Related papers: Lecture Notes in Statistical Mechanics and Mesosco…
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…
We introduce a numerical method to sample the distributions of charge, heat, and entropy production in open quantum systems coupled strongly to macroscopic reservoirs, with both temporal and energy resolution and beyond the linear-response…
Introduction to Machine learning covering Statistical Inference (Bayes, EM, ML/MaxEnt duality), algebraic and spectral methods (PCA, LDA, CCA, Clustering), and PAC learning (the Formal model, VC dimension, Double Sampling theorem).
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as…
These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…
In the so-called "microscopic" models of vehicular traffic, attention is paid explicitly to each individual vehicle each of which is represented by a "particle"; the nature of the "interactions" among these particles is determined by the…
This article begins by reviewing the causal set approach in discrete quantum gravity. In our version of this approach a special role is played by covariant causal sets which we call $c$-causets. The importance of $c$-causets is that they…
Quantum computing is a new emerging computer technology. Current quantum computing devices are at a development stage where they are gradually becoming suitable for small real-world applications. This lecture is devoted to the practical…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
Recent developments in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical probability and statistics. On the other hand, the unique character of quantum physics sets many of the questions…
These are lecture notes for a mini-course on stochastic sewing, taught at the University of Edinburgh and Beijing Institute of Technology in Spring/Summer 2025. The aim is to introduce the reader to stochastic sewing techniques and to show…
The theory of quantum computation is presented in a self contained way from a computer science perspective. The basics of classical computation and quantum mechanics is reviewed. The circuit model of quantum computation is presented in…
The Gaussian state description of continuous variables is adapted to describe the quantum interaction between macroscopic atomic samples and continuous-wave light beams. The formalism is very efficient: a non-linear differential equation…
Nanomechanics has brought mesoscopic physics into the world of vibrations. Because nanomechanical systems are small, fluctuations are significant, the vibrations become nonlinear already for comparatively small amplitudes, and new…
The theory of quantum thermodynamics investigates how the concepts of heat, work, and temperature can be carried over to the quantum realm, where fluctuations and randomness are fundamentally unavoidable. These lecture notes provide an…
Non-adiabatic charge pumping through a single-level quantum dot with periodically modulated parameters is studied theoretically. By means of a quantum-master-equation approach the full counting statistics of the system is obtained. We find…
In this paper we give a pedagogical introduction to the ideas of quantum thermodynamics and work fluctuations, using only basic concepts from quantum and statistical mechanics. After reviewing the concept of work, as usually taught in…
This paper collects and extends the lectures I gave at the "XXIV International Fall Workshop on Geometry and Physics" held in Zaragoza (Spain) August 31 - September 4, 2015. Within these lectures I review the formulation of Quantum…
In this paper we discuss and analyse the idea of trying to see (non-relativistic) quantum mechanics as a ``space-time statistical mechanics'', by using the classical statistical mechanical method on objective microscopic space-time…
We consider the scattering matrix approach to quantum electron transport in meso- and nano-conductors. This approach is an alternative to the more conventional kinetic equation and Green's function approaches, and often is more efficient…