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1.
A general statistical model is proposed for describing network-forming systems. The model is based on the representation of
the partition function for all possible configurations of a thermoreversible network in the form of a functional integral
over a scalar field. According to this model, two types of first-order phase transitions can occur in the systems under consideration:
macroscopic phase separation with the structural phase transition due to the change in the configuration of the spatial network
and the sol-gel transition due to the formation of a thermoreversible percolation cluster consisting of bound structural units.
A detailed analysis is performed of the thermodynamic and structural properties of a solution of monomers that have f functional groups and can form thermoreversible chemical bonds. The influence of specific features of the chemical and volume
interactions on the phase diagram of the system is investigated. The mutual position of the sol-gel transition line and the
phase diagram is determined for different model parameters. It is revealed that two substantially different regimes of the
behavior of the sol-gel transition line in the “temperature-volume fraction of structural units” plane are observed with a
change in the rigidity of chemical bonds. 相似文献
2.
T. Schlathölter M.W. Newman T.R. Niedermayr G.A. Machicoane J.W. McDonald T. Schenkel R. Hoekstra A.V. Hamza 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2000,12(2):323-327
The emission of small (hydrogenated) carbon cluster ions CnHm
+
(n
=2-22) upon highly charged Xeq+ (q
=20-44) impact on C84 surfaces is studied by means of time-of-flight secondary ion mass spectrometry. The respective stage of hydrogenation/protonation
of a certain carbon cluster ion Cn
+
is a strong indication for its geometrical structure. From the cluster ion yield as a function of cluster size it can be
concluded, that the hydrogenation takes place after the initial carbon cluster formation. The carbon clusters seem to be emitted
as an entity in agreement with “equilibrium” and “shock wave” models.
Received 4 February 2000 相似文献
3.
Two-component bottle-brush polymers, where flexible side chains containing N = 20, 35 and 50 effective monomers are grafted alternatingly to a rigid backbone, are studied by Molecular Dynamics simulations,
varying the grafting density s \sigma and the solvent quality. Whereas for poor solvents and large enough s \sigma the molecular brush is a cylindrical object with monomers of different type occupying locally the two different halves of
the cylinder, for intermediate values of s \sigma an axially inhomogeneous structure of “pearl-necklace” type is formed, where microphase separation between monomers of different
type within a cluster takes place. These “pearls” have a strongly non-spherical ellipsoidal shape, due to the fact that several
side chains cluster together in one “pearl”. We discuss the resulting structures in detail and we present a comparison with
the single-component bottle-brush case. 相似文献
4.
M. V. Krasin’kova 《Technical Physics》1998,43(11):1347-1349
The question of the dimensionality of superconductivity is considered within the framework of a model of superconductivity
via asymmetric, delocalized “crystalline” π orbitals (analogous to the corresponding molecular orbitals) extending along chains of covalently bonded copper and oxygen
ions. It is shown that superconductivity is preceded by a separation of the bonds in the CuO2 layer into covalent and ionic bonds with ordering of the covalent bonds into chains. Such an ordering facilitates the formation
of a crystalline π orbital lowering the crystal energy by the resonance energy of the π bond and is therefore favored. The superconducting current is created by non-dissipative motion of π-electron pairs along the asymmetric, “crystalline” π orbitals extending along chains of covalently bonded copper and oxygen ions, in the presence of an ionic bond between neighboring
chains extending through the easily polarizable O2− ions. This ionic bond correlates the motion of the electron pairs along all the π orbitals and stabilizes the superconducting state. Only in this sense is the apparent “onedimensionality” of superconductivity
in cuprate superconductors to be understood.
Zh. Tekh. Fiz. 68, 82–84 (November 1998) 相似文献
5.
