Phase transitions for a continuous system of classical particles in a box

A continuous classical system involving an infinite number of distinguishable particles is analyzed along the same lines as its quantum analogue, considered in [1]. A commutativeC*-algebra is set up on the phase space of the system, and a representation-dependent definition of equilibrium involving the static KMS condition is given. For a special class of interactions the set of equilibrium states is realized as a convex Borel set whose extremal states are characterized by solutions to a system of integral equations. By analyzing these integral equations, we prove the absence of phase transitions for high temperature and construct a phase transition for low temperature. The construction also provides an example of a translation-invariant state whose decomposition at infinity yields states that are not translation-invariant. Thus we have an example in the classical situation of continuous symmetry breaking.This article is a part of the author's doctoral thesis, which was submitted to the mathematics department at Duke University     

Phase transitions in unstable cancer cell populations

The dynamics of cancer evolution is studied by means of a simple quasispecies model involving cells displaying high levels of genetic instability. Both continuous, mean-field and discrete, bit-string models are analysed. The string model is simulated on a single-peak landscape. It is shown that a phase transition exists at high levels of genetic instability, thus separating two phases of slow and rapid growth. The results suggest that, under a conserved level of genetic instability the cancer cell population will be close to the threshold level. Implications for therapy are outlined.Received: 22 April 2003, Published online: 22 September 2003PACS: 87.10.+e Biological physics: General theory and mathematical aspects - 87.23.Kg Dynamics of evolution - 87.23.-n Ecology and evolution - 89.75.Fb Structures and organization in complex systems     

Phase transitions in a system of two coupled quantum wells

It is predicted that an excitonic liquid is formed in a system of spatially separated electrons (e) and holes (h) in a system of two coupled quantum wells. The ground-state energy and the equilibrium density of the excitonic liquid are calculated as a function of the distance D between the wells. A gas-liquid quantum transition with increasing D is studied. The Berezinskii-Kosterlitz-Thouless transition temperatures at which superfluidity appears in the system are found (for different D). A quantum Mott metal-insulator transition in an anisotropic double-quantum-well structure is investigated. The region of existence of crystalline order in a system of spatially separated e and h is studied. Possible experimental manifestations of the predicted effects are discussed. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 8, 526–531 (25 October 1996)     

Phase transitions in a system of coupled Boson oscillators on a sphere

The solutions of mean-field equations for a system of coupled Boson oscillators on an infinite k-dimensional sphere are discussed in the low density - high temperature region and high density — low temperature region. It is shown that for k = 2 the system exhibits only spatial condensation, whereas for k ⩾ 3 both spatial condensation and Bose-Einstein condensation.     

Phase transitions in a system of spatially separated electrons and holes

The formation of a superfluid exciton liquid in a system of spatially separated electrons and holes in a system of two coupled quantum wells is predicted and its properties are investigated. The ground-state energy and the equilibrium density of the exciton liquid are calculated as functions of distance D between the quantum wells. The properties of a rarefied exciton gas with dipole-dipole repulsions are considered, where this gas is the metastable phase for D<1.9a* and the stable phase for D<1.9a* (a* is the radius of the two-dimensional exciton). The gas-liquid quantum transition is examined for increasing D. The Berezinskii-Kosterlitz-Thouless transition temperatures, at which superfluidity arises in the system, are found for different values of D. Possible experimental manifestations of the predicted effects are discussed. Zh. éksp. Teor. Fiz. 111, 1879–1895 (May 1997)     

Phase transitions in a titanium-silicon system under laser treatment in alkanes

An investigation is made of the phase transitions taking place in a titanium-silicon composite exposed to λ=1.06 μm laser treatment in pentane and hexane. It is shown that the formation of titanium carbide, oxides, and silicides depends on the treatment parameters and conditions. The phase changes were investigated over the thickness of the film and their influence on the electrophysical parameters of the titanium-silicon contact was studied. Zh. Tekh. Fiz. 69, 63–66 (June 1999)     

Phase transitions in a bistable system driven by two colored noises

The colored noise problem is studied from the point of view of consistent Markovian approximations through extending unified colored-noise approximation to the case of two-colored-noise driving systems. A bistable system simultaneously driven by multiplicative and additive colored noise is investigated by means of the extended unified colored-noise approximation. It is found that, for weak strength and color of the additive noise, the form of the stationary probability distribution changes from a unimodal to a bimodal structure via a three modal one as the correlation time of the multiplicative colored noise increases, showing the system undergoes a first order phase transition from a monostable to a bistable state. Numerical simulations support our results. Received 10 August 1998 and Received in final form 23 April 1999     

