共查询到20条相似文献,搜索用时 31 毫秒
1.
The partition function zeros of the anisotropic XY chain in a complex transverse field are studied analytically and numerically. It is found that the partition function zeros of the periodic and quasiperiodic quantum Ising chain lie on the circle at zero temperature and the radius equal to the values of the critical field. For the periodic and quasiperiodic anisotropic XY chains, the closed curves are split to two or three closed curves as the anisotropic parameter gamma decreases at a given ratio of two kinds of exchange interactions. For the isotropic XX case, the partition function zeros lie on the straight segments which are parallel to the real axis and the segments move towards the real axis as the temperature goes to zero. 相似文献
2.
The structural and thermodynamic properties of a matrix model of homo-RNA folding with linear external interaction are studied.
The interaction distinguishes paired bases of the homo-RNA chain from the unpaired bases hence dividing the possible RNA structures
given by the linear model into two structural regimes. The genus distribution functions show that the total number of structures
for any given length of the chain are reduced for the simple linear interaction considered. The partition function of the
model exhibits a scaling relation with the matrix model in which the base pairing strength parameter is re-scaled (G. Vernizzi,
H. Orland, A. Zee, Phys. Rev. Lett. 94, 168103 (2005)). The thermodynamics of the model are computed for i) largely secondary structures, (with tertiary structures
suppressed by a factor 10-4) and ii) secondary plus tertiary structures. A structural change for large even lengths is observed in the free energy and
specific heat. This change with largely secondary structures appears much before (with respect to length of the chain) than
when all the structures (secondary and pseudoknots) are considered. The appearance of different structures which dominate
the ensemble with varying temperatures is also found as a function of the interaction parameter for different types of structures
(given by different numbers of pairings). 相似文献
3.
Emil J. Martinec 《Communications in Mathematical Physics》1991,138(3):437-449
The matrix integrals involved in 2d lattice gravity are studied at finiteN. The integrable systems that arise in the continuum theory are shown to result directly from the formulation of the matrix integrals in terms of orthogonal polynomials. The partition function proves to be a tau function of the Toda lattice hierarchy. The associated linear problem is equivalent to finding the polynomial basis which diagonalizes the partition function. The cases of one Hermitian matrix, one unitary matrix, and Hermitian matrix chains all fall within the Toda framework.Research supported in part by DOE contract DE-FG02-90ER-40560, an NSF Presidential Young Investigator Award, and the Alfred P. Sloan Foundation 相似文献
4.
Using the Feynman's path integral with topological constraints arising from the presence of one singular line, we find the homotopic probability distribution PLn for the winding number n and the partition function PL of the entangled system around a ribbon segment chain. We find that when the width of the ribbon segment chain 2a increases,the partition function exponentially decreases, whereas the free energy increases an amount, which is proportional to the square of the width. When the width tends to zero we obtain the same results as those of a single chain with one singular point. 相似文献
5.
We introduce a model for semiflexible polymer chains based on the integral of an appropriate Gaussian process. The stiffness
is characterized physically by adding a bending energy. The degree of stiffness in the polymer chain is quantified by means
of a parameter and as this parameter tends to infinity, the limiting case reduces to the Brownian model of completely flexible
chains studied in earlier work. The calculation of the partition function for the configuration statistical mechanics (i.e.,
the distribution of shapes) of such polymers in elongational flow or quadratic potentials is equivalent to the probabilistic
problem of finding the law of a quadratic functional of the associated Gaussian process. An exact formula for the partition
function is presented; however, in practice, this formula is too complicated for most computations. We therefore develop an
asymptotic expansion for the partition function in terms of the stiffness parameter and obtain the first-order term which
gives the first-order deviation from the completely flexible case. In addition to the partition function, the method presented
here can also deal with other quadratic functionals such as the “stochastic area” associated with two polymer chains. 相似文献
6.
G.N. Katomeris S.N. Evangelou 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,16(1):133-136
We examine the validity of the recently proposed semi-Poisson level spacing distribution function P(S), which characterizes “critical quantum chaos”, in 2D disordered systems with spin-orbit coupling. At the Anderson transition
we show that the semi-Poisson P(S) can describe closely the critical distribution obtained with averaged boundary conditions, over Dirichlet in one direction
with periodic in the other and Dirichlet in both directions. We also obtain a sub-Poisson linear number variance , with asymptotic value . The obtained critical statistics, intermediate between Wigner and Poisson, is discussed for disordered systems and chaotic
models.
Received 1 September 1999 相似文献
7.
