Related papers: Convergence to equilibrium for many particle syste…
We extend the systematic calculation of an approximately relativistic Hamiltonian for centre of mass and internal dynamics of an electromagnetically bound two-particle system by Sonnleitner and Barnett [1] to the case including a weak…
In the framework of semiclassical theory the universal properties of quantum systems with classically chaotic dynamics can be accounted for through correlations between partner periodic orbits with small action differences. So far, however,…
We discuss the form of the entropy for classical hamiltonian systems with long-range interaction using the Vlasov equation which describes the dynamics of a $N$-particle in the limit $N\to\infty$. The stationary states of the hamiltonian…
The approach to equilibrium for systems interacting with their environment by being regularly exposed to low energy, low intensity pulses of some type of quanta is studied. Assuming a randomness condition on the interaction of these quanta…
Systems reaching thermal equilibrium are ubiquitous. For classical systems, this phenomenon is typically understood statistically through ergodicity in phase space, but translating this to quantum systems is a long-standing problem of…
We study equilibrium configurations of infinitely many identical particles on the real line or finitely many particles on the circle, such that the (repelling) force they exert on each other depends only on their distance. The main question…
We consider a system of N classical particles, interacting via a smooth, short- range potential, in a weak-coupling regime. This means that N tends to infinity when the interaction is suitably rescaled. The j-particle marginals, which obey…
Recent studies of interacting systems of quantum spins, ultracold atoms and correlated fermions have shed a new light on how isolated many-body systems can avoid rapid equilibration to their thermal state. It has been shown that many such…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the $N-$body phase space with the given total energy. Due to Boltzmann's principle,…
The recent discovery that for large Hilbert spaces, almost all (that is, typical) Hamiltonians have eigenstates that place small subsystems in thermal equilibrium, has shed much light on the origins of irreversibility and thermalization.…
The system of N particles moving on a circle and interacting via a global repulsive cosine interaction is well known to display spatially inhomogeneous structures of extraordinary stability starting from certain low energy initial…
We examine quantum normal typicality and ergodicity properties for quantum systems whose dynamics are generated by Hamiltonians which have residual degeneracy in their spectrum and resonance in their energy gaps. Such systems can be…
We discuss a simple singular system in one dimension, two heavy particles interacting with a light particle via an attractive contact interaction. It is natural to apply Born-Oppenheimer approximation to this problem. We present a detailed…
From its beginning, there have been attempts by physicists to formulate quantum mechanics without requiring the use of wave functions. An interesting recent approach takes the point of view that quantum effects arise solely from the…
We discuss the condition for the validity of equilibrium quantum statistical mechanics in the light of recent developments in the understanding of classical and quantum chaotic motion. In particular, the ergodicity parameter is shown to…
The Temporal Fluctuation Model proposed in present paper represents an attempt for a unitary vision for gravity, inertia and electromagnetism. We obtain the main results of General Relativity and Electromagnetism and the theory, until now,…
In this work we report on a loss of ergodicity in a simple hopping model, motivated by the Hubbard Hamiltonian, of a many body quantum system at zero temperature, quantized in Euclidean time. We show that this quantum system may lose…
Through the development of many-body methodology and algorithms, it has become possible to describe quantum systems composed of a large number of particles with great accuracy. Essential to all these methods is the application of auxiliary…
We consider an electronic bound state of the usual, non-relativistic, molecular Hamiltonian with Coulomb interactions and fixed nuclei. Away from appropriate collisions, we prove the real analyticity of all the reduced densities and density…
We show that classical particle mechanics (Hamiltonian and Lagrangian consistent with relativistic electromagnetism) can be derived from three fundamental assumptions: infinite reducibility, deterministic and reversible evolution, and…