1,721,112 research outputs found
Local mean field models of uniform to nonuniform density (fluid-crystal) transitions
Full text linkWe investigate the existence of nontranslation invariant (periodic) density profiles, for systems interacting via translation invariant long-range potentials, as minimizers of local mean field free energy functionals. The existence of a second-order transition from a uniform to a nonuniform density at a specified temperature beta(-1)(0) is proven for a class of model systems
Metastability in the two-dimensional Ising model with free boundary conditions
No full textWe investigate metastability in the two dimensional Ising model in a square with free boundary conditions at low temperatures. Starting with all spins down in a small positive magnetic field, we show that the exit From this metastable phase occurs via the nucleation of a critical droplet in one of the four corners of the system. We compute the lifetime of the metastable phase analytically in the limit T --> 0, h --> 0 and via Monte Carlo simulations at fixed Values of T and h and find good agreement. This system models the effects of boundary domains in magnetic storage systems exiting from a metastable phase when a small external field is applied
Modulated phases of a 1D sharp interface model in a magnetic field
No full textWe investigate the ground states of one-dimensional continuum models having short-range ferromagnetic-type interactions and a wide class of competing longer-range antiferromagnetic-type interactions. The model is defined in terms of an energy functional, which can be thought of as the Hamiltonian of a coarse-grained microscopic system or as a mesoscopic free-energy functional describing various materials. We prove that the ground state is simple periodic whatever the prescribed total magnetization might be. Previous studies of this model of frustrated systems assumed this simple periodicity but, as in many examples in condensed-matter physics, it is neither obvious nor always true that ground states do not have a more complicated, or even chaotic structure
Long-time behavior of macroscopic quantum systems
No full textThe renewed interest in the foundations of quantum statistical mechanics in recent years
has led us to study John von Neumann’s 1929 article on the quantum ergodic theorem. We
have found this almost forgotten article, which until now has been available only in
German, to be a treasure chest, and to be much misunderstood. In it, von Neumann studied
the long-time behavior of macroscopic quantum systems. While one of the two theorems
announced in his title, the one he calls the “quantum H-theorem”, is
actually a much weaker statement than Boltzmann’s classical H-theorem,
the other theorem, which he calls the “quantum ergodic theorem”, is a beautiful and very
non-trivial result. It expresses a fact we call “normal typicality” and can be summarized
as follows: for a “typical” finite family of commuting macroscopic observables, every
initial wave function ψ0 from a micro-canonical energy shell
so evolves that for most times t in the long run, the joint probability
distribution of these observables obtained from
ψt is close to their micro-canonical
distribution
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