Condensation Phase Transition Research Articles

Finite density scaling laws of condensation phase transition in zero-range processes on scale-free networks**Project supported by the National Natural Science Foundation of China (Grant No. 11505115).

The dynamics of zero-range processes on complex networks is expected to be influenced by the topological structure of underlying networks. A real space complete condensation phase transition in the stationary state may occur. We study the finite density effects of the condensation transition in both the stationary and dynamical zero-range processes on scale-free networks. By means of grand canonical ensemble method, we predict analytically the scaling laws of the average occupation number with respect to the finite density for the steady state. We further explore the relaxation dynamics of the condensation phase transition. By applying the hierarchical evolution and scaling ansatz, a scaling law for the relaxation dynamics is predicted. Monte Carlo simulations are performed and the predicted density scaling laws are nicely validated.

Demonstrating the Critical Role of Solvation in Supported Ti and Nb Epoxidation Catalysts via Vapor-Phase Kinetics

Catalytic oxidation of hydrocarbons with hydrogen peroxide (H2O2) has been of the utmost importance for several decades. The vast majority of studies have been performed in the condensed phase, even though condensed phases introduce complex solvent effects and can promote the leaching of active sites. In response, we have built a custom reactor system to understand H2O2 activation and selective oxidation in the vapor-phase. In this report, we study the epoxidation of cyclohexene with H2O2 over four Lewis-acidic metal oxide catalysts: Ti and Nb grafted on SiO2 and on the Zr based metal–organic framework, NU-1000. The M–SiO2 materials are highly selective to the formation of epoxides and diols, as they can be in the condensed phase, while the NU-1000 based materials are far more prone to overoxidation to CO2, which appears to be connected to their strong reactant adsorption. Apparent activation energies are calculated for all materials when operating in the same kinetic regime, and the heats of cyclohexene adsorption into their pores are then used to directly compare intrinsic enthalpies of activation in the vapor vs condensed phase for the M–SiO2 catalysts. Nb–SiO2 catalysts exhibit similar intrinsic enthalpies of activation in the vapor and condensed phases, whereas the condensed phase transition state in Ti–SiO2 is 24 kJ/mol lower in energy than that of the same material in the vapor phase. These experiments establish another methodology for understanding the various roles of solvent in selective oxidation reactions and studying these reactions under conditions that differ significantly from the thousands of prior studies in the condensed phase.

Study of spontaneous combinatorial scattering spectroscopy in condensed phase transitions

In this work, in the field of molecular spectroscopy, the dynamics of the study of relaxation processes in optical research and the methods of their detection using various methods are considered in detail. Calculations of the recorded contours of the combinatorial scattering lines Fure, when examined by analysis, have been shown to play an important role in the restoration of orientation and oscillation relaxations, correlation functions. Furthermore, for mixed cases, the method of high-spectral moments was analyzed on the basis of formulas based on the analysis of the oscillation contours of the combined scattering spectra in the liquid phase.

The replica symmetric phase of random constraint satisfaction problems

AbstarctRandom constraint satisfaction problems play an important role in computer science and combinatorics. For example, they provide challenging benchmark examples for algorithms, and they have been harnessed in probabilistic constructions of combinatorial structures with peculiar features. In an important contribution (Krzakala et al. 2007, Proc. Nat. Acad. Sci.), physicists made several predictions on the precise location and nature of phase transitions in random constraint satisfaction problems. Specifically, they predicted that their satisfiability thresholds are quite generally preceded by several other thresholds that have a substantial impact both combinatorially and computationally. These include the condensation phase transition, where long-range correlations between variables emerge, and the reconstruction threshold. In this paper we prove these physics predictions for a broad class of random constraint satisfaction problems. Additionally, we obtain contiguity results that have implications for Bayesian inference tasks, a subject that has received a great deal of interest recently (e.g. Banks et al. 2016, Proc. 29th COLT).

