共查询到20条相似文献,搜索用时 265 毫秒
1.
LetQ n β be the law of then-step random walk on ?d obtained by weighting simple random walk with a factore ?β for every self-intersection (Domb-Joyce model of “soft polymers”). It was proved by Greven and den Hollander (1993) that ind=1 and for every β∈(0, ∞) there exist θ*(β)∈(0,1) and such that under the lawQ n β asn→∞: $$\begin{array}{l} (i) \theta ^* (\beta ) is the \lim it empirical speed of the random walk; \\ (ii) \mu _\beta ^* is the limit empirical distribution of the local times. \\ \end{array}$$ A representation was given forθ *(β) andµ β β in terms of a largest eigenvalue problem for a certain family of ? x ? matrices. In the present paper we use this representation to prove the following scaling result as β?0: $$\begin{array}{l} (i) \beta ^{ - {\textstyle{1 \over 3}}} \theta ^* (\beta ) \to b^* ; \\ (ii) \beta ^{ - {\textstyle{1 \over 3}}} \mu _\beta ^* \left( {\left\lceil { \cdot \beta ^{ - {\textstyle{1 \over 3}}} } \right\rceil } \right) \to ^{L^1 } \eta ^* ( \cdot ) . \\ \end{array}$$ The limitsb *∈(0, ∞) and are identified in terms of a Sturm-Liouville problem, which turns out to have several interesting properties. The techniques that are used in the proof are functional analytic and revolve around the notion of epi-convergence of functionals onL 2(?+). Our scaling result shows that the speed of soft polymers ind=1 is not right-differentiable at β=0, which precludes expansion techniques that have been used successfully ind≧5 (Hara and Slade (1992a, b)). In simulations the scaling limit is seen for β≦10?2. 相似文献
2.
Let $\mathcal {A}_{2}(t)$ be the Airy2 process. We show that the random variable $$\sup_{t\leq\alpha} \bigl\{\mathcal {A}_2(t)-t^2 \bigr\}+\min\{0,\alpha \}^2 $$ has the same distribution as the one-point marginal of the Airy2→1 process at time α. These marginals form a family of distributions crossing over from the GUE Tracy-Widom distribution F GUE(x) for the Gaussian Unitary Ensemble of random matrices, to a rescaled version of the GOE Tracy-Widom distribution F GOE(41/3 x) for the Gaussian Orthogonal Ensemble. Furthermore, we show that for every α the distribution has the same right tail decay $e^{-\frac{4}{3} x^{3/2} }$ . 相似文献
3.
Oliver A. McBryan 《Communications in Mathematical Physics》1978,61(3):275-284
We exhibit the λ? 2 4 quantum field theory as the limit of Sine-Gordon fields as suggested by the identity $$\varphi ^4 /4! = \mathop {\lim }\limits_{\varepsilon \to 0} (\varepsilon ^{ - 4} \cos \varepsilon \varphi - \varepsilon ^{ - 4} + \tfrac{1}{2}\varepsilon ^{ - 2} \varphi ^2 ).$$ The proofs of finite volume stability for the two models, due to Nelson and Fröhlich respectively, are unrelated. We find a generalized stability argument that incorporates ideas from both of the simpler cases. The above limit, for the Schwinger functions, then proceeds uniformly in ?. As a by-product, let (?,dμ) be a Gaussian random field, ? K (1≦κ<∞) a regularization of ?, andV a function satisfying:
- V(? K )≧?ak α
- ∥V(?) ?V(? K )∥ p≦bp β k ?γ, 2≦p < ∞
4.
