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1.
Evgeni Korotyaev 《Communications in Mathematical Physics》2000,213(2):471-489
The spectral properties of the Schr?dinger operator T(t)=−d
2/dx
2+q(x,t) in L
2(ℝ) are studied, where the potential q is defined by q=p(x+t), x>0, and q=p(x), x<0; p is a 1-periodic potential and t∈ℝ is the dislocation parameter. For each t the absolutely continuous spectrum σ
ac
(T(t))=σ
ac
(T(0)) consists of intervals, which are separated by the gaps γ
n
(T(t))=γ
n
(T(0))=(α
n
−,α
n
+), n≥1. We prove: in each gap γ
n
≠?, n≥ 1 there exist two unique “states” (an eigenvalue and a resonance) λ
n
±(t) of the dislocation operator, such that λ
n
±(0)=α
n
± and the point λ
n
±(t) runs clockwise around the gap γ
n
changing the energy sheet whenever it hits α
n
±, making n/2 complete revolutions in unit time. On the first sheet λ
n
±(t) is an eigenvalue and on the second sheet λ
n
±(t) is a resonance. In general, these motions are not monotonic. There exists a unique state λ0(t) in the basic gap
γ0(T(t))=γ0(T(0))=(−∞ ,α0
+). The asymptotics of λ
n
±(t) as n→∞ is determined.
Received: 5 April 1999 / Accepted: 3 March 2000 相似文献
2.
Anna De Masi Immacolata Merola Errico Presutti Yvon Vignaud 《Journal of statistical physics》2009,134(2):243-306
This is the second of two papers on a continuum version of the Potts model, where particles are points in ℝ
d
, d≥2, with a spin which may take S≥3 possible values. Particles with different spins repel each other via a Kac pair potential of range γ
−1, γ>0. In this paper we prove phase transition, namely we prove that if the scaling parameter of the Kac potential is suitably
small, given any temperature there is a value of the chemical potential such that at the given temperature and chemical potential
there exist S+1 mutually distinct DLR measures. 相似文献
3.
We consider a 2-dimensional planar rotator on a large, but finite lattice with a ferromagnetic Kac potential J
γ(i)=γ 2
J(γ i), J with compact support. The system is subject to boundary conditions with vorticity. Using a gradient-flow dynamics, we compute
minimizers of the free energy functional at low temperature, i.e. in the regime of phase transition. We have the numerical
evidence of a vortex structure for minimizers, which present many common features with those of the Ginzburg-Landau functional.
We extend the results to spins valued in S
2 and compare with the celebrated Belavin and Polyakov model. 相似文献
4.
A. A. Zhukov M. R. Trunin A. T. Sokolov N. N. Kolesnikov 《Journal of Experimental and Theoretical Physics》1997,85(6):1211-1217
The real part R
s and the imaginary part X
s of the surface impedance Z
s=R
s+ iX
s of Tl2Ba2CaCu2O8−δ
and YBa2Cu3O6.95 single crystals have been measured with high precision at frequency ω/2π=9.4 GHz in the temperature range 0<T<140 K. In the Tl2Ba2CaCu2O8−δ
crystal a linear temperature dependence R
s(T) has been found for T⩽50 K, and the magnetic field penetration depth λ(4.2 K)=X
s(4.2 K)/ω μ
0≈3760 Å has been measured. Along with well known features of the function Z
s(T) in high-quality YBa2Cu3O6.95 single crystals, such as the linearity of λ(T) and R
s(T) for T<T
c/3 and a maximum of R
s(T) at T∼T
c/2, the linearity range of λ(T) extends to T≃50 K, and this curve has a plateau in the range 60<T<85 K. The curve of R
s(T) in both the superconducting and normal states of YBa2Cu3O6.95 is well described by a two-fluid model with the electron-phonon mechanism of quasiparticle relaxation. A formula describing
the curve of λ
2(0)/λ
2(T) throughout the studied temperature range is also given.
Zh. éksp. Teor. Fiz. 112, 2210–2222 (December 1997) 相似文献
5.
BaBar’s observation of significant deviations of the pion transition form factor (TFF) from the asymptotic expectation with
Q
2>9 GeV2 has brought about a serious crisis to the fundamental picture established for such a simple q[`(q)]q\bar{q} system by perturbative QCD, i.e. the dominance of collinear factorization at high momentum transfers for the pion TFF. We
show that non-factorizable contributions due to open flavors in γγ
∗→π
0 could be an important source that contaminates the pQCD asymptotic limit and causes such deviations with Q
2>9 GeV2. Within an effective Lagrangian approach, the non-factorizable amplitudes can be related to intermediate hadron loops, i.e.
K
(∗) and D
(∗) etc., and their corrections to the π
0 and η TFFs can be estimated. 相似文献
6.
