Stability of Matter

  title={Stability of Matter},
  author={Michael Loss},
We review results concerning the problem of ‘Stability of Matter’. Non-relativistic, relativistic quantum mechanics as well as matter interacting with classical fields is discussed and the strategies of the various proofs of these results is given in some detail. This is followed by a short discussion of the corresponding problem of matter interacting with the radiation field. 

Book review: Stability of Matter in Quantum Mechanics, by Elliott H. Lieb and Robert Seiringer

Review of Stability of Matter in Quantum Mechanics, by Elliott H. Lieb and Robert Seiringer, Cambridge University Press, Cambridge, 2010, xv+293 pp, ISBN 978-0-521-19118-0.

The Stability of Matter in Quantum Mechanics

Preface 1. Prologue 2. Introduction to elementary quantum mechanics and stability of the first kind 3. Many-particle systems and stability of the second kind 4. Lieb-Thirring and related inequalities

Existence of the thermodynamic limit for disordered quantum Coulomb systems

Following a recent method introduced by Hainzl, Solovej, and Lewin, we prove the existence of the thermodynamic limit for a system made of quantum electrons, and classical nuclei whose positions and

The Scott conjecture for large Coulomb systems: a review

We review some older and more recent results concerning the energy and particle distribution in ground states of heavy Coulomb systems. The reviewed results are asymptotic in nature: they describe


We present two recent works on the thermodynamic limit of quantum Coulomb systems, in which we provided a general method allowing to show the existence of the limit for many different models.

Lieb-Thirring Inequality for a Model of Particles with Point Interactions

We consider a model of quantum-mechanical particles interacting via point interactions of infinite scattering length. In the case of fermions we prove a Lieb-Thirring inequality for the energy, i.e.,

The Vacuum in Nonisentropic Gas Dynamics

The Energy of Charged Matter

In this talk I will discuss some of the techniques that have been developed over the past 35 years to estimate the energy of charged matter. These techniques have been used to solve stability of

Differential equations of quantum mechanics

  • I. Sigal
  • Physics, Mathematics
    Quarterly of Applied Mathematics
  • 2022
We review very briefly the main mathematical structures and results in some important areas of Quantum Mechanics involving PDEs and formulate open problems.

The Thermodynamic Limit for Matter Interacting with Coulomb Forces and with the Quantized Electromagnetic Field: I. The Lower Bound

The proof of the existence of the thermodynamic limit for electrons and nuclei interacting via the Coulomb potential, was accomplished decades ago in the framework of non-relativistic quantum



Relativistic Stability of Matter - I

In this article, we study the quantum mechanics of N electrons and M nuclei interacting by Coulomb forces. Motivated by an important idea of Chandrasekhar and following Herbst [H], we modify the

Stability of nonrelativistic quantum mechanical matter coupled to the (ultraviolet cutoff) radiation field.

We announce a proof of H-stability for the quantized radiation field, with ultraviolet cutoff, coupled to arbitrarily many non-relativistic quantized electrons and static nuclei. Our result holds for

Instability of a pseudo-relativistic model of matter with self-generated magnetic field

For a pseudo-relativistic model of matter, based on the no-pair Hamiltonian, we prove that the inclusion of the interaction with the self-generated magnetic field leads to instability for all

A new approach to the stability of matter problem. I

The stability of matter problem solved by Dyson and Lenard is studied by more field theoretic techniques. Stability is proven for matter in a periodic cube.

Stability of Ultraviolet-Cutoff¶Quantum Electrodynamics with Non-Relativistic Matter

Abstract:We prove that the quantum-mechanical ground state energy of a system consisting of an arbitrary number, M, of static nuclei of atomic number ≤Z and of an arbitrary number, N, of Pauli

The stability of matter in magnetic fields

  • E. Lieb
  • Physics
    Physical review letters
  • 1995
The proof of the stability of matter is three decades old, but the question of stability when arbitrarily large magnetic fields are taken into account was settled only recently. Even more recent is

Stability of Relativistic Matter via Thomas-Fermi Theory

A Thomas-Fermi-Weizsacker type theory is constructed, by means of which we are able to give a relatively simple proof of the stability of relativistic matter. Our procedure has the advantage over

Stability of Coulomb systems with magnetic fields

The analysis of the ground state energy of Coulomb systems interacting with magnetic fields, begun in Part I, is extended here to two cases. Case A: The many electron atom; Case B: One electron with

The stability and instability of relativistic matter

We consider the quantum mechanical many-body problem of electrons and fixed nuclei interacting via Coulomb forces, but with a relativistic form for the kinetic energy, namelyp2/2m is replaced by