E. Caglioti P. L. Lions C. Marchioro M. Pulvirenti 《Communications in Mathematical Physics》1992,143(3):501-525
We consider the canonical Gibbs measure associated to aN-vortex system in a bounded domain Λ, at inverse temperature \(\widetilde\beta \) and prove that, in the limitN→∞, \(\widetilde\beta \) /N→β, αN→1, where β∈(?8π, + ∞) (here α denotes the vorticity intensity of each vortex), the one particle distribution function ?N = ? N x,x∈Λ converges to a superposition of solutions ? α of the following Mean Field Equation: $$\left\{ {\begin{array}{*{20}c} {\varrho _{\beta (x) = } \frac{{e^{ - \beta \psi } }}{{\mathop \smallint \limits_\Lambda e^{ - \beta \psi } }}; - \Delta \psi = \varrho _\beta in\Lambda } \\ {\psi |_{\partial \Lambda } = 0.} \\ \end{array} } \right.$$ Moreover, we study the variational principles associated to Eq. (A.1) and prove thai, when β→?8π+, either ?β → δ x 0 (weakly in the sense of measures) wherex 0 denotes and equilibrium point of a single point vortex in Λ, or ?β converges to a smooth solution of (A.1) for β=?8π. Examples of both possibilities are given, although we are not able to solve the alternative for a given Λ. Finally, we discuss a possible connection of the present analysis with the 2-D turbulence. 相似文献
5.
Let μ be the measure onI′ (? d ) corresponding to the Gaussian process with mean zero and covariance (f,(?Δ+1)?1 g) onI (? d ). It is proven that the set $$( - \Delta _{d - 1} + 1)^{d/4 - \tfrac{1}{2} + \alpha } (1 + x^2 )^{d/4} [\log (2 + x^2 )]^\beta L^2 (\mathbb{R}^d )$$ has μ measure one if α>0 and β>1/2 and μ measure zero if α>0 and β<1/2; here Δ d?1 is the Laplacian in anyd?1 dimensions whend>1 and Δ0=Δ. 相似文献
6.
We prove the simplicity and analyticity of the eigenvalues of the cubic oscillator Hamiltonian, $$\begin{array}{ll}H(\beta)=-\frac{d^2}{dx^2}+x^2+i\sqrt{\beta}x^3\end{array}$$ , for β in the cut plane ${\mathcal{C}_c:=\mathcal{C}\backslash \mathcal{R}_-}$ . Moreover, we prove that the spectrum consists of the perturbative eigenvalues {E n (β)} n ≥ 0 labeled by the constant number n of nodes of the corresponding eigenfunctions. In addition, for all ${\beta \in \mathcal{C}_c, E_n(\beta)}$ can be computed as the Stieltjes-Padé sum of its perturbation series at β = 0. This also gives an alternative proof of the fact that the spectrum of H(β) is real when β is a positive number. This way, the main results on the repulsive PT-symmetric and on the attractive quartic oscillators are extended to the cubic case. 相似文献
7.
The general theory of inhomogeneous mean-field systems of Raggio and Werner provides a variational expression for the (almost sure) limiting free energy density of the Hopfield model $$H_{N,p}^{\{ \xi \} } (S) = - \frac{1}{{2N}}\sum\limits_{i,j = 1}^N {\sum\limits_{\mu = 1}^N {\xi _i^\mu \xi _j^\mu S_i S_j } } $$ for Ising spinsS i andp random patterns ξμ=(ξ 1 μ ,ξ 2 μ ,...,ξ N μ ) under the assumption that $$\mathop {\lim }\limits_{N \to \gamma } N^{ - 1} \sum\limits_{i = 1}^N {\delta _{\xi _i } = \lambda ,} \xi _i = (\xi _i^1 ,\xi _i^2 ,...,\xi _i^p )$$ exists (almost surely) in the space of probability measures overp copies of {?1, 1}. Including an “external field” term ?ξ μ p hμμξ i=1 N ξ i μ Si, we give a number of general properties of the free-energy density and compute it for (a)p=2 in general and (b)p arbitrary when λ is uniform and at most the two componentsh μ1 andh μ2 are nonzero, obtaining the (almost sure) formula $$f(\beta ,h) = \tfrac{1}{2}f^{ew} (\beta ,h^{\mu _1 } + h^{\mu _2 } ) + \tfrac{1}{2}f^{ew} (\beta ,h^{\mu _1 } - h^{\mu _2 } )$$ for the free energy, wheref cw denotes the limiting free energy density of the Curie-Weiss model with unit interaction constant. In both cases, we obtain explicit formulas for the limiting (almost sure) values of the so-called overlap parameters $$m_N^\mu (\beta ,h) = N^{ - 1} \sum\limits_{i = 1}^N {\xi _i^\mu \left\langle {S_i } \right\rangle } $$ in terms of the Curie-Weiss magnetizations. For the general i.i.d. case with Prob {ξ i μ =±1}=(1/2)±?, we obtain the lower bound 1+4?2(p?1) for the temperatureT c separating the trivial free regime where the overlap vector is zero from the nontrivial regime where it is nonzero. This lower bound is exact forp=2, or ε=0, or ε=±1/2. Forp=2 we identify an intermediate temperature region between T*=1?4?2 and Tc=1+4?2 where the overlap vector is homogeneous (i.e., all its components are equal) and nonzero.T * marks the transition to the nonhomogeneous regime where the components of the overlap vector are distinct. We conjecture that the homogeneous nonzero regime exists forp≥3 and that T*=max{1?4?2(p?1),0}. 相似文献
8.