Potts Models in the Continuum. Uniqueness and Exponential Decay in the Restricted Ensembles 总被引:1,自引:1,他引:0
Anna De Masi Immacolata Merola Errico Presutti Yvon Vignaud 《Journal of statistical physics》2008,133(2):281-345
In this paper we study a continuum version of the Potts model, where particles are points in ℝ
d
, d≥2, with a spin which may take S≥3 possible values. Particles with different spins repel each other via a Kac pair potential of range γ
−1, γ>0. In mean field, for any inverse temperature β there is a value of the chemical potential λ
β
at which S+1 distinct phases coexist. We introduce a restricted ensemble for each mean field pure phase which is defined so that the
empirical particles densities are close to the mean field values. Then, in the spirit of the Dobrushin-Shlosman theory (Dobrushin
and Shlosman in J. Stat. Phys. 46(5–6):983–1014, 1987), we prove that while the Dobrushin high-temperatures uniqueness condition does not hold, yet a finite size condition is
verified for γ small enough which implies uniqueness and exponential decay of correlations. In a second paper (De Masi et al. in Coexistence
of ordered and disordered phases in Potts models in the continuum, 2008), we will use such a result to implement the Pirogov-Sinai scheme proving coexistence of S+1 extremal DLR measures. 相似文献
7.
G. M. Molchan 《Communications in Mathematical Physics》1999,205(1):97-111
Let b
γ (t), b
γ(0)= 0 be a fractional Brownian motion, i.e., a Gaussian process with the structure function , 0 < γ < 2. We study the logarithmic asymptotics of P
T
= P{b
γ (t) < 1,□t∈TΔ} as T→∞, where Δ is either the interval (0,1) or a bounded region that contains a vicinity of 0 for the case of multidimensional
time. It is shown that ln P
T
= - D ln T(1 + o(1)), where D is the dimension of zeroes of b
γ (t) in the former case and the dimension of time in the latter.
Received: 28 September 1998 / Accepted: 19 February 1999 相似文献
8.
V. A. Schegelsky A. V. Sarantsev A. V. Anisovich M. P. Levchenko 《The European Physical Journal A - Hadrons and Nuclei》2006,27(2):199-205
The reaction γγ → π+π-π0 with quasi-real photons is studied with a total integrated luminosity of 663pb^-1, collected by the L3 detector at LEP at
center-of-mass energies from 183 to 209GeV. The results of an energy-dependent partial wave analysis in the mass region 1.1≤M(π+π-π0)≤2.2GeV are presented. The reaction is dominated by a2(1320) formation. A strong signal consistent with the first radial excitation of the isovector tensor state, a2(1700), is present and confirms the previous L3 observation. Its two-photon partial width is found to be
Br(3π) = 0.37+0.12-0.08keV, the relative branching ratio of ρ(770)π to f2(1270)π is 3.4±0.4. For all observed states the product of γγ partial width and 3π branching ratios is measured. 相似文献
9.
M. V. Zagidullin 《Optics and Spectroscopy》2010,109(4):538-542
In the temperature range of T = 150–400 K, the dependence of spectral widths (cm−1) on temperature, 182 + 0.38(±0.01)T and 217 + 0.48(±0.01)T, respectively, has been obtained for dimole emission of O2(a, 0) + O2(a, 0) → O2(X, 1) + O2(X, 0) + hν (λ = 703 nm) and O2(a, 0) + O2(a, 0) → O2(X, 0) + O2(X, 0) + hν (λ = 634 nm). It was shown that the ratio of dimole emission rate constants does not depend on temperature in the range
of 150–400 K and is 1.06 ± 0.01. 相似文献
10.
According to recent progresses in the finite size scaling theory of
disordered systems, thermodynamic observables are not self-averaging
at critical points when the disorder is relevant in the
Harris criterion sense. This lack of
self-averageness at criticality is directly related to the distribution
of pseudo-critical temperatures Tc(i,L) over the ensemble of
samples (i) of size L. In this paper, we apply this analysis to
disordered Poland-Scheraga models with different loop exponents c,
corresponding to marginal and relevant disorder. In all cases, we
numerically obtain a Gaussian
histogram of pseudo-critical temperatures Tc(i,L) with mean
Tcav(L) and width ΔTc(L).
For the marginal case c=1.5 corresponding to two-dimensional wetting,
both the width ΔTc(L) and the shift
[Tc(∞)-Tcav(L)] decay as L-1/2, so the exponent is
unchanged (νrandom=2=νpure) but disorder is relevant and
leads to non self-averaging at criticality.
For relevant disorder
c=1.75, the width ΔTc(L) and the shift
[Tc(∞)-Tcav(L)] decay with the same new exponent
L-1/νrandom (where νrandom ∼2.7 > 2 > νpure) and
there is again no self-averaging at criticality. Finally for the value
c=2.15, of interest in the context of DNA denaturation, the
transition is first-order in the pure case. In the presence of
disorder, the width ΔTc(L) ∼L-1/2
dominates over the shift [Tc(∞)-Tcav(L)] ∼L-1,
i.e. there are two correlation length exponents ν=2 and
that govern respectively the averaged/typical loop distribution. 相似文献
11.
We consider ad=2 Ising system with a Kac potential whose mean-field critical temperature is 1. Calling >0 the Kac parameter, we prove that there existsc
*>0 so that the true inverse critical temperature cr() > 1 +by
2 log -1, for anyb<c
* and correspondingly small. We also show that if 0 andbc
*, suitably, then the correlation functions (normalized and rescaled) converge to those of a non-Gaussian Euclidean field theory. 相似文献
12.