Phase transitions in a vortex gas

It has been shown recently that the motion of solitons at couplings around a critical coupling can be reduced to the dynamics of particles (the zeros of the Higgs field) on a curved manifold with potential. The curvature gives a velocity-dependent force, and the magnitude of the potential is proportional to the distance from a critical coupling. In this paper we apply this approximation to determining the equation of state of a gas of vortices in the abelian Higgs model. We derive a virial expansion using certain known integrals of the metric, and the second virial coefficient is calculated, determining the behaviour of the gas at low densities. A formula for determining higher-order coefficients is given. At low densities and temperatures T ⪢ λ the equation of state is of the Van der Waals form (P + bN²/A²) (A - aN) = NT with a = 4π and b = -4.89πλ where λ is a measure of the distance from critical coupling. It is found that there is no phase transition in a low-density type-I1 gas, but there is a transition in the type-I case between a condensed and gaseous state. We conclude with a discussion of the relation of our results to vortex behaviour in superconductors.     

Phase transitions in the tantalum-hydrogen system observed by PAC

The perturbation felt by¹⁸¹Hf probes in a¹⁸¹HfTa lattice loaded with 30 at% hydrogen was observed by PAC as a function of temperature. Three different interactions were identified: 1) Ν_Q1=433 (6) MHz, η=0.45 2) Ν_Q2=142 (9) MHz, η=0.9, and 3) Ν_Q?0, σ=4–14 Μ^?1 which are attributed to the Β^?, ε^? and α-phase in TaH system, respectively.     

Phase transitions of a feedback amplifier

The phase transition behaviour of an amplifier with positive feedback is experimentally studied. The results are interpreted using catastrophe theory language. Zero (in Gilmore’s classification), first and second-order transitions are demonstrated by driving the system along appropriate trajectories in control parameter space and the cusp and the spinodal are mapped. The fluctuations of the order parameter are investigated and their relationship to system response time established. Quench experiments analogous to those familiar in condensed matter have also been performed and with similar results.     

Phase transitions in small particles formed at the initial stages of electrocrystallization of metals

The diagram of possible phase transitions occurring in small particles with variations in the electrodeposition parameters is constructed and justified using the data obtained from experimental investigations into the formation and evolution of pentagonal crystals on an indifferent substrate during electrocrystallization of copper.     

Phase transitions in a two-dimensional vortex system with defects: Monte Carlo simulation

AbstractThe phase states and phase transitions in a system consisting of a two-dimensional vortex lattice with defects are studied by the Monte Carlo method. It is shown that a “rotating lattice” phase, which is an intermediate phase between the vortex crystal and vortex liquid phases, is present. The dependence of the temperature of the transition from the rotating lattice phase into a vortex liquid on the strength of the defect potential is determined. The current-voltage characteristics of the system are calculated at various temperatures for point, square, and linear defects. It is shown that the phase state of the system strongly affects its transport properties.     

Phase transitions in a two-dimensional dipole ferrimagnet

The magnetic configurations of the system of magnetic dipoles that have different values and are arranged in a staggered order on a square lattice are studied. A numerical simulation is used to study the phase transitions in the system when the mismatch between the dipoles changes. The restructuring of the magnetic configuration of the system induced by a change in the mismatch is shown to proceed via sequential second-order phase transitions between collinear and noncollinear phases. The numerical simulation results are supported by analytical calculations performed with trial functions.     

Phase transitions in hadronic systems and thermodynamics of a system with an exponential spectrum

Both nuclear matter and hadronic matter at high excitations can be described by a liquid-vapor phase transition. For the hadronic systems, a system with an exponential mass spectrum (Hagedorn-like or bag-like) leads to a thermodynamics which is identical to that of a two phase coexistence at a fixed temperature.     

Phase transitions in geometrothermodynamics

Using the formalism of geometrothermodynamics, we investigate the geometric properties of the equilibrium manifold for diverse thermodynamic systems. Starting from Legendre invariant metrics of the phase manifold, we derive thermodynamic metrics for the equilibrium manifold whose curvature becomes singular at those points where phase transitions of first and second order occur. We conclude that the thermodynamic curvature of the equilibrium manifold, as defined in geometrothermodynamics, can be used as a measure of thermodynamic interaction in diverse systems with two and three thermodynamic degrees of freedom.