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The 2-fold degeneracy of the ground state of a quasi-one-dimensional system allows it to support topological excitations such as solitons. We study the combined effects of Coulomb interactions and confinement due to interchain coupling on the statistics of such defects. We concentrate on a 2D case which may correspond to monolayers of polyacetylene or other charge density waves. The theory is developped by a mapping to the 2D Ising model with long-range 4-spin interactions. The phase diagram exhibits deconfined phases for liquids and Wigner crystals of kinks and confined ones for bikinks. Also we find aggregated phases with either infinite domain walls of kinks or finite rods of bikinks. Roughening effects due to both temperature and Coulomb repulsion are observed. Applications may concern the melting of stripes in doped correlated materials.
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While equilibrium phase transitions are well described by a free-energy landscape, there are few tools to describe general features of their non-equilibrium counterparts. On the other hand, near-equilibrium free-energies are easily accessible but their full geometry is only explored in non-equilibrium, e.g. after a quench. In the particular case of a non-stationary system, however, the concepts of an order parameter and free energy become ill-defined, and a comprehensive understanding of non-stationary (transient) phase transitions is still lacking. Here, we probe transient non-equilibrium dynamics of an optically pumped, dye-filled microcavity which exhibits near-equilibrium Bose-Einstein condensation under steady-state conditions. By rapidly exciting a large number of dye molecules, we quench the system to a far-from-equilibrium state and, close to a critical excitation energy, find delayed condensation, interpreted as a transient equivalent of critical slowing down. We introduce the two-time, non-stationary, second-order correlation function as a powerful experimental tool for probing the statistical properties of the transient relaxation dynamics. In addition to number fluctuations near the critical excitation energy, we show that transient phase transitions exhibit a different form of diverging fluctuations, namely timing jitter in the growth of the order parameter. This jitter is seeded by the randomness associated with spontaneous emission, with its effect being amplified near the critical point. The general character of our results are then discussed based on the geometry of effective free-energy landscapes. We thus identify universal features, such as the formation timing jitter, for a larger set of systems undergoing transient phase transitions. Our results carry immediate implications to diverse systems, including micro- and nano-lasers and growth of colloidal nanoparticles.
Most common types of symmetry breaking in quasi-one-dimensional electronic systems possess a combined manifold of states degenerate with respect to both the phase $theta$ and the amplitude $A$ sign of the order parameter $Aexp(itheta)$. These degrees of freedom can be controlled or accessed independently via either the spin polarization or the charge densities. To understand statistical properties and the phase diagram in the course of cooling under the controlled parameters, we present here an analytical treatment supported by Monte Carlo simulations for a generic coarse-grained two-fields model of XY-Ising type. The degeneracies give rise to two coexisting types of topologically nontrivial configurations: phase vortices and amplitude kinks -- the solitons. In 2D, 3D states with long-range (or BKT type) orders, the topological confinement sets in at a temperature $T=T_1$ which binds together the kinks and unusual half-integer vortices. At a lower $T=T_2$, the solitons start to aggregate into walls formed as rods of amplitude kinks which are ultimately terminated by half-integer vortices. With lowering $T$, the walls multiply passing sequentially across the sample. The presented results indicate a possible physical realization of a peculiar system of half-integer vortices with rods of amplitude kinks connecting their cores. Its experimental realization becomes feasible in view of recent successes in real space observations and even manipulations of domain walls in correlated electronic systems.
We analyze the diffusive motion of kink solitons governed by the thermal sine-Gordon equation. We analytically calculate the correlation function of the position of the kink center as well as the diffusion coefficient, both up to second-order in temperature. We find that the kink behavior is very similar to that obtained in the overdamped limit: There is a quadratic dependence on temperature in the diffusion coefficient that comes from the interaction among the kink and phonons, and the average value of the wave function increases with $sqrt{t}$ due to the variance of the centers of individual realizations and not due to kink distortions. These analytical results are fully confirmed by numerical simulations.
While the canonical ensemble has been tremendously successful in capturing thermal statistics of macroscopic systems, deviations from canonical behavior exhibited by small systems are not well understood. Here, using a small two dimensional Ising magnet embedded inside a larger Ising magnet heat bath, we characterize the failures of the canonical ensemble when describing small systems. We find significant deviations from the canonical behavior for small systems near and below the critical point of the two dimensional Ising model. Notably, the agreement with the canonical ensemble is driven not by the system size but by the statistical decoupling between the system and its surrounding. A superstatistical framework wherein we allow the temperature of the small magnet to vary is able to capture its thermal statistics with significantly higher accuracy than the Gibbs-Boltzmann distribution. We discuss future directions.
Multivariate fluctuation relations are established in three stochastic models of transistors, which are electronic devices with three ports and thus two coupled currents. In the first model, the transistor has no internal state variable and particle exchanges between the ports is described as a Markov jump process with constant rates. In the second model, the rates linearly depend on an internal random variable, representing the occupancy of the transistor by charge carriers. The third model has rates nonlinearly depending on the internal occupancy. For the first and second models, finite-time multivariate fluctuation relations are also established giving insight into the convergence towards the asymptotic form of multivariate fluctuation relations in the long-time limit. For all the three models, the transport properties are shown to satisfy Onsagers reciprocal relations in the linear regime close to equilibrium as well as their generalizations holding in the nonlinear regimes farther away from equilibrium, as a consequence of microreversibility.
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