C. Borgs J. T. Chayes H. Kesten J. Spencer 《Communications in Mathematical Physics》2001,224(1):153-204
We address the question of finite-size scaling in percolation by studying bond percolation in a finite box of side length
n, both in two and in higher dimensions. In dimension d= 2, we obtain a complete characterization of finite-size scaling. In dimensions d>2, we establish the same results under a set of hypotheses related to so-called scaling and hyperscaling postulates which
are widely believed to hold up to d= 6.
As a function of the size of the box, we determine the scaling window in which the system behaves critically. We characterize
criticality in terms of the scaling of the sizes of the largest clusters in the box: incipient infinite clusters which give
rise to the infinite cluster. Within the scaling window, we show that the size of the largest cluster behaves like n
d
π
n
, where π
n
is the probability at criticality that the origin is connected to the boundary of a box of radius n. We also show that, inside the window, there are typically many clusters of scale n
d
π
n
, and hence that “the” incipient infinite cluster is not unique. Below the window, we show that the size of the largest cluster
scales like ξ
d
πξ log(n/ξ), where ξ is the correlation length, and again, there are many clusters of this scale. Above the window, we show that the
size of the largest cluster scales like n
d
P
∞, where P
∞ is the infinite cluster density, and that there is only one cluster of this scale. Our results are finite-dimensional analogues
of results on the dominant component of the Erdős–Rényi mean-field random graph model.
Received: 6 December 2000 / Accepted: 25 May 2001 相似文献
6.
Hans-Thomas Elze 《International Journal of Theoretical Physics》2007,46(8):2063-2081
We explore how energy-parity, a protective symmetry for the cosmological constant [Kaplan and Sundrum, 2005], arises naturally
in the classical phase space dynamics of matter.We derive and generalize the Liouville operator of electrodynamics, incorporating
a “varying alpha” and diffusion.In this model, a one-parameter deformation connects classical ensemble and quantum field theory.
PACS:03.65.Ta, 03.70+k, 05.20.-y 相似文献
7.
E.V. Votyakov A. De Martino D.H.E. Gross 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,29(4):593-603
We investigate the statistical equilibrium properties of a system of classical particles interacting via Newtonian gravity, enclosed in a three-dimensional spherical volume. Within a mean-field approximation, we derive an equation
for the density profiles maximizing the microcanonical entropy and solve it numerically. At low angular momenta, i.e. for a slowly rotating system, the well-known gravitational collapse “transition” is recovered. At higher angular momenta,
instead, rotational symmetry can spontaneously break down giving rise to more complex equilibrium configurations, such as
double-clusters (“double stars”). We analyze the thermodynamics of the system and the stability of the different equilibrium
configurations against rotational symmetry breaking, and provide the global phase diagram.
Received 8 July 2002 Published online 15 October 2002
RID="a"
ID="a"e-mail: demartino@hmi.de 相似文献
8.
In this paper we introduce a kind of “noncommutative neighbourhood” of a semiclassical parameter corresponding to the Planck
constant. This construction is defined as a certain filtered and graded algebra with an infinite number of generators indexed
by planar binary leaf-labelled trees. The associated graded algebra (the classical shadow) is interpreted as a “distortion”
of the algebra of classical observables of a physical system. It is proven that there exists a q-analogue of the Weyl quantization, where q is a matrix of formal variables, which induces a nontrivial noncommutative analogue of a Poisson bracket on the classical
shadow. 相似文献
9.
Y. Shimizu S. Sawada K.S. Ikeda 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》1998,4(3):365-372
“Spontaneous alloying” observed by Yasuda, Mori et al. for metallic small clusters is simulated using classical Hamiltonian dynamics. Very rapid alloying occurs homogeneously and
cooperatively starting from the solid phase of the cluster if the heat of solution is negative and the size of cluster is
less than a critical size. Analysis of 2D models reveals that the alloying rate obeys an Arrhenius-type law, which predicts
the alloying time much less than second at room temperature. Evidences manifesting that the spontaneous alloying proceeds in the solid phase without melting are
also presented. The simulation reproduces the essential features of the experiments.
