Configurational Entropy of Confined Yukawa Clusters

Confined strongly coupled systems, such as dust clusters in complex plasmas, are known to support multiple stable configurations corresponding to the same number of particles. In this work, we exploit the recently introduced concept of configurational entropy as a robust measure of the uncertainty arising due to the existence of multiple stable states with different occurrence probabilities. We apply this concept to classical Yukawa clusters of up to 100 particles in two‐ and three‐dimensional parabolic traps and investigate the dependence of the entropy on the system size, dimensionality, interparticle interaction range and anisotropy of the parabolic confinement. A universal behaviour of the configurational entropy close to the dimensional (zigzag) transition is reported (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Construction of analytical many-body wave functions for correlated bosons in a harmonic trap

We develop an analytical many-body wave function to accurately describe the crossover of a one-dimensional bosonic system from weak to strong interactions in a harmonic trap. The explicit wave function, which is based on the exact two-body states, consists of symmetric multiple products of the corresponding parabolic cylinder functions and respects the analytically known limits of zero and infinite repulsion for arbitrary number of particles. For intermediate interaction strengths we demonstrate that the energies, as well as the reduced densities of first and second order, are in excellent agreement with large scale numerical calculations.     

Configurational transitions in processes involving metal clusters

We define the configurational state of an atomic system, e.g. a cluster of metal atoms, in terms of the nuclear coordinates of a specific local minimum of the potential energy surface (PES). Three types of configurational transitions are reviewed: chemical reactions, phase transitions in clusters and catalytic chemical processes involving clusters as catalysts. The analysis of the first two cases shows that although vibrational degrees of freedom of nuclei and configurational degrees of freedom are separable in lowest order, thermal motion of nuclei nevertheless influences the rate of a configurational transition. Therefore the height of the barrier that separates configurational states of the transition for the PES differs from the effective activation energy for this transition. For example, ignoring the thermal motion of atoms in Lennard-Jones clusters leads to a predicted value of their melting points twice which accounts for the thermal motion of atoms. Hence, in determining parameters governing configurational transitions, evaluation of the PES parameters, say, within the framework of DFT (density functional theory) must be augmented by information from molecular dynamics or some other method that accounts for nuclear motion.     

Continuum fluids with a discontinuity in the pressure

A class of one-dimensional continuum fluid models is defined in which classical particles interact through translationally invariant, strongly tempered manybody potentials meeting conditions sufficient to ensure a proper thermodynamic limit. However, an exact analysis demonstrates that for certain ranges of parameter values the pressure versus density isotherms arediscontinuous. The basic models also entail discontinuous temperature versus configurational entropy isobars but extended models are described which exhibit either type of anomaly alone and various unobserved but thermodynamically allowed, anomalous types of first-order transitions.     

On the existence of the thermodynamic limit for classical systems with nonspherical potentials

It is shown, that the configurational partition function for a classical system of molecules interacting with nonspherical pair potential is proportionals to the configurational partition function for a system of particles interacting with temperature-dependent spherical k-body potentials (k ?2). Therefore, the thermodynamic limit for nonspherical molecules exists if the effective k-body interaction is stable and tempered. A number of criteria for the nonspherical potential are developed which ensure these properties. In case the nonsphericity is small in a certain sense, stability and temperedness of the angle-averaged nonspherical potential are sufficient to ensure thermodynamic behaviour.     

The Strength of First and Second Order Phase Transitions from Partition Function Zeroes

We present a numerical technique employing the density of partition function zeroes (i) to distinguish between phase transitions of first and higher order, (ii) to examine the crossover between such phase transitions and (iii) to measure the strength of first and second order phase transitions in the form of latent heat and critical exponents. These techniques are demonstrated in applications to a number of models for which zeroes are available.     

Bell-CHSH function approach to quantum phase transitions in matrix product systems

Recently, nonlocality and Bell inequalities have been used to investigate quantum phase transitions (QPTs) in low-dimensional quantum systems. Nonlocality can be detected by the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) function. In this work, we extend the study of the Bell-CHSH function (BCF) to QPTs in matrix product systems (MPSs). In these kinds of QPTs, the ground-state energy remains analytical in the vicinity of the QPT points, and they are usually called MPS-QPTs. For several typical models, our results show that the BCF can signal MPS-QPTs very well. In addition, we find the BCF can capture signal of QPTs in unentangled states and classical states, for which other measures of quantum correlation (quantum entanglement and quantum discord) fail. Furthermore, we find that in these MPSs, there exists some kind of quantum correlation which cannot be characterized by entanglement, or by nonlocality.     