We estimate $BR(K \to \pi \nu \bar \nu )$ in the context of the Standard Model by fitting for λ t≡V tdV ts * of the “kaon unitarity triangle” relation. To find the vertex of this triangle, we fit data from |? K|, the CP-violating parameter describing K mixing, and a ψ,K , the CP-violating asymmetry in B d 0 → J/ψK 0 decays, and obtain the values $\left. {BR(K \to \pi \nu \bar \nu )} \right|_{SM} = (7.07 \pm 1.03) \times 10^{ - 11} $ and $\left. {BR(K_L^0 \to \pi ^0 \nu \bar \nu )} \right|_{SM} = (2.60 \pm 0.52) \times 10^{ - 11} $ . Our estimate is independent of the CKM matrix element V cb and of the ratio of B-mixing frequencies ${{\Delta m_{B_s } } \mathord{\left/ {\vphantom {{\Delta m_{B_s } } {\Delta m_{B_d } }}} \right. \kern-0em} {\Delta m_{B_d } }}$ . We also use the constraint estimation of λ t with additional data from $\Delta m_{B_d } $ and |V ub|. This combined analysis slightly increases the precision of the rate estimation of $K^ + \to \pi ^ + \nu \bar \nu $ and $K_L^0 \to \pi ^0 \nu \bar \nu $ (by ?10 and ?20%, respectively). The measured value of $BR(K^ + \to \pi ^ + \nu \bar \nu )$ can be compared both to this estimate and to predictions made from ${{\Delta m_{B_s } } \mathord{\left/ {\vphantom {{\Delta m_{B_s } } {\Delta m_{B_d } }}} \right. \kern-0em} {\Delta m_{B_d } }}$ . 相似文献
9.
V. Rabinovich 《Russian Journal of Mathematical Physics》2013,20(4):508-522
We consider a diffraction problem in a multi-connected domain ?2 \ Γ, where Γ is an oriented graph with finitely many edges some of which are infinite. The problem is described by the Helmholtz equation (1) $\mathcal{H}u(x) = \rho (x)\nabla \cdot \rho ^{ - 1} (x)\nabla u(x) + k^2 (x)u(x) = 0,x \in \mathbb{R}^2 \backslash \Gamma ,$ where ρ and k are functions bounded together with all derivatives, and by the transmission conditions (2) $u_ + (t) - u_ - (t) = 0,t \in \Gamma \backslash \mathcal{V},$ (3) $a_ + (t)(\partial u/\partial n_t )_ + (t) - a_ - (t)(\partial u/\partial n_t )_ - (t) + a_0 (t)u(t) = f(t),t \in \Gamma \backslash \mathcal{V},$ where V is the set of vertices, a ± and a 0 are functions bounded on Γ, slowly oscillating discontinuous at the vertices in V, and slowly oscillating at infinity, and f ∈ L 2(Γ). Using Green’s function for the Helmholtz operator H, we introduce simple- and double-layer potentials and reduce the diffraction problem (1)–(3) to a boundary integral equation. The main objective of the paper is to study the essential spectrum, the Fredholm property, and the index of boundary operators on Γ associated with the problem (1)–(3). 相似文献
10.
11.