Received: 2 March 1998 / Revised: 21 May 1998 / Accepted: 28 May 1998 相似文献
10.
S. O. Gladkov 《Technical Physics》1997,42(7):724-727
It is shown that the heat conduction process in a one-dimensional flow of a fluid moving with a velocity V in a constant temperature field follows a law that is considerably more complicated than an “ordinary” exponential law. It
is demonstrated that in the quasi-one-dimensional case the heat conduction process in an abstract space of dimension 1+ɛ, where ɛ varies from zero to unity, is described by a modified Fourier equation. Its solution for an infinite space is found.
Zh. Tekh. Fiz. 67, 8–12 (July 1997) 相似文献
11.
A. A. Polyakov 《JETP Letters》1997,65(8):670-675
A method is proposed for constructing a quasiperiodic structure of symmetry elements — regular pentagons and five-pointed
stars — in a plane. The growth of the structure is determined by the action of the symmetry operations, whose effect is not
completely identical to that of similar operations in classical crystallography. The tiling (“flower of pentagons”), consisting
of a central pentagon and five side pentagons joined along the edges, is studied. The growth of this tiling is accompanied
by the appearance of a “flower of stars” and by the formation of isolated pores in the form of rhombi. The relation between
the obtained structure and Penrose tiling is examined, and it is noted that some vertices of the Penrose tiling coincide with
all vertices of the polygons of the packing obtained.
Pis’ma Zh. éksp. Teor. Fiz. 65, No. 8, 635–640 (25 April 1997) 相似文献
12.
As in the ordinary bosonic Liouville field theory, in its N = 1 supersymmetric version, an infinite set of operator valued relations, the “higher equations of motions,” hold. The equations
are in one to one correspondence with the singular representations of the super Virasoro algebra and enumerated by a pair
of natural numbers (m, n). We explicitly demonstrate these equations in the classical case, where the equations of type (1, n) survive and can be interpreted directly as relations for classical fields. The general form of higher equations of motion
is established in the quantum case, both for the Neveu-Schwarz and Ramond series.
The text was submitted by the authors in English. 相似文献
13.
G. V. Shpatakovskaya 《JETP Letters》1999,70(5):334-339
A quasiclassical method for calculating shell effects, which has been used previously in atomic and plasma physics, is used
to describe electronic supershells in metal clusters. An analytical expression is obtained, in the spherical jellium model,
for the oscillating part of the binding energy of electrons of a cluster as a sum of contributions from supershells with quantum
numbers 2n
r
+l, 3n
r
+l, 4n
r
+l,... This expression is written in terms of the classical characteristics of the motion of an electron with the Fermi energy
in a self-consistent potential. The conditions under which a new supershell appears and the relative contribution of this
shell are investigated as a function of the cluster size and form of the potential. Specific calculations are performed for
a “square well” of finite depth.
Pis’ma Zh. éksp. Teor. Fiz. 70, No. 5, 333–337 (10 September 1999) 相似文献
14.
In this paper we give a logical analysis of both classical and quantum correlations. We propose a new logical system to reason
about the information carried by a complex system composed of several parts. Our formalism is based on an extension of epistemic
logic with operators for “group knowledge” (the logic GEL), further extended with atomic sentences describing the results of “joint observations” (the logic LCK). As models we introduce correlation models, as a generalization of the standard representation of epistemic models as vector models. We give sound and complete axiomatizations
for our logics, and we use this setting to investigate the relationship between the information carried by each of the parts
of a complex system and the information carried by the whole system. In particular we distinguish between the “distributed
information”, obtainable by simply pooling together all the information that can be separately observed in any of the parts,
and “correlated information”, obtainable only by doing joint observations of the parts (and pooling together the results).
Our formalism throws a new light on the difference between classical and quantum information and gives rise to an informational-logical
characterization of the notion of “quantum entanglement”. 相似文献
15.
