Quantum Limit of Deterministic Theories

Limit cycles in quantum theories.

Renormalization group limit cycles and more chaotic behavior may be commonplace for quantum Hamiltonians requiring renormalization, in contrast to experience based on classical models with critical behavior, where fixed points are far more common. We discuss the simplest quantum model Hamiltonian identified so far that exhibits a renormalization group with both limit cycle and chaotic behavior....

Central and Local Limit Theories in Markov Dependent Random Variables

Quantum phase transitions in spin systems and the high temperature limit of continuum quantum field theories

We study the finite temperature crossovers in the vicinity of a zero temperature quantum phase transition. The universal crossover functions are observables of a continuum quantum field theory. Particular attention is focussed on the high temperature limit of the continuum field theory, the socalled “quantum-critical” region. Basic features of crossovers are illustrated by a simple solvable mod...

The quasi-deterministic limit of population dynamics

We discuss and compare three different, but related, approximations to the stochastic dynamics of populations, all of them having as limit the same deterministic dynamics. The diffusion approximation (van Kampen (1981a); Arnold (1997)), linearized diffusion approximation (Kurtz (1971)) and the Poisson approximation (Aparicio & Solari (2001a); Solari & Natiello (2003b)) are briefly revisited and...

Determined theories and limit laws

We provide a new model theoretic technique for proving 0-1 and convergence laws. As an application, we obtain a new (slightly less computational) proof of convergence laws due to Spencer and Thoma for the probability functions: pn = ln(n) n + l·ln(ln(n)) n + c n .