I. Alfter E. Bodenstedt W. Knichel J. Schüth R. Vianden 《Zeitschrift für Physik A Hadrons and Nuclei》1996,355(1):363-376
g-factors of rotational states in176Hf and180Hf were measured with the twelve detector IPAC-apparatus of our laboratory [1]. The natural radioactivity 3.78·1010y176Lu and the 5.5 h isomer180mHf were used which populate the ground-state rotational bands of176Hf and180Hf. The integral rotations ofγ-γ directional correlations in strong external magnetic fields and in static hyperfine fields of (Lu→Hf)Fe2 and HfFe2 were observed. The following results were obtained: $$\begin{array}{l} ^{176} Hf: g\left( {4_1^ + } \right) = + 0.334\left( {38} \right) \\ ^{180} Hf: g\left( {2_1^ + } \right) = + 0.305\left( {14} \right) \\ g\left( {4_1^ + } \right) = + 0.358\left( {43} \right) \\ {{ g\left( {6_1^ + } \right)} \mathord{\left/ {\vphantom {{ g\left( {6_1^ + } \right)} {g\left( {4_1^ + } \right)}}} \right. \kern-\nulldelimiterspace} {g\left( {4_1^ + } \right)}} = + 0.95\left( {12} \right) \\ \end{array}$$ . The hyperfine field in (Lu→Hf)Fe2 was calibrated by observing the integral rotation of the 9/2? first excited state of177Hf populated in the decay of 6.7d177Lu. Theg-factor of this state was redetermined in an external magnetic field as $$^{177} Hf: g\left( {{9 \mathord{\left/ {\vphantom {9 {2^ - }}} \right. \kern-\nulldelimiterspace} {2^ - }}} \right) = + 0.228\left( 7 \right)$$ . Finally theg-factor of the 2 1 + state of176Hf was derived from the measuredg(2 1 + ) of180Hf by use of the precisely known ratiog(2 1 + ,176Hf)/g(2 1 + ,180Hf) [2] as $$^{176} Hf: g\left( {2_1^ + } \right) = + 0.315\left( {30} \right)$$ . 相似文献
12.
David Gurarie 《Communications in Mathematical Physics》1987,112(3):491-502
We study perturbationsL=A+B of the harmonic oscillatorA=1/2(??2+x 2?1) on ?, when potentialB(x) has a prescribed asymptotics at ∞,B(x)~|x|?α V(x) with a trigonometric even functionV(x)=Σa mcosω m x. The eigenvalues ofL are shown to be λ k =k+μ k with small μ k =O(k ?γ), γ=1/2+1/4. The main result of the paper is an asymptotic formula for spectral fluctuations {μ k }, $$\mu _k \sim k^{ - \gamma } \tilde V(\sqrt {2k} ) + c/\sqrt {2k} ask \to \infty ,$$ whose leading term \(\tilde V\) represents the so-called “Radon transform” ofV, $$\tilde V(x) = const\sum {\frac{{a_m }}{{\sqrt {\omega _m } }}\cos (\omega _m x - \pi /4)} .$$ as a consequence we are able to solve explicitly the inverse spectral problem, i.e., recover asymptotic part |x ?α|V(x) ofB from asymptotics of {µ k }. 1 ∞ 相似文献
13.
F. Merle 《Communications in Mathematical Physics》1992,149(2):377-414
We consider the solutionu ?(t) of the saturated nonlinear Schrödinger equation (1) $$i\partial u/\partial t = - \Delta u - \left| u \right|^{4/N} u + \varepsilon \left| u \right|^{q - 1} uandu(0,.) = \varphi (.)$$ where \(N \geqslant 2,\varepsilon > 0,1 + 4/N< q< (N + 2)/(N - 2),u:\mathbb{R} \times \mathbb{R}^N \to \mathbb{C},\varphi \) , ? is a radially symmetric function inH 1(R N ). We assume that the solution of the limit equation is not globally defined in time. There is aT>0 such that \(\mathop {\lim }\limits_{t \to T} \left\| {u(t)} \right\|_{H^1 } = + \infty \) , whereu(t) is solution of (1) $$i\partial u/\partial t = - \Delta u - \left| u \right|^{4/N} uandu(0,.) = \varphi (.)$$ For ?>0 fixed,u ?(t) is defined for all time. We are interested in the limit behavior as ?→0 ofu ?(t) fort≥T. In the case where there is no loss of mass inu ? at infinity in a sense to be made precise, we describe the behavior ofu ? as ? goes to zero and we derive an existence result for a solution of (1) after the blow-up timeT in a certain sense. Nonlinear Schrödinger equation with supercritical exponents are also considered. 相似文献
14.