Quantum phase transitions in the itinerant ferromagnet ZrZn2

We report a study of the ferromagnetism of ZrZn2, the most promising material to exhibit ferromagnetic quantum criticality, at low temperatures T as a function of pressure p. We find that the ordered ferromagnetic moment disappears discontinuously at p(c)=16.5 kbar. Thus a tricritical point separates a line of first order ferromagnetic transitions from second order (continuous) transitions at higher temperature. We also identify two lines of transitions of the magnetization isotherms up to 12 T in the p-T plane where the derivative of the magnetization changes rapidly. These quantum phase transitions (QPT) establish a high sensitivity to local minima in the free energy in ZrZn2, thus strongly suggesting that QPT in itinerant ferromagnets are always first order.     

Quantum phase transitions in mesoscopic systems

Quantum phase transitions in mesoscopic systems are studied. It is shown that the main features of phase transitions, defined for infinite number of particles, N--> infinity, persist even for moderate N approximately 10. A Landau analysis of first order transitions is done and a "critical" exponent at the spinodal point is defined. Two order parameters are introduced to distinguish first from second order transitions. Applications to atomic nuclei, molecules, atomic clusters, and finite polymers are mentioned. Experimental evidence in atomic nuclei is presented.     

The Quantum-Classical Comparison of the Arrival-Time Distribution Through the Probability Current

We consider the arrival time distribution defined through the quantum probability current for a Gaussian wave packet representing free particles in quantum mechanics in order to explore the issue of the classical limit of arrival time. We formulate the classical analogue of the arrival time distribution for an ensemble of free particles represented by a phase space distribution function evolving under the classical Liouville's equation. The classical probability current so constructed matches with the quantum probability current in the limit of minimum uncertainty. Further, it is possible to show in general that smooth transitions from the quantum mechanical probability current and the mean arrival time to their respective classical values are obtained in the limit of large mass of the particles.     

Hexagonal to square lattice conversion in bilayer systems

We report the results of extensive molecular dynamics simulations of the reconstructive hexagonal to square lattice conversion in bilayer colloid systems. Two types of interparticle potential were used to represent the colloid-colloid interactions in the suspension. One potential, due to Marcus and Rice, is designed to describe the interaction of sterically stabilized colloid particles. This potential has a term that represents the attraction between colloid particles when there is incipient overlap between the stabilizing brushes on their surfaces, a (soft repulsion) term that represents the entropy cost associated with interpenetration of the stabilizing brushes, and a term that represents core-core repulsion. The other potential we used is an almost hard core repulsion with continuous derivatives. Our results clearly show that the character of the reconstructive hexagonal to square lattice conversion in bilayer colloid systems is potential dependent. For a system with colloid-colloid interactions of the Marcus-Rice type, the packing of particles in the square array exhibits a large interlayer lattice spacing, with the particles located at the minima of the attractive well. In this case the hexagonal to square lattice transition is first order. For a system with hard core colloid-colloid interactions there are two degenerate stable intermediate phases, linear and zigzag rhombic, that are separated from the square lattice by strong first order transitions, and from the hexagonal lattice by either weak first or second order transitions.     

The penetrable sphere and related models of liquid—vapour equilibrium

The equation of state of the penetrable sphere model of liquid—vapour equilibrium is calculated by three different sequences of approximations; the first is based on the virial expansion of the equivalent two-component model in powers of the densities, the second on expansion in powers of the activity, and the third on a cumulant expansion of the configurational energy in powers of the reciprocal temperature. These sequences are examined both with the inclusion of all coefficients and with the sub-sets of coefficients appropriate to the first and second Percus-Yevick (PY) approximations. The first PY approximation gives a classical critical point whose density and temperature are accurately determined. The second PY and the complete set of coefficients yield badly-behaved series from which few conclusions can be drawn.

The penetrable sphere model is generalized to a wider class of potentials and one of these, in which the configurational energy is expressed in terms of gaussian functions is related to a two-component model of Helfand and Stillinger. It is more tractable than the original model and is examined by the same sequences of approximations. They have shown that the complete series leads to a non-classical critical point in their version of the model; here we show that the first PY approximation is classical but the second nonclassical.     

Quasi first order transitions for an n-component field in one dimension

An n-component 1-D field theoretic model exhibiting first and second transitions in the mean field approximation is studied by exact methods. In the n → ∞ limit the second order transitions are found to broaden but a line of first order transitions terminating at a critical point remains. For large but finite n, the first order transitions have a width of order exp (-const. n).     

Statistical mechanics and stability of random lattice field theory

The averaging procedure in the random lattice field theory is studied by viewing it as a statistical mechanics of a system of classical particles. The corresponding thermodynamic phase is shown to determine the random lattice configuration which contributes dominantly to the generating function. The non-abelian gauge theory in four (space plus time) dimensions in the annealed and quenched averaging versions is shown to exist as an ideal classical gas, implying that macroscopically homogeneous configurations dominate the configurational averaging. For the free massless scalar field theory with O(n) global symmetry, in the annealed average, the pressure becomes negative for dimensions greater than two when n exceeds a critical number. This implies that macroscopically inhomogeneous collapsed configurations contribute dominantly. In the quenched averaging, the collapse of the massless scalar field theory is prevented and the system becomes an ideal gas which is at infinite temperature. Our results are obtained using exact scaling analysis. We also show approximately that SU(N) gauge theory collapses for dimensions greater than four in the annealed average. Within the same approximation, the collapse is prevented in the quenched average. We also obtain exact scaling differential equations satisfied by the generating function and physical quantities.     