Synthesis and emerging properties of 2D layered III–VI metal chalcogenides

Atomically thin layered III–VI metal chalcogenides are an emerging class of 2D materials that have attracted increasing attention in recent years due to their remarkable physical properties and technological applications. Thanks to the recently developed theoretical and experimental methods, a number of exciting discoveries for these materials have revealed their new phases, a unique “Mexican hat”-shaped electronic band structure, and superior optical and electronic properties that distinguish them from other 2D materials such as transition metal dichalcogenides. This review summarizes the novel properties, structures, and synthesis strategies for these materials and emphasizes the most cutting-edge and seminal achievements in this rapidly growing field in order to provide input for future research works. We first present the rich crystal structure and phases that have been found in these materials, with an emphasis on the possibility of phase engineering. Then, we discuss the synthesis strategies for 2D layered III–VI metal chalcogenides from the top-down, bottom-up, and template-based chemical conversion approaches. We focus on the highly controlled synthesis methods that provide fine-tuning of the thickness, phase, edge structure, and other morphological characteristics. Third, we discuss the properties and applications of these materials, focusing on their unique electronic structure including the Mexican hat-shaped valence band, their superior nonlinear optical properties, high-performance electronic devices, promising photoelectrochemical properties, and emerging quantum properties such as quantum emission, exciton condensation, ferromagnetism, and topological quantum phase transition. Finally, we provide our perspective on the current challenges and future directions in this field.

Effect of magnetophoresis and Brownian diffusion on mechanical processes in magnetic fluids: The role of a condensation phase transition

In this work, we study theoretically the effect of the mass transfer processes on the volume magnetic force and viscous friction of the magnetic fluid subjected to a magnetic field gradient and a shear flow between two rotating cylinders. The model is based on the diffusion equations and takes into account a condensation phase transition in the magnetic fluid. The results of experimental and theoretical studies of the diffusion processes in a thin layer of the magnetic fluid are also presented.

Determination of Polariton Condensates’ Critical Temperature

The thermal robustness of traveling polariton condensates is investigated. We create remote condensates that have never been in contact, and study their interference in momentum space, when they travel with the same velocity, by means of time‐resolved photoluminescence. We determine the condensed to thermal, uncondensed polariton fraction, which shows a gradual decay with increasing temperature, and obtain the critical temperature for the Bose‐Einstein‐like condensate (BEC) phase transition. We tentatively compare our experimental findings with theoretical models, developed for atomic condensates, to describe the condensates’ coherence fading with temperature.

Interactions of Monovalent and Divalent Cations with Cardiolipin Monolayers.

Cardiolipin is a mitochondrial phospholipid with four alkyl chains and two phosphate moieties. Tetramyristoyl cardiolipin (TMCL, (14:0)4CL) monolayers at the air-water interface are characterized by compression isotherms, which show a liquid expanded/liquid condensed phase transition. The phase transition surface pressure πc depends on the composition of the aqueous solution. In a calculation, this is attributed to the electrostatic double layer, which is induced by the head groups of the model membrane, and competitive ion binding. The intrinsic binding constant is large for protons ( KH = 10 L/mol) and small for monovalent cations ( KM (Na+, K+, Cs+) = 10-3 L/mol). The different intrinsic binding constants explain the non-monotonic behavior of πc on increasing the salt concentration: raising the monovalent salt concentration increases πc by charging the TMCL monolayer until 0.1 mol/L, then screening effects dominate and decrease πc by reducing the electrostatic repulsion between lipid head groups. When at fixed 0.15 mol/L NaCl concentration, the concentration of divalent cations is increased, πc decreases. The intrinsic binding constants of divalent cations follow the sequence Sr2+ < Mg2+ < Mn2+ ≈ Zn2+ ≈ Ca2+ ( KD,Ca = 1.2 L/mol). The predictive power of the calculations was tested with different solutions.

Phase transition and thermodynamic properties of &lt;i&gt;N&lt;/i&gt; two-level atoms in an optomechanical cavity at finite temperature

