Related papers: Phase transitions for rotational states within an …
We study the properties of quantum cusp and butterfly catastrophes from an algebraic viewpoint. The analysis employs an interacting boson model Hamiltonian describing quantum phase transitions between specific quadrupole shapes by…
The most important recent results in the theory of phase transitions and quantum effects in quantum anharmonic crystals are presented and discussed. In particular, necessary and sufficient conditions for a phase transition to occur at some…
We discuss the application of an extended version of the coupled cluster method to systems exhibiting a quantum phase transition. We use the lattice O(4) non-linear sigma model in (1+1)- and (3+1)-dimensions as an example. We show how…
We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the…
We discuss the semiclassical approximation to transport problems in quantum chaotic systems. The figures of merit are moments of the transmission matrix and of the time delay matrix. After reviewing a few results obtained by treating these…
We discuss here phase transitions in quantum field theory in the context of vacuum realignment through an explicit construction. Vacuum destabilisation may occur through a scalar attaining a nonzero expectation value, or through a…
Collapse, or a gravitational-like phase transition is studied in a microcanonical ensemble of particles with an attractive $1/r^{\alpha}$ potential. A mean field continuous integral equation is used to determine a saddle-point density…
Cluster structures and monopole transitions in positive parity states of $^{16}$O were investigated based on the generator coordinate method calculation of an extended $^{12}$C+$\alpha$ cluster model. The ground and excited states of a…
The identification and classification of phases in small systems, e.g. nuclei, social and financial networks, clusters, and biological systems, where the traditional definitions of phase transitions are not applicable, is important to…
Ecosystems often undergo abrupt regime shifts in response to gradual external changes. These shifts are theoretically understood as a regime switch between alternative stable states of the ecosystem dynamical response to smooth changes in…
Three classes of finite-dimensional models of quantum systems exhibiting spectral degeneracies called quantum catastrophes are described in detail. Computer-assisted symbolic manipulation techniques are shown unexpectedly efficient for the…
Nonequilibrium phase transitions between an active and an absorbing state are found in models of populations, epidemics, autocatalysis, and chemical reactions on a surface. While absorbing-state phase transitions fall generically in the DP…
We investigate properties of the Generator Coordinate Method (GCM) on a collective basis of Antisymmetrized Quasi-Cluster (AQC) states to describe the cluster-shell competition in $^{20}$Ne and $^{24}$Mg due to the spin-orbit interaction.…
$^{20}$Ne has been known as a typical example of a nucleus with $\alpha$ cluster structure ($^{16}$O+$\alpha$ structure). However according to the spherical shell model, the spin-orbit interaction acts attractively for four nucleons outside…
The phase diagram of the Blume--Capel model on a semi--infinite simple cubic lattice with a (100) free surface is studied in the pair approximation of the cluster variation method. Six main topologies are found, of which two are new, due to…
Background: In the last few decades quantum phase transitions have been of great interest in Nuclear Physics. In this context, two-fluid algebraic models are ideal systems to study how the concept of quantum phase transition evolves when…
This article first gives a concise introduction to quantum phase transitions, emphasizing similarities with and differences to classical thermal transitions. After pointing out the computational challenges posed by quantum phase…
The dynamics of phase transitions plays a crucial r\^ole in the so-called interface between high energy particle physics and cosmology. Many of the interesting results generated during the last fifteen years or so rely on simplified…
First-order phase transitions produce gravitational waves and primordial black holes. They always occur in field theories where symmetries are radiatively broken and masses are correspondingly generated. These theories predict a period of…
The thermodynamic formalism for dynamical systems with many degrees of freedom is extended to deal with time averages and fluctuations of some macroscopic quantity along typical orbits, and applied to coupled map lattices exhibiting phase…