field variations in these systems. We show that in this quasi-ballistic regime, the high-velocity tail structure is due to pure ballistic transport, whereas the strong broadening is due to electron scattering within the channel, and at the source(drain) interfaces.Comment: 4 pages, 2 figure

On the Limited Communication Analysis and Design for Decentralized Estimation

This paper pertains to the analysis and design of decentralized estimation schemes that make use of limited communication. Briefly, these schemes equip the sensors with scalar states that iteratively merge the measurements and the state of other sensors to be used for state estimation. Contrarily to commonly used distributed estimation schemes, the only information being exchanged are scalars, there is only one common time-scale for communication and estimation, and the retrieval of the state of the system and sensors is achieved in finite-time. We extend previous work to a more general setup and provide necessary and sufficient conditions required for the communication between the sensors that enable the use of limited communication decentralized estimation~schemes. Additionally, we discuss the cases where the sensors are memoryless, and where the sensors might not have the capacity to discern the contributions of other sensors. Based on these conditions and the fact that communication channels incur a cost, we cast the problem of finding the minimum cost communication graph that enables limited communication decentralized estimation schemes as an integer programming problem.Comment: Updates on the paper in CDC 201

Decentralized Observability with Limited Communication between Sensors

In this paper, we study the problem of jointly retrieving the state of a dynamical system, as well as the state of the sensors deployed to estimate it. We assume that the sensors possess a simple computational unit that is capable of performing simple operations, such as retaining the current state and model of the system in its memory. We assume the system to be observable (given all the measurements of the sensors), and we ask whether each sub-collection of sensors can retrieve the state of the underlying physical system, as well as the state of the remaining sensors. To this end, we consider communication between neighboring sensors, whose adjacency is captured by a communication graph. We then propose a linear update strategy that encodes the sensor measurements as states in an augmented state space, with which we provide the solution to the problem of retrieving the system and sensor states. The present paper contains three main contributions. First, we provide necessary and sufficient conditions to ensure observability of the system and sensor states from any sensor. Second, we address the problem of adding communication between sensors when the necessary and sufficient conditions are not satisfied, and devise a strategy to this end. Third, we extend the former case to include different costs of communication between sensors. Finally, the concepts defined and the method proposed are used to assess the state of an example of approximate structural brain dynamics through linearized measurements.Comment: 15 pages, 5 figures, extended version of paper accepted at IEEE Conference on Decision and Control 201