Critical and multicritical behavior in the Ising–Heisenberg universality class

Critical behavior of three-dimensional classical frustrated antiferromagnets with a collinear spin ordering and with an additional twofold degeneracy of the ground state is studied. We consider two lattice models, whose continuous limit describes a single phase transition with a symmetry class differing from the class of non-frustrated magnets as well as from the classes of magnets with non-collinear spin ordering. A symmetry breaking is described by a pair of independent order parameters, which are similar to order parameters of the Ising and O(N) models correspondingly. Using the renormalization group method, it is shown that a transition is of first order for non-Ising spins. For Ising spins, a second order phase transition from the universality class of the O(2) model may be observed. The lattice models are considered by Monte Carlo simulations based on the Wang–Landau algorithm. The models are a ferromagnet on a body-centered cubic lattice with the additional antiferromagnetic exchange interaction between next-nearest-neighbor spins and an antiferromagnet on a simple cubic lattice with the additional interaction in layers. We consider the cases N = 1, 2, 3 and in all of them find a first-order transition. For the N = 1 case we exclude possibilities of the second order or pseudo-first order of a transition. An almost second order transition for large N is also discussed.     

分片抛物线对流守恒重映方法

引进一种守恒的分片抛物线对流重映方法,通过交替扫描平均法提高对流重映方法的对称性,使用分片抛物线分布函数提高对流重映方法的精度.给出一维算例和二维算例检验分片抛物线对流重映方法的精度和对称性.     

A lattice-gas model with Coulomb interactions: Application to α-AgI

The pair correlation function g(r) for diffusing ions has been calculated within a lattice-gas model using the tetrahedral sites of α-AgI as lattice sites and the Ag ions as particles. The Coulomb and hard core interactions between the ions have been taken into account in the hypernetted chain approximation. Using parameters appropriate for α-AgI we find that g(r) exhibits many well pronounced oscillations extending up to about 10 nearest neighbor distances. Furthermore the direct correlation function approaches the Debye—Hückel form very rapidly beyond second nearest neighbor sites. Using g we have calculated the configurational entropy and its contribution to the specific heat as functions of the temperature. Our results are compared with experiment and computer simulations.     

Statistical mechanics of an ideal gas of non-Abelian anyons

We study the thermodynamical properties of an ideal gas of non-Abelian Chern–Simons particles and we compute the second virial coefficient, considering the effect of general soft-core boundary conditions for the two-body wavefunction at zero distance. The behaviour of the second virial coefficient is studied as a function of the Chern–Simons coupling, the isospin quantum number and the hard-core parameters. Expressions for the main thermodynamical quantities at the lower order of the virial expansion are also obtained: we find that at this order the relation between the internal energy and the pressure is the same found (exactly) for 2D Bose and Fermi ideal gases. A discussion of the comparison of obtained findings with available results in literature for systems of hard-core non-Abelian Chern–Simons particles is also supplied.     

ON THE APPROXIMATE PARTITION FUNCTION IN THE STATISTICAL THEORY OF ADSORPTION

Wang's theory for determining the approximate configurational partition function of the adsorbed layer is modified in two different ways. One is to assume that the configurational energy should be corrected: the other to advocate that the deficiency due to a wrong expression for the a priori probability of the. central site is more significant.The configurational partition function is evaluated is both methods and the adsorptipn isotherin and the beat of adsorption computed for the case of quadratic lattice With dipole interaction. values for the last two quantities when a uniform continuous distribution of the distant adsorbed particles is assumed are further given for comparison. The second method, which surpasses the first, is compared with Kirkwood's method. in the case of hexagonal lattice with neighbour interaction. Numerical work is also carried out in this case.     

Mosaic multistate scenario versus one-state description of supercooled liquids

According to the mosaic scenario, relaxation in supercooled liquids is ruled by two competing mechanisms: surface tension, opposing the creation of local excitations, and entropy, providing the drive to the configurational rearrangement of a given region. We test this scenario through numerical simulations well below the Mode Coupling temperature. For an equilibrated configuration, we freeze all the particles outside a sphere and study the thermodynamics of this sphere. The frozen environment acts as a pinning field. Measuring the overlap between the unpinned and pinned equilibrium configurations of the sphere, we can see whether it has switched to a different state. We do not find any clear evidence of the mosaic scenario. Rather, our results seem compatible with the existence of a single (liquid) state. However, we find evidence of a growing static correlation length, apparently unrelated to the mosaic one.