We define the partition and n-point functions for a vertex operator algebra on a genus two Riemann surface formed by sewing two tori together. We obtain
closed formulas for the genus two partition function for the Heisenberg free bosonic string and for any pair of simple Heisenberg
modules. We prove that the partition function is holomorphic in the sewing parameters on a given suitable domain and describe
its modular properties for the Heisenberg and lattice vertex operator algebras and a continuous orbifolding of the rank two
fermion vertex operator super algebra. We compute the genus two Heisenberg vector n-point function and show that the Virasoro vector one point function satisfies a genus two Ward identity for these theories. 相似文献
8.
We consider the adsorption of an isolated, Gaussian, random, and quenched copolymer chain at an interface. We first propose
a simple analytical method to obtain the adsorption/depletion transition, by averaging over the disorder the partition function
instead of the free energy. The adsorption thresholds obtained by previous authors at a solid/liquid and at a liquid/liquid
interface for multicopolymer chains can be rederived using this method. We also compare the adsorption thresholds obtained
for bimodal and for Gaussian disorder; they only agree for small disorder. We focus on the specific case of an ideally flat
asymmetric liquid/liquid interface, and consider the situation where the chain is composed of monomers of two different chemical
species A and B. The replica method is developed for this case. We show that the Hartree approximation, coupled to a replica symmetry assumption,
leads to the same adsorption thresholds as obtained from our general method. In order to describe the properties of the adsorbed
(or depleted) chain, we develop a new approximation for long chains, within the framework of the replica theory. In most cases,
the behavior of a random copolymer chain can be mapped onto that of a homopolymer chain at an asymmetric attractive interface.
The values of the effective adsorption energy are different for a random and a periodic copolymer chain. Finally, we consider
the case of uncorrelated annealed disorder. The behavior of an annealed chain can be mapped onto that of a homopolymer chain
at an asymmetric non attractive interface; hence, an annealed chain cannot adsorb at an asymmetric interface.
Received 21 January 1999 相似文献
9.
We define the partition and n-point correlation functions for a vertex operator superalgebra on a genus two Riemann surface formed by sewing two tori together.
For the free fermion vertex operator superalgebra we obtain a closed formula for the genus two continuous orbifold partition
function in terms of an infinite dimensional determinant with entries arising from torus Szegő kernels. We prove that the
partition function is holomorphic in the sewing parameters on a given suitable domain and describe its modular properties.
Using the bosonized formalism, a new genus two Jacobi product identity is described for the Riemann theta series. We compute
and discuss the modular properties of the generating function for all n-point functions in terms of a genus two Szegő kernel determinant. We also show that the Virasoro vector one point function
satisfies a genus two Ward identity. 相似文献
10.
首先建立起玻色-爱因斯坦凝聚孤子链的微扰复数Toda链理论,然后深入研究玻色-爱因斯坦凝聚N-孤子间的绝热相互作用,分别通过对二次外势场、周期性外势场和二者叠加的复合外势场所引起的三类微扰,利用微扰的复数Toda链理论给出了解析处理, 并和基于分步傅里叶变换的直接数值方法进行比较,发现微扰的复数Toda链方程能够充分揭示上述三类外势场中的N-孤子链的动力学行为和特征.同时还给出了从孤子链中提取一个或多个局域态的倾斜势场或周期性势场的强度临界值,这可为玻色-爱因斯坦凝聚的实验研究
关键词:
玻色-爱因斯坦凝聚
Gross-Pitaevskii方程
物质波孤子
相互作用 相似文献
11.
In this paper we study Inozemtsev's su(m) quantum spin model with hyperbolic interactions and the associated spin chain of Haldane–Shastry type introduced by Frahm and Inozemtsev. We compute the spectrum of Inozemtsev's model, and use this result and the freezing trick to derive a simple analytic expression for the partition function of the Frahm–Inozemtsev chain. We show that the energy levels of the latter chain can be written in terms of the usual motifs for the Haldane–Shastry chain, although with a different dispersion relation. The formula for the partition function is used to analyze the behavior of the level density and the distribution of spacings between consecutive unfolded levels. We discuss the relevance of our results in connection with two well-known conjectures in quantum chaos. 相似文献
12.
13.
The Ising partition function for a graph counts the number of bipartitions of the vertices with given sizes, with a given size of the induced edge cut. Expressed as a 2-variable generating function it is easily translatable into the corresponding partition function studied in statistical physics. In the current paper a comparatively efficient transfer matrix method is described for computing the generating function for the n×n grid with periodic boundary. We have applied the method to up to the 15×15 grid, in total 225 vertices. We examine the phase transition that takes place when the edge cut reaches a certain critical size. From the physical partition function we extract quantities such as magnetisation and susceptibility and study their asymptotic behaviour at the critical temperature. 相似文献
14.
