Related papers: Stein's method, many interacting worlds and quantu…
We show that the density of energy levels of a wide class of finite-dimensional quantum systems tends to a Gaussian distribution as the number of degrees of freedom increases. Our result is based on a nontrivial modification of the…
We study the interactions of a possibly dense and/or quantum degenerate gas with driving light. Both the atoms and the electromagnetic fields are represented by quantum fields throughout the analysis. We introduce a field theory version of…
These lecture notes treat the mean-field approximation for equilibrium states of N body systems in classical and quantum statistical mechanics. A general strategy to justify effective models based on assumptions of statistical independence…
We prove a bound for the Wasserstein distance between vectors of smooth complex random variables and complex Gaussians in the framework of complex Markov diffusion generators. For the special case of chaotic eigenfunctions, this bound can…
These lectures advocate the idea that quantum entanglement provides a unifying foundation for both statistical physics and high-energy interactions. I argue that, at sufficiently long times or high energies, most quantum systems approach a…
We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex of classical N-point probability…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
New lower bounds for the binding energy of a quantum-mechanical system of interacting particles are presented. The new bounds are expressed in terms of two-particle quantities and improve the conventional bounds of the Hall-Post type. They…
We study a quantum theory based on two assumptions: In the intrinsic frame of reference of an isolated, macroscopic system, (i) the system has no global motion and is not entangled with any other system, (ii) time evolution of statevectors…
In this paper, we quantify some known approximation to the Curie-Weiss model via applying the Stein method to the Markov chain whose stationary distribution coincides with Curie-Weiss model.
A new approach to the concept of particles and their production in quantum field theory is developed. A local operator describing the current of particle density is constructed for scalar and spinor fields in arbitrary gravitational and…
We give a rigorous argument that long--range repulsion stabilizes quantum systems; ground states of such quantum systems exist even when the ground state energy is precisely at the ionization threshold. For atomic systems at the critical…
It is emphasized that a many-worlds interpretation of quantum theory exists only to the extent that the associated basis problem is solved. The core basis problem is that the robust enduring states specified by environmental decoherence…
We provide a general theorem bounding the error in the approximation of a random measure of interest--for example, the empirical population measure of types in a Wright-Fisher model--and a Dirichlet process, which is a measure having…
The interpretation of quantum mechanics has been discussed since this theme first was brought up by Einstein and Bohr. This article describes a proposal for a new foundation of quantum theory, partly drawing upon ideas from statistical…
By a delicate analysis for the Stein's equation associated to the $\alpha$-stable law approximation with $\alpha \in (0,2)$, we prove a quantitative stable central limit theorem in Wasserstein type distance, which generalizes the results in…
We combine Stein's method with Malliavin calculus in order to obtain explicit bounds in the multidimensional normal approximation (in the Wasserstein distance) of functionals of Gaussian fields. Our results generalize and refine the main…
Probability distributions play a central role in quantum mechanics, and even more so in quantum optics with its rich diversity of theoretically conceivable and experimentally accessible quantum states of light. Quantifiers that compare two…
An analysis of the Dicke model, N two-level atoms interacting with a single radiation mode, is done using the Holstein-Primakoff transformation. The main aim of the paper is to show that, changing the quantization axis with respect to the…
Let $(W,W')$ be an exchangeable pair. Assume that \[E(W-W'|W)=g(W)+r(W),\] where $g(W)$ is a dominated term and $r(W)$ is negligible. Let $G(t)=\int_0^tg(s)\,ds$ and define $p(t)=c_1e^{-c_0G(t)}$, where $c_0$ is a properly chosen constant…