Adiabatically switched-on electrical bias in continuous systems, and the Landauer-Buttiker formula

Consider a three dimensional system which looks like a cross-connected pipe system, i.e. a small sample coupled to a finite number of leads. We investigate the current running through this system, in the linear response regime, when we adiabatically turn on an electrical bias between leads. The main technical tool is the use of a finite volume regularization, which allows us to define the current coming out of a lead as the time derivative of its charge. We finally prove that in virtually all physically interesting situations, the conductivity tensor is given by a Landauer-B{\"u}ttiker type formula.Comment: 20 pages, submitte

Strict Deformation Quantization for a Particle in a Magnetic Field

Recently, we introduced a mathematical framework for the quantization of a particle in a variable magnetic field. It consists in a modified form of the Weyl pseudodifferential calculus and a C*-algebraic setting, these two points of view being isomorphic in a suitable sense. In the present paper we leave Planck's constant vary, showing that one gets a strict deformation quantization in the sense of Rieffel. In the limit h --> 0 one recovers a Poisson algebra induced by a symplectic form defined in terms of the magnetic field.Comment: 23 page

Magnetic calculus and semiclassical trace formulas

The aim of these notes is to show how the magnetic calculus developed in \cite{MP, IMP1, IMP2, MPR, LMR} permits to give a new information on the nature of the coefficients of the expansion of the trace of a function of the magnetic Schr\"odinger operator whose existence was established in \cite{HR2}

The Free Education Project: Higher Education Funding, E2 Implementation, and Crowdsourcing Crypto Development

This short paper, written in three different sections, explores how a cryptocurrency’s issuance and network effects could fund higher education. Synthesizing research from the Bronx Community College Cryptocurrency Research Lab, Bernard Lietaer’s notion of creating money for the needs of society, lessons learned by Galia Benartzi and the Hearts Project, and an exploration of how communities coalesce around open-source cryptocurrency projects, the authors provide an overview of the problem of funding higher education, the ways in which money that is needed could be created, and the key components to building a highly effective developer community. These three distinct yet vitally interconnected facets lay the groundwork for the Free Education Project. Lastly, based on the models herein, this paper calls for academics, entrepreneurs, and financial professionals to work together in ways that facilitate and generate the needed capital, built outside of taxation, to fund the noble purposes of education writ large

Perturbation Theory and Control in Classical or Quantum Mechanics by an Inversion Formula

We consider a perturbation of an ``integrable'' Hamiltonian and give an expression for the canonical or unitary transformation which ``simplifies'' this perturbed system. The problem is to invert a functional defined on the Lie- algebra of observables. We give a bound for the perturbation in order to solve this inversion. And apply this result to a particular case of the control theory, as a first example, and to the ``quantum adiabatic transformation'', as another example.Comment: Version 8.0. 26 pages, Latex2e, final version published in J. Phys.

The Free Education Project: Higher Education Funding, E2 Implementation, and Crowdsourcing Crypto Development

This short paper, written in three different sections, explores how a cryptocurrency’s issuance and network effects could fund higher education. Synthesizing research from the Bronx Community College Cryptocurrency Research Lab, Bernard Lietaer’s notion of creating money for the needs of society, lessons learned by Galia Benartzi and the Hearts Project, and an exploration of how communities coalesce around open-source cryptocurrency projects, the authors provide an overview of the problem of funding higher education, the ways in which money that is needed could be created, and the key components to building a highly effective developer community. These three distinct yet vitally interconnected facets lay the groundwork for the Free Education Project. Lastly, based on the models herein, this paper calls for academics, entrepreneurs, and financial professionals to work together in ways that facilitate and generate the needed capital, built outside of taxation, to fund the noble purposes of education writ large

Adiabatic non-equilibrium steady states in the partition free approach

Consider a small sample coupled to a finite number of leads, and assume that the total (continuous) system is at thermal equilibrium in the remote past. We construct a non-equilibrium steady state (NESS) by adiabatically turning on an electrical bias between the leads. The main mathematical challenge is to show that certain adiabatic wave operators exist, and to identify their strong limit when the adiabatic parameter tends to zero. Our NESS is different from, though closely related with the NESS provided by the Jak{\v s}i{\'c}-Pillet-Ruelle approach. Thus we partly settle a question asked by Caroli {\it et al} in 1971 regarding the (non)equivalence between the partitioned and partition-free approaches

TIA1 Mutations in Amyotrophic Lateral Sclerosis and Frontotemporal Dementia Promote Phase Separation and Alter Stress Granule Dynamics.

Amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD) are age-related neurodegenerative disorders with shared genetic etiologies and overlapping clinical and pathological features. Here we studied a novel ALS/FTD family and identified the P362L mutation in the low-complexity domain (LCD) of T cell-restricted intracellular antigen-1 (TIA1). Subsequent genetic association analyses showed an increased burden of TIA1 LCD mutations in ALS patients compared to controls (p = 8.7 × 1