V. N. Folomeshkin 《International Journal of Theoretical Physics》1974,10(3):145-151
It is shown that a coordinate system with simple coordinate conditions can be chosen such that one can explicitly see that the Schwarzschildian mass of an asymptotically Euclidian time-symmetrical system of gravitational waves is equal to zero. It is explicitly seen in the coordinate system with coordinate conditions ? i (?gg ik)=0 and in the set of coordinate systems with the coordinate condition ? i (?gg 0i )=0. In this set of coordinate systems one of the field equations can be written in the form \( - 8\pi \surd ( - g)(T_0^0 - \tfrac{1}{2}T) = \partial _\alpha L_0^{0\alpha } \) where \(L_i^{kn} = \tfrac{1}{2}\surd ( - g)(g^{mn} \Gamma _{im}^k - g^{km} \Gamma _{im}^k )\) , α=1, 2, 3. From this equation it follows that \(m = 2\smallint ({\rm T}_0^0 - \tfrac{1}{2}T)\surd ( - g) dV\) , andm=0 atT i k =0. 相似文献
15.
V. N. Folomeshkin 《International Journal of Theoretical Physics》1975,12(3):169-176
A class of asymptotically Euclidian space-times is shown to exist for which the Schwarzschild mass is equal to zero. The coordinate atlases of these space-times satisfy two additional conditions: \(\partial _\kappa ( - gg^{0_k } ) = 0\) and \(\Gamma _{ik}^0 \partial _0 g^{ik} - \Gamma _{ik}^k \partial _0 g^{0_i } = 0\) . In aT-orthogonal metricds 2 =g 00 dt 2 ?g αβ dx α dx β these conditions take a simple form: ?0(detg αβ ) = 0 and (?0 g αβ )(?0 g αβ ) = 0. 相似文献
16.
A. Hoferichter V. K. Mitrjushkin M. Müller-Preussker 《Zeitschrift fur Physik C Particles and Fields》1997,74(3):541-548
The chiral limit κ ? κ c (β) in lattice gauge theories with Wilson fermions and problems related to near-to-zero (’exceptional’) eigenvalues of the fermionic matrix are studied. For this purpose we employ compact lattice QED in the confinement phase. A new estimator $\tilde m_\pi$ for the calculation of the pseudoscalar mass m π is proposed which does not suffer from ’divergent’ contributions at κ ? κ c (β)We conclude that the main contribution to the pion mass comes from larger modes, and ’exceptional’ eigenvalues play no physical role. The behaviour of the subtracted chiral condensate $\left\langle {\bar \psi \psi } \right\rangle _{subt}$ near κ c (β) is determined. We observe a comparatively large value of $\left\langle {\bar \psi \psi } \right\rangle _{subt} \cdot Z_P^{ - 1}$ , which could be interpreted as a possible effect of the quenched approximation. 相似文献
17.
We analyze a deterministic cellular automaton σ ?=(σ n :n≥0) corresponding to the zero-temperature case of Domany's stochastic Ising ferromagnet on the hexagonal lattice $\mathbb{N}$ . The state space $\mathcal{S}_\mathbb{H} = \left\{ { - 1, + 1} \right\}^\mathbb{H}$ consists of assignments of ?1 or +1 to each site of $\mathbb{H}$ and the initial state $\sigma ^0 = \left\{ {\sigma _{^x }^0 } \right\}_{x \in \mathbb{H}}$ is chosen randomly with P(σ 0 x=+1)=p∈[0,1]. The sites of $\mathbb{H}$ are partitioned in two sets $\mathcal{A}$ and $\mathcal{B}$ so that all the neighbors of a site x in $\mathcal{A}$ belong to $\mathcal{B}$ and vice versa, and the discrete time dynamics is such that the σ ? x 's with ${x \in \mathcal{A}}$ (respectively, $\mathcal{B}$ ) are updated simultaneously at odd (resp., even) times, making σ ? x agree with the majority of its three neighbors. In ref. 1 it was proved that there is a percolation transition at p=1/2 in the percolation models defined by σ n , for all times n∈[1,∞]. In this paper, we study the nature of that transition and prove that the critical exponents β, ν, and η of the dependent percolation models defined by σ n , n∈[1,∞], have the same values as for standard two-dimensional independent site percolation (on the triangular lattice). 相似文献
18.