Optomechanical cavity is a powerful connection between a nanomechanical oscillator and a quantized electromagnetic field. In this system, a novel photon-phonon nonlinear interaction arising from the nanomechanical oscillation is produced through the radiation pressure. Now this nonlinear photon-phonon interaction has become an important resource for implementing high-precision measurements and processing quantum information. Motivated by T. Esslinger group’s experiment, it is very meaningful to explore the exotic quantum phenomena when a ultra-cold BEC is trapped in an optomechanical cavity. In this paper, we mainly investigate phase transition and the finite-temperature thermodynamic properties of a Bose-Einstein condensate in an optomechanical cavity. It’s worth mentioning that at zero temperature many different mean-field approximate methods have been used to analyze the ground state properties of a Bose-Einstein condensate in an optomechanical cavity. Two common methods are Holstein-Primakoff transformation and spin coherent state variation. In this paper, an interesting imaginary-time path integral approach has been introduced to study finite temperature thermodynamic properties and phase transition of a Bose-Einstein condensate in an optomechanical cavity. First, we obtained system's partition function by taking imaginary-time path integration. Meanwhile, an effective action has been obtained by means of this method, which is the basic of the variation to get the numerical solution of photon number and the expression of the atomic number. At zero temperature, these results are consistent with what we have obtained by Holstein-Primakoff transformation or spin coherent state variational method. By adjusting the atom-field coupling strength and other parameters the second-order phase transition from the normal phase to the superradiant phase has been revealed. Meanwhile, a new unstable superradiant state was also found. And we found that in addition to the normal phase and superradiation phase, there exists an un-solution region of the mean photon number. Meanwhile, we find that the nonlinear photon-phonon interaction does not affect the normal phase. However, in the superradiant phase, the nonlinear photon-phonon interaction can enhance the macroscopic collective excitations. At the same time, the thermodynamic properties of the system are also discussed. According to the obtained distribution function, we can derive the analytical expression of the average energy and the free energy. Furthermore, the expression of entropy at finite temperature can also be obtained. we find the nonlinear photon-phonon interaction does not affect the average energy in the normal phase, but the average energy in the superradiant phase can deeply deviate in the large nonlinear photon-phonon interaction. It’s worth mentioning that the mean photon number and average energy in the finite-temperature tend to be consistent with the case in absolute zero temperature in the strong coupling region, while the entropy in the superradiant phase is rapidly reduced to zero as the atom-field coupling strength increases. In other words, strongly coupled collective excited states are highly ordered and are not affected by thermal fluctuations in the temperature range we are considering. The thermodynamic properties, such as the entropy and corresponding specific heat, characterize the Dicke phase transition.

Hypergraph coloring up to condensation

Improving a result of Dyer, Frieze and Greenhill [Journal of Combinatorial Theory, Series B, 2015], we determine the q‐colorability threshold in random k‐uniform hypergraphs up to an additive error of , where . The new lower bound on the threshold matches the “condensation phase transition” predicted by statistical physics considerations [Krzakala et al., PNAS 2007].

Maximum cumulant method for studying condensation-evaporation phase transitions

In a previous paper [G. J. dos Santos, D. H. Linares, and A. J. Ramirez-Pastor, J. Stat. Mech. (2017) 073211] a methodology for the determination of the critical point of the condensation phase transition occurring in monolayers of linear adsorbates ($k$-mers) was presented. The maximum cumulant method was developed from the phenomenological observation that the fourth-order Binder cumulant and the isotherm inflection point are produced at the same value of chemical potential. In the present work, mathematical arguments are presented to show analytically that the previously mentioned relationship is satisfied by evaporation-condensation systems under the conditions that: (i) the surface coverage distribution function is a bimodal distribution composed of a linear combination of two normalized functions ${g}_{1}(\ensuremath{\theta})$ and ${g}_{2}(\ensuremath{\theta})$ with zero overlap and mean values ${\ensuremath{\theta}}_{1}$ and ${\ensuremath{\theta}}_{2}$, respectively; and (ii) ${g}_{1}(\ensuremath{\theta})$ and ${g}_{2}(\ensuremath{\theta})$ are unimodal distributions that are symmetric with respect to the middle point $({\ensuremath{\theta}}_{1}+{\ensuremath{\theta}}_{2})/2$. In addition, numerical results from Monte Carlo simulations of four different adsorption-desorption systems (linear $k$-mers on square and triangular lattices, $S$-shaped $k$-mers on square lattices and ${k}^{2}$-mers on square lattices) are presented to check the theoretical results and to provide evidence of the general validity and robustness of the method.

Photon-Number-Resolved Measurement of an Exciton-Polariton Condensate.