A. A. Ovchinnikov M. Ya. Ovchinnikova E. A. Plekhanov 《Journal of Experimental and Theoretical Physics》1999,88(2):356-369
The phase diagram, nature of the normal state pseudogap, type of the Fermi surface, and behavior of the superconducting gap
in various cuprates are discussed in terms of a correlated state with valence bonds. The variational correlated state, which
is a band analogue of the Anderson (RVB) states, is constructed using local unitary transformations. Formation of valence
bonds causes attraction between holes in the d-channel and corresponding superconductivity compatible with antiferromagnetic spin order. Our calculations indicate that
there is a fairly wide range of doping with antiferromagnetic order in isolated CuO2 planes. The shape of the Fermi surface and phase transition curve are sensitive to the value and sign of the hopping interaction
t′ between diagonal neighboring sites. In underdoped samples, the dielectrization of various sections of the Fermi boundary,
depending on the sign of t′, gives rise to a pseudogap detected in photoemission spectra for various quasimomentum directions. In particular, in bismuth-and
yttrium-based ceramics (t′>0), the transition from the normal state of overdoped samples to the pseudogap state of underdoped samples corresponds to
the onset of dielectrization on the Brillouin zone boundary near k=(0,π) and transition from “large” to “small” Fermi surfaces. The hypothesis about s-wave superconductivity of La-and Nd-based ceramics has been revised: a situation is predicted when, notwithstanding the d-wave symmetry of the superconducting order parameter, the excitation energy on the Fermi surface does not vanish at all points
of the phase space owing to the dielectrization of the Fermi boundary at k
x=±
k
y. The model with orthorhombic distortions and two peaks on the curve of T
c versus doping is discussed in connection with experimental data for the yttrium-based ceramic.
Zh. éksp. Teor. Fiz. 115, 649–674 (February 1999) 相似文献
16.
A DNA molecule is simulated by an anisotropic elastic fiber which defines the configuration of the molecule central line and
is supplemented with a chain of quantum two-level systems imitating hydrogen bonds between two polynucleotide chains in the
DNA double helix. The system Hamiltonian consists of Kirchhoff’s classical elastic energy and the energy of a quantum anisotropic
chain of “spins” 1/2. The two-level systems and macroscopic vector variables which determine the conformation of the central
line are coupled by a classical vector field q, which is introduced to take into account the existence of two polynucleotide strands. Averaging over fast (microscopic)
variables yields an effective potential U(q). In the approximation of weak coupling between the systems, the spectrum of elementary excitations and effective potential
U(q) have been calculated in explicit form. The relation between elementary excitations in the “magnetic” subsystem and so-called
breathing modes [C. Mandel, N. R. Kallenbach, and S. W. Englander, J. Mol. Biol. 135, 391 (1980); G. Manning, Biopolymers 22, 689 (1983)] corresponding to low-frequency excitations in DNA molecules is discussed.
Zh. éksp. Teor. Fiz. 111, 1833–1844 (May 1997) 相似文献
17.
Normal (N) metallic (Ag) mesoscopic conductors with two superconducting (S) faces (Al), arranged mirror-symmetrically relative
to the streamlines of the current, periodically switch into the normal state as the superconducting phase difference Δϕ between
the NS boundaries approaches the values Δϕ =(2n+1)π, n=0,1,2,..., irrespective of temperature and applied voltage. For Δϕ =2nπ and low applied voltages the conductance passes through a maximum and approaches the normal value as temperature decreases
(reentrance). As the voltage subsequently increases, the conductance increases and passes through a maximum. As the phase
difference moves away from the values Δϕ=2nπ, the maxima shift in the direction of low temperatures and voltages. The latter result shows unequivocally that in our metal
structures it is necessary to take into account the next-order corrections to the “weak” proximity effect approximation.
Pis’ma Zh. éksp. Teor. Fiz. 67, No. 7, 489–494 (10 April 1998) 相似文献
18.