H. D. Maison 《Communications in Mathematical Physics》1971,22(2):166-172
The partition functionZ(β,λ)=Tre -β(T+λV) for a finite quantized system is investigated. If the interactionV is a relatively bounded operator with respect to the kinetic energyT withT-boundb<1,Z(β,λ) is shown to be a holomorphic function of β and λ for $$\left| {\arg \beta } \right|< arctg\frac{{\sqrt {1 - b^2 \left| \lambda \right|^2 } }}{{b\left| \lambda \right|}}and\left| \lambda \right|< b^{ - 1} .$$ Forb=0Z(β,λ) is an entire function of λ and holomorphic in β for Re β>0. 相似文献
19.
C. Becchi S. Narison E. de Rafael F. J. Yndurain 《Zeitschrift fur Physik C Particles and Fields》1981,8(4):335-348
We derive model independent lower bounds for the sums of effective quark masses \(\bar m_u + \bar m_d \) and \(\bar m_u + \bar m_s \) . The bounds follow from the combination of the spectral representation properties of the hadronic axial currents two-point functions and their behavior in the deep euclidean region (known from a perturbative QCD calculation to two loops and the leading non-perturbative contribution). The bounds incorporate PCAC in the Nambu-Goldstone version. If we define the invariant masses \(\hat m\) by $$\bar m_i = \hat m_i \left( {{{\frac{1}{2}\log Q^2 } \mathord{\left/ {\vphantom {{\frac{1}{2}\log Q^2 } {\Lambda ^2 }}} \right. \kern-\nulldelimiterspace} {\Lambda ^2 }}} \right)^{{{\gamma _1 } \mathord{\left/ {\vphantom {{\gamma _1 } {\beta _1 }}} \right. \kern-\nulldelimiterspace} {\beta _1 }}} $$ and <F 2> is the vacuum expectation value of $$F^2 = \Sigma _a F_{(a)}^{\mu v} F_{\mu v(a)} $$ , we find, e.g., $$\hat m_u + \hat m_d \geqq \sqrt {\frac{{2\pi }}{3} \cdot \frac{{8f_\pi m_\pi ^2 }}{{3\left\langle {\alpha _s F^2 } \right\rangle ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} }}} $$ ; with the value <α u F 2?0.04GeV4, recently suggested by various analysis, this gives $$\hat m_u + \hat m_d \geqq 35MeV$$ . The corresponding bounds on \(\bar m_u + \bar m_s \) are obtained replacingm π 2 f π bym K 2 f K . The PCAC relation can be inverted, and we get upper bounds on the spontaneous masses, \(\hat \mu \) : $$\hat \mu \leqq 170MeV$$ where \(\hat \mu \) is defined by $$\left\langle {\bar \psi \psi } \right\rangle \left( {Q^2 } \right) = \left( {{{\frac{1}{2}\log Q^2 } \mathord{\left/ {\vphantom {{\frac{1}{2}\log Q^2 } {\Lambda ^2 }}} \right. \kern-\nulldelimiterspace} {\Lambda ^2 }}} \right)^d \hat \mu ^3 ,d = {{12} \mathord{\left/ {\vphantom {{12} {\left( {33 - 2n_f } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {33 - 2n_f } \right)}}$$ . 相似文献
20.
XIE KePing KE WeiYao LIANG WuYang FU XiMing JIAO ChangFeng PEI JunChen XU FuRong 《中国科学:物理学 力学 天文学(英文版)》2014,57(2):189-193
Using the total-Routhian-surface(TRS)method,the rotational behaviors of fission isomers in the second well of actinide nuclei234 242U,236 244Pu and238 246Cm were investigated.The pairing-deformation-frequency self-consistent TRS calculations reproduced reasonably the experimental moments of inertia extracted from spectroscopic data.It is calculated that,in these largelyelongated(β2≈0.65 andβ4≈0.03)fission isomers,theν12[981]neutron andπ12+[651]proton align simultaneously at rotational frequencyω≈0.4 0.6 MeV(corresponding to spin I≈80),which leads to clear upbending in moments of inertia(MoI’s).Our calculations have indicated that the hexadecapole deformationβ4influenced significantly the frequency of the rotational alignment of the proton12+[651]orbit. 相似文献