We measure the full photon-number distribution emitted from a Bose condensate of microcavity exciton polaritons confined in a micropillar cavity. The statistics are acquired by means of a photon-number-resolving transition edge sensor. We directly observe that the photon-number distribution evolves with the nonresonant optical excitation power from geometric to quasi-Poissonian statistics, which is canonical for a transition from a thermal to a coherent state. Moreover, the photon-number distribution allows one to evaluate the higher-order photon correlations, shedding further light on the coherence formation and phase transition of the polariton condensate. The experimental data are analyzed in terms of thermal-coherent states, which gives direct access to the thermal and coherent fraction from the measured distributions. These results pave the way for a full understanding of the contribution of interactions in light-matter condensates in the coherence buildup at threshold.

Dynamical equilibration across a quenched phase transition in a trapped quantum gas

The formation of an equilibrium state from an uncorrelated thermal one through the dynamical crossing of a phase transition is a central question of quantum many-body physics. During such crossing, the system breaks its symmetry by establishing numerous uncorrelated regions separated by spontaneously generated defects, whose emergence obeys a universal scaling law with quench duration. The ensuing re-equilibrating or “coarse-graining” stage is governed by the evolution and interactions of such defects under system-specific and external constraints. We perform a detailed numerical characterisation of the entire non-equilibrium process associated with the Bose–Einstein condensation phase transition in a three-dimensional gas of ultracold atoms, addressing subtle issues and demonstrating the quench-induced decoupling of condensate atom number and coherence growth during the re-equilibration process. Our findings agree, in a statistical sense, with experimental observations made at the later stages of the quench, and provide valuable information and useful dynamical visualisations in currently experimentally inaccessible regimes.

Information-theoretic thresholds from the cavity method

Vindicating a sophisticated but non-rigorous physics approach called the cavity method, we establish a formula for the mutual information in statistical inference problems induced by random graphs and we show that the mutual information holds the key to understanding certain important phase transitions in random graph models. We work out several concrete applications of these general results. For instance, we pinpoint the exact condensation phase transition in the Potts antiferromagnet on the random graph, thereby improving prior approximate results (Contucci et al., 2013) [34]. Further, we prove the conjecture from Krzakala et al. (2007) [55] about the condensation phase transition in the random graph coloring problem for any number q≥3 of colors. Moreover, we prove the conjecture on the information-theoretic threshold in the disassortative stochastic block model (Decelle et al., 2011) [35]. Additionally, our general result implies the conjectured formula for the mutual information in Low-Density Generator Matrix codes (Montanari, 2005) [73].

The explicit expression of the fugacity for weakly interacting Bose and Fermi gases

In this paper, we calculate the explicit expression for the fugacity for two- and three-dimensional weakly interacting Bose and Fermi gases from their equations of state in isochoric and isobaric processes, respectively, based on the mathematical result of the boundary problem of analytic functions --- the homogeneous Riemann-Hilbert problem. We also discuss the Bose-Einstein condensation phase transition of three-dimensional hard-sphere Bose gases.

Universal Behavior of Quantum Spin Liquid and Optical Conductivity in the Insulator Herbertsmithite

We analyze optical conductivity with the goal to demonstrate experimental manifestation of a new state of matter, the so-called fermion condensate. Fermion condensates are realized in quantum spin liquids, exhibiting typical behavior of heavy fermion metals. Measurements of the low-frequency optical conductivity collected on the geometrically frustrated insulator herbertsmithite provide important experimental evidence of the nature of its quantum spin liquid composed of spinons. To analyze recent measurements of the herbertsmithite optical conductivity at different temperatures, we employ a model of strongly correlated quantum spin liquid located near the fermion condensation phase transition. Our theoretical analysis of the optical conductivity allows us to expose the physical mechanism of its temperature dependence. We also predict a dependence of the optical conductivity on a magnetic field. We consider an experimental manifestation (optical conductivity) of a new state of matter (so-called fermion condensate) realized in quantum spin liquids, for, in many ways, they exhibit typical behavior of heavy-fermion metals. Measurements of the low-frequency optical conductivity collected on the geometrically frustrated insulator herbertsmithite produce important experimental evidence of the nature of its quantum spin liquid composed of spinons. To analyze recent measurements of the herbertsmithite optical conductivity at different temperatures, we employ a model of strongly correlated quantum spin liquid located near the fermion condensation phase transition. Our theoretical analysis of the optical conductivity allows us to reveal the physical mechanism of its temperature dependence. We also predict a dependence of the optical conductivity on a magnetic field.