We consider a melt of cyclic polymers (N monomers per chain) containing a small volume fraction ϕ of open cycles (P monomers
per chain, with P< N) with reactive ends. The reaction leads to the formation of small P-rings. If these P-rings trap a sufficient
number ofN-rings, a macroscopic cluster (“Olympic” gel) will appear. Using a very primitive theory (where the statistics of knots is
replaced by a statistics of proximity), we expect gelation to occur when ϕ > max P1/2/N,(1/N) exp(const/P). Our study is restricted to N-rings that are small enough for their conformations to be Gaussian. 相似文献
19.
A vibronic charge-transfer exciton, which is a pair of Jahn-Teller electron and hole polarons, is considered as a possible
cause of the appearance of the Müller phase in the virtual ferroelectric SrTiO3 and the “green” luminescence in the virtual ferroelectric KTaO3. The two “green” luminescence bands can be associated with emission from two states of a typical intrinsic defect, viz.,
a vibronic charge-transfer exciton trapped by an oxygen vacancy and an isolated vibronic charge-transfer exciton. In both
cases the “green” luminescence corresponds to the recombination of the electron and the hole in the vibronic charge-transfer
exciton, which is accompanied by the emission of light. The properties of the Müller phase can be attributed to mixing of
the normal state and states of the vibronic charge-transfer exciton phase when they interact with polarization in the soft
SrTiO3 matrix under the conditions of a pseudo-Jahn-Teller (pseudo-JT) effect on a soft TO mode of the displacement type. In this
case the vibronic charge-transfer exciton phase forming the low-lying excited states has “order-disorder” degrees of freedom
and exists at temperatures significantly below the point of the order-disorder ferroelectric transition in SrTiO3 at T=T
Q≈37 K. The corresponding lowering of the symmetry of the vibronic charge-transfer exciton phase to polar symmetry leads to
the possibility of a long-period incommensurate phase in such excited states, which arises as a result of the appearance of
a Lifshitz invariant. The valence-band state making the largest contribution of the pseudo-JT effect corresponds to a wave
vector equal to the critical wave vector of the incommensurate vibronic charge-transfer exciton phase. When the temperature
is lowered, the pseudo-JT distortion increases down to ∼T
Q and subsequently saturates in accordance with the saturation of the dielectric constant. The basic assumption in the model
is that the temperature T=T
Q corresponds to the narrow temperature range for the transition from an intermediate to a strong pseudo-JT effect under the
conditions for the realization of polarization tunneling states. The appearance of a significant admixture of states of the
modulated ferroelectric vibronic charge-transfer exciton phase to the ground state under the conditions for the realization
of polarization tunneling states at low temperatures provides an explanation for the principal properties of the Müller phase.
Fiz. Tverd. Tela (St. Petersburg) 40, 907–909 (May 1998) 相似文献
20.
G. E. Astrakharchik A. I. Belousov Yu. E. Lozovik 《Journal of Experimental and Theoretical Physics》1999,89(4):696-703
A two-dimensional mesoscopic cluster of “dusty plasma” particles, which can be interpreted as a system of microparticles in
an rf gas discharge, is investigated. The ground-state configurations and corresponding eigenfrequencies and eigenvectors
are found for clusters of N=22–40 particles in a harmonic confining potential. It is shown that a change in the Debye screening length R of the particle charge in the plasma can cause structural transformations of the ground state of the system, manifested as
first-order or second-order phase transitions with respect to the parameter R. The disorder (“melting”) of the clusters is analyzed in detail by Monte Carlo simulation and molecular dynamics. By varying
the characteristic range of particle interaction in a cluster, it is possible to modulate its thermodynamic properties and
the character of the phase transitions, thereby causing a controlled transition of the system into the fully ordered, orientationally
disordered, or fully disordered state. The possibility of dusty plasma clusters coexisting in different states is discussed.
Zh. éksp. Teor. Fiz. 116, 1300–1312 (October 1999) 相似文献