We investigate the conditions which determine the shape of a particle condensate in situations when it emerges as a result of spontaneous breaking of translational symmetry. We consider a model with particles hopping between sites of a one-dimensional grid and interacting if they are at the same site or at neighboring sites. We predict the envelope of the condensate and the scaling of its width with the system size for various interaction potentials and show how to tune the shape from a delta peak to a rectangular or paraboliclike form.
We study a disordered, driven zero range process which models a closed system of attractive particles that hop with site-dependent rates and whose steady state shows a condensation transition with increasing density. We characterize the dynamical properties of the mass fluctuations in the steady state in one dimension both analytically and numerically and show that there is a dynamic phase transition in the density-disorder plane. We also determine the form of the scaling function which describes the growth of the condensate as a function of time, starting from a uniform density distribution.
Non-equilibrium real-space condensation is a phenomenon in which a finite fraction of some conserved quantity (mass, particles, etc.) becomes spatially localised. We review two popular stochastic models of hopping particles that lead to condensation and whose stationary states assume a factorized form: the zero-range process and the misanthrope process, and their various modifications. We also introduce a new model - a misanthrope process with parallel dynamics - that exhibits condensation and has a pair-factorized stationary state.
We consider the phenomenon of condensation of a globally conserved quantity $H={\ensuremath{\sum}}_{i=1}^{N}{\ensuremath{\epsilon}}_{i}$ distributed on
N sites, occurring when the density
h=H/N exceeds a critical density
hc. We numerically study the dependence of the participation ratio ${Y}_{2}=\ensuremath{\langle}{\ensuremath{\epsilon}}_{i}^{2}\ensuremath{\rangle}/(N{h}^{2})$ on the size
N of the system and on the control parameter $\ensuremath{\delta}=(h\ensuremath{-}{h}_{c})$, for various models: (i) a model with two conservation laws, derived from the discrete nonlinear Schr\"odinger equation; (ii) the continuous version of the zero-range process class, for different forms of the function $f(\ensuremath{\epsilon})$ defining the factorized steady state. Our results show that various localization scenarios may appear for finite
N and close to the transition point. These scenarios are characterized by the presence or the absence of a minimum of
Y2 when plotted against
N and by an exponent $\ensuremath{\gamma}\ensuremath{\ge}2$ defined through the relation ${N}^{*}\ensuremath{\simeq}{\ensuremath{\delta}}^{\ensuremath{-}\ensuremath{\gamma}}$, where
N∗ separates the delocalized region ($N\ensuremath{\ll}{N}^{*}$,
Y2 vanishes with increasing
N) from the localized region ($N\ensuremath{\gg}{N}^{*}$,
Y2 is approximately constant). We finally compare our results with the structure of the condensate obtained through the single-site marginal distribution.
Recent experiments in hybrid-quantum systems facilitate the potential realization of one of the most fundamental interacting Hamiltonian-reservoir systems, namely the single-site Bose-Hubbard model coupled to two reservoirs at different temperatures. Using Redfield equations in a Born-Markov approximation, we compute nonequilibrium average particle number, energy, and currents beyond linear response regime, both time dynamics and steady state, and investigate its dependence on various tunable parameters analytically. We find interesting scaling laws in high-temperature regimes that are independent of choice of bath spectral functions. We also demonstrate that the system shows very interesting particle and energy current rectification properties which can be controlled via the relative strength of interaction and temperatures, as well as via the degree of asymmetry in system-bath coupling. Specifically, we find inversion of direction of energy rectification as a function of the relative strength of the interaction strength and the temperatures. We also show that, in the limit of low-temperature and high interaction strength, our results are consistent with the nonequilibrium spin-Boson model. Our results are experimentally relevant not only to hybrid quantum systems but also in other areas such as molecular junctions.
An RF superconducting quantum interference device (RF SQUID), which is an important bistable system, has attracted much attention for its important applications in nonlinear fields. With different potential shapes at 20 mK, we perform detailed research on the relationship between the probability of the phase particle in the left potential well (PL) of an RF SQUID and the external noise intensity (D), which provides a method to identify the symmetry of any tunable bistable systems. A qualitative model is proposed to understand the physical process, and the numerical results are well consistent with the experimental results.