An Effective Model of QCD Monopoles

In this work, we carried out quantum many-body studies of magnetic monopole ensembles through numerical simulations of the path integral for one- and two-component Coulomb Bose systems. We found the relation between the critical temperature for the Bose-Einstein condensation phase transition and the Coulomb coupling strength using two methods, the finite-size scaling of the superfluid fraction and statistical analysis of permutation cycles. After finding parameters that match the correlation functions measured in our system with the correlation functions previously measured on the lattice, we arrived at an effective quantum model of color magnetic monopoles in QCD. From this matched model, we were able to extract the monopole contribution to QCD equation of state near Tc. This proceeding and the given talk are based on [A. Ramamurti and E. Shuryak, Phys. Rev. D 95, 076019 (2017). doi:10.1103/PhysRevD.95.076019].

Reflectance and fluorescence spectroscopy of ultrathin PTCDI-C5 films on muscovite mica

We have monitored the evolution of the optical properties of ultrathin N,N′-dipentylperylene-3,4,9,10-tetracarboxylic diimide (PTCDI-C5) molecular thin films during their growth on muscovite mica surfaces using differential reflectance spectroscopy (DRS) and fluorescence spectroscopy (FL). In the monolayer regime, the DRS shows a monomer-like absorption, whereas the FL reveals a transition from monomeric to excimer-like emission accompanied by a quenching of the intensity with the increase of coverage. The observed evolution of the FL signals can be explained by a two dimensional (2D) gas to condensed phase transition. The characteristic fluorescence of the condensed phase implies an enhancement of the intermolecular coupling and the opening of new channels for the relaxation of the excited state. The π–π stacking, which is manifested by both DR and FL spectroscopies, emergences only after the completion of the first monolayer. Finally, by analyzing the variation of the fluorescence spectrum, we have revealed the dewetting of the uncompleted PTCDI-C5 monolayer upon air exposure. This observation has been verified by atomic force microscopy (AFM).

Effective model of QCD magnetic monopoles from numerical study of one- and two-component Coulomb quantum Bose gases

Magnetic monopoles are suggested to play an important role in strongly coupled quark-gluon plasma (sQGP) near the deconfinement temperature. So far, their many-body treatment has only been done classically, with just binary scattering solved in quantum mechanics. In this paper we start quantum many-body studies of the monopole ensembles. Specifically, we carry out numerical simulations of the path integral for one- and two-component Coulomb Bose systems. We determine the relation between the critical temperature for the Bose-Einstein condensation phase transition $T_\text{c}$ and the Coulomb coupling strength using two methods, the classic finite-size scaling of the condensate and a lattice-tested method based on permutation cycles. For a one-component Coulomb Bose gas, we observe the same behavior of the critical temperature -- initially rising slightly then falling as interaction strength is increased -- as seen in the case of hard spheres; we also observe the same behavior for a two-component Coulomb Bose gas. We then calculate sets of radial correlation functions between the like and unlike charged particles. By matching those with the correlation functions previously calculated on the lattice, we derive an effective quantum model of color magnetic monopoles in QCD. From this matched model, we are able to extract the monopole contribution to QCD equation of state near $T_\text{c}$.

Dependence of in-situ Bose condensate size on final frequency of RF-field in evaporative cooling

We report the results of in-situ characterization of 87Rb atom cloud in a quadrupole Ioffe configuration (QUIC) magnetic trap after a radio-frequency (RF) evaporative cooling of the trapped atom cloud. The in-situ absorption images of the atom cloud have shown clear bimodal optical density (OD) profiles which indicate the Bose–Einstein condensation (BEC) phase transition in the trapped gas. Also, we report here, for the first time, the measured variation in the sizes of the condensate and thermal clouds with the final frequency selected in the frequency scan of the RF-field for evaporative cooling. These results on frequency-dependent sizes of the clouds are consistent with the theoretical understanding of the BEC phenomenon in the trap.