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A new method for investigating quantum confinement effects in MOSFETs is presented. The method is based on the numerical solution of the Schrödinger and Boltzmann system of equations. A quantum Boltzmann equation is developed by replacing the classical potential with a quantum potential. The technique naturally accounts for highly nonequilibrium effects including velocity overshoot. The subbands are calculated and then populated using nonequilibrium statistics. Modeling results show the electron concentration and electron current density peaks shifted away from the interface. Calculations show reduced channel concentration which leads to lower drain current for the quantum case. A quantum distribution function is obtained.

The recent stimulating proposal of a "Gauge Theory of Finance" by Ilinsky et al. is connected here with traditional approaches. First, the derivation of the log-normal distribution is shown to be equivalent both in information and mathematical content to the simpler and well-known derivation, dating back from Bachelier and Samuelson. Similarly, the re-derivation of Black–Scholes equation is shown equivalent to the standard one because the limit of no uncertainty is equivalent to the standard risk-free replication argument. Both re-derivations of the log-normality and Black–Scholes result do not provide a test of the theory because it is not uniquely specified in the limits where these results apply. Third, the choice of the exponential form a la Boltzmann, of the weight of a given market configuration, is a key postulate that requires justification. In addition, the "Gauge Theory of Finance" seems to lead to "virtual" arbitrage opportunities for a pure Markov random walk market when there should be none. These remarks are offered in the hope to improve the formulation of the "Gauge Theory of Finance" into a coherent and useful framework.

We present a brief review to our recent study concerning dynamic spin transport induced by AC-biased gate in low-dimensional semiconductor systems, in which dynamic spin-orbit interaction plays a crucial role. We construct a Boltzmann spin-transport model and a spin-drift-diffusion model to describe the time-dependent spin transport starting with the framework of Keldysh formalism. Methods for the generation and direct detection of spin current are proposed without optical and magnetic mediators.

In [C. G. Weaver Found. Phys. 51, 1 (2021)], I showed that Boltzmann’s H-theorem does not face a significant threat from the reversibility paradox. I argue that my defense of the H-theorem against that paradox can be used yet again for the purposes of resolving the recurrence paradox without having to endorse heavy-duty statistical assumptions outside of the hypothesis of molecular chaos. As in [C. G. Weaver Found. Phys. 51, 1 (2021)], lessons from the history and foundations of physics reveal precisely how such resolution is achieved.

We investigate higher order entropies for compressible fluid models and related a priori estimates. Higher order entropies are kinetic entropy estimators suggested by Enskog expansion of Boltzmann entropy. These quantities are quadratic in the density ρ, velocity v, and temperature T renormalized derivatives. We investigate governing equations of higher order entropy correctors and related differential inequalities in the natural situation where the volume viscosity, the shear viscosity, and the thermal conductivity depend on temperature, essentially in the form T^ϰ, as given by the kinetic theory of gases. Entropic inequalities are established when ‖log ρ‖_BMO, , ‖log T‖_BMO, ‖h∂_x ρ/ρ ‖_L^∞, , ‖ h∂_xT/T‖_L^∞, and are small enough, where is a weight associated with the dependence of the local mean free path on density and temperature. As an example of application, we investigate global existence of solutions when the initial values log(ρ₀/ρ_∞), , and log(T₀/T_∞) are small enough in appropriate spaces.

Sprays are complex flows made of liquid droplets surrounded by a gas. The aim of this paper is to study the local in time well-posedness of a collisional thin spray model, that is a coupling between Euler equations for a perfect gas and a Vlasov–Boltzmann equation for the droplets. We prove the existence and uniqueness of (local in time) solutions for this problem as soon as initial data are smooth enough.

A new method for investigating quantum confinement effects in MOSFETs is presented. The method is based on the numerical solution of the SchrÖdinger and Boltzmann system of equations. A quantum Boltzmann equation is developed by replacing the classical potential with a quantum potential. The technique naturally accounts for highly nonequilibrium effects including velocity overshoot. The subbands are calculated and then populated using nonequilibrium statistics. Modeling results show the electron concentration and electron current density peaks shifted away from the interface. Calculations show reduced channel concentration which leads to lower drain current for the quantum case. A quantum distribution function is obtained.

Having long been the realm of molecular chemistry, astronomy, and plasma diagnostics, the upper millimeter-wave band (∼100 to 300 GHz) and the THz region above it have recently become the subject of heightened activity in the engineering community because of exciting new technology (e.g., sub-picosecond optoelectronics) and promising new “terrestrial” applications (e.g., counter-terrorism and medical imaging). The most challenging of these applications are arguably those that demand remote sensing at a stand-off of roughly 10 m or more between the target and the sensor system. As in any other spectral region, remote sensing in the THz region brings up the complex issues of sensor modality and architecture, free-space electromagnetic effects and components, transmit and receive electronics, signal processing, and atmospheric propagation. Unlike other spectral regions, there is not much literature that addresses these issues from a conceptual or system-engineering viewpoint. So a key theme of this chapter is to review or derive the essential engineering concepts in a comprehensive fashion, starting with fundamental principles of electromagnetics, quantum mechanics, and signal processing, and building up to trade-off formulations using system-level metrics such as noiseequivalent power and receiver operating characteristics. A secondary theme is to elucidate aspects of the THz region and its incumbent technology that are unique, whether advantageous or disadvantageous, relative to other spectral regions. The end goal is to provide a useful tutorial for graduate students or practicing engineers considering the upper mm-wave or THz regions for system research or development.

Previous work by the author [David Sands 2008 Eur. J. Phys. 29 129 doi:10.1088/0143-0807/29/1/013] has compared the Boltzmann entropy, k lnW, with the thermodynamic entropy, ClnT, in the case of a temperature-independent heat capacity, C. The simple form of both entropy expressions allows for a simple expression for W and a physical interpretation on the accessible states behind this expression was presented. For the case when C varies with temperature, as in a solid below the Debye temperature, it is not so obvious that this interpretation applies. If there is no simple interpretation of the accessible states it is by no means clear that the Boltzmann entropy is the same as the thermodynamic entropy. In this paper the accessible states of more complex systems is examined. It is shown that the same idea of the accessible states can be applied, but that a real difference between the Boltzmann and thermodynamic entropies is implied by this interpretation.