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We introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner…

Quantum Physics · Physics 2013-06-11 Timo Fischer , Clemens Gneiting , Klaus Hornberger

We develop a theory of non-relativistic bosons in two spatial dimensions with a weak short range attractive interaction. In the limit as the range of the interaction becomes small, there is an ultra-violet divergence in the problem. We…

High Energy Physics - Theory · Physics 2007-05-23 S. G. Rajeev

A rigorous microscopic theory for the description of quantum-transport phenomena in systems with open boundaries is proposed. We shall show that the application of the conventional Wigner-function formalism to this problem leads to…

Condensed Matter · Physics 2007-05-23 Remo Proietti Zaccaria , Fausto Rossi

We consider the mean field theory of the Random Field Ising Model obtained by weighing the many solutions of the mean field equations with Boltzmann-like factors. These solutions are found numerically in three dimensions and we observe…

Condensed Matter · Physics 2009-10-22 David Lancaster , Enzo Marinari , Giorgio Parisi

In this paper we study the semiclassical behavior of quantum states acting on the C*-algebra of canonical commutation relations, from a general perspective. The aim is to provide a unified and flexible approach to the semiclassical analysis…

Functional Analysis · Mathematics 2018-11-21 Marco Falconi

Fundamental phase-shift detection properties of optical multimode interferometers are analyzed. Limits on perfectly distinguishable phase shifts are derived for general quantum states of a given average energy. In contrast to earlier work,…

Quantum Physics · Physics 2008-12-18 Jonas Soderholm , Gunnar Bjork , Bjorn Hessmo , Shuichiro Inoue

We announce a new theorem bearing on high-temperature 2D Bose gases. In a certain mean-field-like regime, the grand-canonical quantum Gibbs state reduces to a nonlinear Gibbs measure constructed from a renormalized mean-field energy…

Mathematical Physics · Physics 2018-05-10 Mathieu Lewin , Phan Thành Nam , Nicolas Rougerie

Important gaps remain in our understanding of the thermodynamics and statistical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems…

Statistical Mechanics · Physics 2009-10-31 Peter J. Klinko , Bruce N. Miller

We consider a quantum mechanical system of N bosons with relativistic dispersion interacting through a mean field Coulomb potential (attractive or repulsive). We choose the initial wave function to describe a condensate, where the N bosons…

Mathematical Physics · Physics 2007-05-23 Alexander Elgart , Benjamin Schlein

The negativity of a given state's Wigner function has been proposed as a measure of quantumness of that state in a unipartite system. This otherwise physically intuitive and useful phase-space measure however does not yield the right…

Quantum Physics · Physics 2008-11-19 Tyler E Keating , Adam T. C. Steege , Arjendu K. Pattanayak

Mean field limits are an important tool in the context of large-scale dynamical systems, in particular, when studying multiagent and interacting particle systems. While the continuous-time theory is well-developed, few works have considered…

Systems and Control · Electrical Eng. & Systems 2023-12-12 Christian Fiedler , Michael Herty , Sebastian Trimpe

We discuss questions pertaining to the definition of `momentum', `momentum space', `phase space', and `Wigner distributions'; for finite dimensional quantum systems. For such systems, where traditional concepts of `momenta' established for…

Quantum Physics · Physics 2009-11-11 S. Chaturvedi , E. Ercolessi , G. Marmo , G. Morandi , N. Mukunda , R. Simon

Understanding quantum many-body systems with long-range or infinite-range interactions is of relevance across a broad set of physical disciplines, including quantum optics, nuclear magnetic resonance and nuclear physics. From a theoretical…

Statistical Mechanics · Physics 2024-03-27 Federico Carollo , Igor Lesanovsky

According to the Quantum de Finetti Theorem, locally normal infinite particle states with Bose-Einstein symmetry can be represented as mixtures of infinite tensor powers of vector states. This note presents examples of infinite-particle…

Quantum Physics · Physics 2009-11-11 Alex D. Gottlieb

We analyze the mean-field limit of a stochastic Schr{\"o}dinger equation arising in quantum optimal control and mean-field games, where N interacting particles undergo continuous indirect measurement. For the open quantum system described…

Analysis of PDEs · Mathematics 2025-07-28 Anne de Bouard , Gaoyue Guo , Théo Hérouard

The phase-space representation for a relativistic linear oscillator in a homogeneous external field expressed through the finite-difference equation is constructed. Explicit expressions of the relativistic oscillator Wigner…

Mathematical Physics · Physics 2009-10-27 S. M. Nagiyev , G. H. Guliyeva , E. I. Jafarov

We consider a large number $N$ of quantum particles coupled via a mean field interaction to another quantum system (reservoir). Our main result is an expansion for the averages of observables, both of the particles and of the reservoir, in…

Mathematical Physics · Physics 2018-05-09 Marco Merkli , Alireza Rafiyi

We provide a rigorous derivation of the Landau-Pekar equations from the Fr\"ohlich Hamiltonian in the mean-field limit using Wigner measure techniques. On the classical side, we extend the global well-posedness results up to $L^2 \oplus…

Mathematical Physics · Physics 2025-09-25 Raphaël Gautier

We determine the form of the Wigner functional for several types of quantum free field theories in order to analyze the representation of QFT in phase space, as well as to compare it to other mainstream formulations. We use Jackiw's…

High Energy Physics - Theory · Physics 2021-08-16 José A. R. Cembranos , Marcos Skowronek

We consider the classical limit of the Nelson model, a system of stable nucleons interacting with a meson field. We prove convergence of the quantum dynamics towards the evolution of the coupled Klein-Gordon-Schr\"odinger equation. Also, we…

Analysis of PDEs · Mathematics 2014-10-03 Zied Ammari , Marco Falconi