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Register a new userNonequilibrium phase transitions in finite arrays of globally coupled Stratonovich models: Strong coupling limit
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A finite array of $N$ globally coupled Stratonovich models exhibits a continuous nonequilibrium phase transition. In the limit of strong coupling there is a clear separation of time scales of center of mass and relative coordinates. The latter relax very fast to zero and the array behaves as a single entity described by the center of mass coordinate. We compute analytically the stationary probability and the moments of the center of mass coordinate. The scaling behaviour of the moments near the critical value of the control parameter $a_c(N)$ is determined. We identify a crossover from linear to square root scaling with increasing distance from $a_c$. The crossover point approaches $a_c$ in the limit $N to infty$ which reproduces previous results for infinite arrays. The results are obtained in both the Fokker-Planck and the Langevin approach and are corroborated by numerical simulations. For a general class of models we show that the transition manifold in the parameter space depends on $N$ and is determined by the scaling behaviour near a fixed point of the stochastic flow.
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We investigate a critical exponent related to synchronization transition in globally coupled nonidentical phase oscillators. The critical exponents of susceptibility, correlation time, and correlation size are significant quantities to characterize fluctuations in coupled oscillator systems of large but finite size and understand a universal property of synchronization. These exponents have been identified for the sinusoidal coupling but not fully studied for other coupling schemes. Herein, for a general coupling function including a negative second harmonic term in addition to the sinusoidal term, we numerically estimate the critical exponent of the correlation size, denoted by $ u_+$, in a synchronized regime of the system by employing a non-conventional statistical quantity. First, we confirm that the estimated value of $ u_+$ is approximately 5/2 for the sinusoidal coupling case, which is consistent with the well-known theoretical result. Second, we show that the value of $ u_+$ increases with an increase in the strength of the second harmonic term. Our result implies that the critical exponent characterizing synchronization transition largely depends on the coupling function.
We consider the Dicke model in the ultra-strong coupling limit to investigate thermal phase transitions and their precursors at finite particle numbers $N$ for bosonic and fermionic systems. We derive partition functions with degeneracy factors that account for the number of configurations and derive explicit expressions for the Landau free energy. This allows us to discuss the difference between the original Dicke (fermionic) and the bosonic case. We find a crossover between these two cases that shows up, e.g., in the specific heat.
Discontinuous phase transitions out of equilibrium can be characterized by the behavior of macroscopic stochastic currents. But while much is known about the the average current, the situation is much less understood for higher statistics. In this paper, we address the consequences of the diverging metastability lifetime -- a hallmark of discontinuous transitions -- in the fluctuations of arbitrary thermodynamic currents, including the entropy production. In particular, we center our discussion on the emph{conditional} statistics, given which phase the system is in. We highlight the interplay between integration window and metastability lifetime, which is not manifested in the average current, but strongly influences the fluctuations. We introduce conditional currents and find, among other predictions, their connection to average and scaled variance through a finite-time version of Large Deviation Theory and a minimal model. Our results are then further verified in two paradigmatic models of discontinuous transitions: Schlogls model of chemical reactions, and a $12$-states Potts model subject to two baths at different temperatures.
We have studied the phase diagram of two capacitively coupled Josephson junction arrays with charging energy, $E_c$, and Josephson coupling energy, $E_J$. Our results are obtained using a path integral Quantum Monte Carlo algorithm. The parameter that quantifies the quantum fluctuations in the i-th array is defined by $alpha_iequiv frac{E_{{c}_i}}{E_{J_i}}$. Depending on the value of $alpha_i$, each independent array may be in the semiclassical or in the quantum regime: We find that thermal fluctuations are important when $alpha lesssim 1.5 $ and the quantum fluctuations dominate when $2.0 lesssim alpha $. We have extensively studied the interplay between vortex and charge dominated individual array phases. The two arrays are coupled via the capacitance $C_{{rm inter}}$ at each site of the lattices. We find a {it reentrant transition} in $Upsilon(T,alpha)$, at low temperatures, when one of the arrays is in the semiclassical limit (i.e. $alpha_{1}=0.5 $) and the quantum array has $2.0 leqalpha_{2} leq 2.5$, for the values considered for the interlayer capacitance. In addition, when $3.0 leq alpha_{2} < 4.0$, and for all the inter-layer couplings considered above, a {it novel} reentrant phase transition occurs in the charge degrees of freedom, i.e. there is a reentrant insulating-conducting transition at low temperatures. We obtain the corresponding phase diagrams and found some features that resemble those seen in experiments with 2D JJA.
Universal scaling laws form one of the central issues in physics. A non-standard scaling law or a breakdown of a standard scaling law, on the other hand, can often lead to the finding of a new universality class in physical systems. Recently, we found that a statistical quantity related to fluctuations follows a non-standard scaling law with respect to system size in a synchronized state of globally coupled non-identical phase oscillators [Nishikawa et al., Chaos $boldsymbol{22}$, 013133 (2012)]. However, it is still unclear how widely this non-standard scaling law is observed. In the present paper, we discuss the conditions required for the unusual scaling law in globally coupled oscillator systems, and we validate the conditions by numerical simulations of several different models.
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