Heat Transport in Mesoscopic Systems

Phonon heat transport in mesoscopic systems is investigated using methods analogous to the Landauer description of electrical conductance. A "universal heat conductance" expression that depends on the properties of the conducting pathway only through the mode cutoff frequencies is derived. Corrections due to reflections at the junction between the thermal body and the conducting bridge are found to be small except at very low temperatures where only the lowest few bridge modes are excited. Various non-equilibrium phonon distributions are studied: a narrow band distribution leads to clear steps in the cooling curve, analogous to the quantized resistance values in narrow wires, but a thermal distribution is too broad to show such features.Comment: To be published in Superlattices and Microstructures, special issue in honor of Rolf Landauer, March 198

Low-temperature heat transfer in nanowires

The new regime of low-temperature heat transfer in suspended nanowires is predicted. It takes place when (i) only ``acoustic'' phonon modes of the wire are thermally populated and (ii) phonons are subject to the effective elastic scattering. Qualitatively, the main peculiarities of heat transfer originate due to appearance of the flexural modes with high density of states in the wire phonon spectrum. They give rise to the $T^{1/2}$ temperature dependence of the wire thermal conductance. The experimental situations where the new regime is likely to be detected are discussed.Comment: RevTex file, 1 PS figur

Self-esteem depends on beliefs about the rate of change of social approval

A major challenge in understanding the neurobiological basis of psychiatric disorders is rigorously quantifying subjective metrics that lie at the core of mental illness, such as low self-esteem. Self-esteem can be conceptualized as a ‘gauge of social approval’ that increases in response to approval and decreases in response to disapproval. Computational studies have shown that learning signals that represent the difference between received and expected social approval drive changes in self-esteem. However, it is unclear whether self-esteem based on social approval should be understood as a value updated through associative learning, or as a belief about approval, updated by new evidence depending on how strongly it is held. Our results show that belief-based models explain self-esteem dynamics in response to social evaluation better than associative learning models. Importantly, they suggest that in the short term, self-esteem signals the direction and rate of change of one’s beliefs about approval within a group, rather than one’s social position

Diamagnetism of quantum gases with singular potentials

We consider a gas of quasi-free quantum particles confined to a finite box, subjected to singular magnetic and electric fields. We prove in great generality that the finite volume grand-canonical pressure is jointly analytic in the chemical potential ant the intensity of the external magnetic field. We also discuss the thermodynamic limit

Effect of phonon scattering by surface roughness on the universal thermal conductance

The effect of phonon scattering by surface roughness on the thermal conductance in mesoscopic systems at low temperatures is calculated using full elasticity theory. The low frequency behavior of the scattering shows novel power law dependences arising from the unusual properties of the elastic modes. This leads to new predictions for the low temperature depression of the thermal conductance below the ideal universal value. Comparison with the data of Schwab et al. [Nature 404, 974 (2000)] suggests that surface roughness on a scale of the width of the thermal pathway is important in the experiment.Comment: 6 pages, 3 figure

Large deviations for ideal quantum systems

We consider a general d-dimensional quantum system of non-interacting particles, with suitable statistics, in a very large (formally infinite) container. We prove that, in equilibrium, the fluctuations in the density of particles in a subdomain of the container are described by a large deviation function related to the pressure of the system. That is, untypical densities occur with a probability exponentially small in the volume of the subdomain, with the coefficient in the exponent given by the appropriate thermodynamic potential. Furthermore, small fluctuations satisfy the central limit theorem.Comment: 28 pages, LaTeX 2

Elastic Wave Transmission at an Abrupt Junction in a Thin Plate, with Application to Heat Transport and Vibrations in Mesoscopic Systems

The transmission coefficient for vibrational waves crossing an abrupt junction between two thin elastic plates of different widths is calculated. These calculations are relevant to ballistic phonon thermal transport at low temperatures in mesoscopic systems and the Q for vibrations in mesoscopic oscillators. Complete results are calculated in a simple scalar model of the elastic waves, and results for long wavelength modes are calculated using the full elasticity theory calculation. We suggest that thin plate elasticty theory provide a useful and tractable approximation to the full three dimensional geometry.Comment: 35 pages, including 12 figure

Lower Spectral Branches of a Particle Coupled to a Bose Field

The structure of the lower part (i.e. $\epsilon$-away below the two-boson threshold) spectrum of Fr\"ohlich's polaron Hamiltonian in the weak coupling regime is obtained in spatial dimension $d\geq 3$. It contains a single polaron branch defined for total momentum $p\in G^{(0)}$, where $G^{(0)}\subset {\mathbb R}^d$ is a bounded domain, and, for any $p\in {\mathbb R}^d$, a manifold of polaron + one-boson states with boson momentum $q$ in a bounded domain depending on $p$. The polaron becomes unstable and dissolves into the one boson manifold at the boundary of $G^{(0)}$. The dispersion laws and generalized eigenfunctions are calculated

Self-esteem depends on beliefs about the rate of change of social approval

A major challenge in understanding the neurobiological basis of psychiatric disorders is rigorously quantifying subjective metrics that lie at the core of mental illness, such as low self-esteem. Self-esteem can be conceptualized as a ‘gauge of social approval’ that increases in response to approval and decreases in response to disapproval. Computational studies have shown that learning signals that represent the difference between received and expected social approval drive changes in self-esteem. However, it is unclear whether self-esteem based on social approval should be understood as a value updated through associative learning, or as a belief about approval, updated by new evidence depending on how strongly it is held. Our results show that belief-based models explain self-esteem dynamics in response to social evaluation better than associative learning models. Importantly, they suggest that in the short term, self-esteem signals the direction and rate of change of one’s beliefs about approval within a group, rather than one’s social position