S. Franz T. Garel H. Orland 《The European Physical Journal B - Condensed Matter and Complex Systems》1999,11(3):463-468
We consider a model of two (fully) compact polymer chains, coupled through an attractive interaction. These compact chains
are represented by Hamiltonian paths (HP), and the coupling favors the existence of common bonds between the chains. We use
a (n=0 component) spin representation for these paths, and we evaluate the resulting partition function within a homogeneous saddle
point approximation. For strong coupling (i.e. at low temperature), one finds a phase transition towards a “frozen” phase where one chain is completely adsorbed onto the
other. By performing a Legendre transform, we obtain the probability distribution of overlaps. The fraction of common bonds
between two HP, i.e. their overlap q, has both lower () and upper () bounds. This means in particular that two HP with overlap greater than coincide. These results may be of interest in (bio)polymers and in optimization problems.
Received 4 December 1998 and Received in final form 10 March 1999 相似文献
15.
M. Biskup C. Borgs J.T. Chayes L.J. Kleinwaks R. Kotecký 《Communications in Mathematical Physics》2004,251(1):79-131
We present a general, rigorous theory of partition function zeros for lattice spin models depending on one complex parameter. First, we formulate a set of natural assumptions which are verified for a large class of spin models in a companion paper [5]. Under these assumptions, we derive equations whose solutions give the location of the zeros of the partition function with periodic boundary conditions, up to an error which we prove is (generically) exponentially small in the linear size of the system. For asymptotically large systems, the zeros concentrate on phase boundaries which are simple curves ending in multiple points. For models with an Ising-like plus-minus symmetry, we also establish a local version of the Lee-Yang Circle Theorem. This result allows us to control situations when in one region of the complex plane the zeros lie precisely on the unit circle, while in the complement of this region the zeros concentrate on less symmetric curves.Reproduction of the entire article for non-commercial purposes is permitted without charge. 相似文献
16.
A continuous-time Markov chain is used to model motion in the neighborhood of a critical invariant circle for a Hamiltonian map. States in the infinite chain represent successive rational approximants to the frequency of the invariant circle. For the case of a noble frequency, the chain is self-similar and the nonlinear integral equation for the first passage time distribution is solved exactly. The asymptotic distribution is a power law times a function periodic in the logarithm of the time. For parameters relevant to the critical noble circle, the decay proceeds ast
–4.05. 相似文献
17.
Bifurcation analysis of dust acoustic (DA) periodic waves in three components, unmagnetized dusty plasma system is investigated using the generalized (r, q) distribution function for ions and electrons. Depending on the different parameters of the system considered, all possible phase portraits, including periodic, homoclinic, superperiodic, and superhomoclinic trajectories, are presented. The existence of rarefactive and compressive solitary waves is proved. Also, the plasma system under consideration supports both nonlinear and supernonlinear DA periodic waves. It has been found that the double spectral indices r and q play a decisive effect on the bifurcation of the waves. 相似文献
18.
We consider the Ising model on a rooted Cayley tree of order two with nearest neighbor interactions and competing next nearest neighbor interactions restricted to spins belonging to the same branch of the tree. This model was studied by Vannimenus who found a new modulated phase, in addition to the paramagnetic, ferromagnetic, antiferromagnetic phases and a (+ + - -) periodic phase. Vannimenus’s results are based on an analysis of the recurrence equations (relating the partition function of an n ? generation tree to the partition function of its subsystems containing (n ?1) generations) and most results are obtained numerically. In this paper we analytically study the recurrence equations and obtain some exact results: critical temperatures and curves, number of phases, partition function. 相似文献
19.
Gyan Bhanot 《Journal of statistical physics》1990,60(1-2):55-75
I present a new method to exactly compute the partition function of a class of discrete models in arbitrary dimensions. The time for the computation for ann-state model on anL
d
lattice scales like
. I show examples of the use of this method by computing the partition function of the 2D Ising and 3-state Potts models for maximum lattice sizes 10×10 and 8×8, respectively. The critical exponentsv and and the critical temperature one obtains from these are very near the exactly known values. The distribution of zeros of the partition function of the Potts model leads to the conjecture that the ratio of the amplitudes of the specific heat below and above the critical temperature is unity. 相似文献
20.
Makoto Oonuki 《Journal of statistical physics》1972,6(2-3):119-131
The time characteristics of a linear network in the brain are obtained by the method of the time partition function, which is analogous to a grand partition function or a distribution function in statistical mechanics. The analogy between the average density in a many-particle system and the reciprocal of the frequency in a network is shown. By this method, the frequency distribution functions are obtained with respect to a network composed of two layers, the network used in information retrieval and the network generating a brain wave. 相似文献