Parongama Sen 《Pramana》2008,71(2):313-317
We consider navigation or search schemes on networks which have a degree distribution of the form P(k) ∝ exp(−k
γ). In addition, the linking probability is taken to be dependent on social distances and is governed by a parameter λ. The searches are realistic in the sense that not all search chains can be completed. An estimate of μ = ρ/s
d, where ρ is the success rate and s
d the dynamic path length, shows that for a network of N nodes, μ ∝ N
−δ
in general. Dynamic small world effect, i.e., δ ≃ 0 is shown to exist in a restricted region of the λ−γ plane.
相似文献
13.
A semi-phenomenological theory of variable-range hopping (VRH) is developed for two-dimensional (2D) quasi-one-dimensional
(quasi-1D) systems such as arrays of quantum wires in the Wigner crystal regime. The theory follows the phenomenology of Efros,
Mott and Shklovskii allied with microscopic arguments. We first derive the Coulomb gap in the single-particle density of states,
g(ε), where ε is the energy of the charge excitation. We then derive the main exponential dependence of the electron conductivity
in the linear (L), i.e. σ(T) ∼exp [-(TL/T)γL], and current in the non-linear (NL), i.e.
, response regimes (
is the applied electric field). Due to the strong anisotropy of the system and its peculiar dielectric properties we show
that unusual, with respect to known results, Coulomb gaps open followed by unusual VRH laws, i.e. with respect to the disorder-dependence
of TL and
and the values of γL and γNL. 相似文献
14.
We construct approximate solutions to the time–dependent Schr?dinger?equation
for small values of ħ. If V satisfies appropriate analyticity and growth hypotheses and , these solutions agree with exact solutions up to errors whose norms are bounded by
for some C and γ>0. Under more restrictive hypotheses, we prove that for sufficiently small T
′, implies the norms of the errors are bounded by
for some C
′, γ′>0, and σ > 0.
Received: 7 January 1999 / Accepted: 30 April 1999 相似文献
15.
V. Kolevzon 《Journal of Experimental and Theoretical Physics》1998,87(6):1105-1109
The temperature dependence of the surface tension γ(T) is treated theoretically and experimentally. The theoretical model based on the Gibbs thermodynamics of a one-component
fluid relates ∂γ/∂T to the surface excess entropy density −ΔS. All specific surface effects, namely ordering, capillary waves, and double layer influence the surface entropy, which in
turn governs the sign and the magnitude of ∂γ/∂T. Experimental data collected at a free Hg surface in the temperature range from 0°C to 30°C show that ∂γ/∂T is negative.
Zh. éksp. Teor. Fiz. 114, 2034–2042 (December 1998)
Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor. 相似文献
16.
We study spectral properties of
the discrete Laplacian H on the half-space
with random boundary condition ;
the V(n) are independent random variables on a
probability
space and λ is the coupling constant.
It is known that if the
V(n) have densities, then on the interval
[-2(d+1), 2(d+1)] (=σ(H
0),
the spectrum of the
Dirichlet Laplacian) the spectrum of H is P-a.s.
absolutely continuous for all λ [JL1].
Here we show that if the random potential P
satisfies the
assumption of Aizenman–Molchanov [AM], then there
are constants λ
d
and
Λ
d
such that for
|λ|<lambda;
d
and |λ|>
Λ
d
the spectrum of
H outside σ(H
0)
is P-a.s. pure point with exponentially decaying
eigenfunctions.
Received: 3 December 1998 / Accepted: 27 May 1999 相似文献
17.
Let λ i (Ω,V) be the i th eigenvalue of the Schrödinger operator with Dirichlet boundary conditions on a bounded domain $\Omega \subset \mathbb{R}^nLet λ
i
(Ω,V) be the i
th
eigenvalue of the Schr?dinger operator with Dirichlet boundary conditions on a bounded domain
and with the positive potential V. Following the spirit of the Payne-Pólya-Weinberger conjecture and under some convexity assumptions on the spherically rearranged potential V
*, we prove that λ2(Ω,V) ≤ λ2(S
1,V
*). Here S
1 denotes the ball, centered at the origin, that satisfies the condition λ1(Ω,V)=λ1(S
1,V
*).Further we prove under the same convexity assumptions on a spherically symmetric potential V, that λ2(B
R
, V) / λ1(B
R
, V) decreases when the radius R of the ball B
R
increases.We conclude with several results about the first two eigenvalues of the Laplace operator with respect to a measure of Gaussian or inverted Gaussian density.R.B. was supported by FONDECYT project # 102-0844.H.L. gratefully acknowledges financial support from DIPUC of the Pontifí cia Universidad Católica de Chile and from CONICYT. 相似文献
18.
I. K. Bensafa P. Achenbach M. Ases Antelo C. Ayerbe D. Baumann R. Böhm D. Bosnar E. Burtin X. Defaÿ N. D'Hose M. Ding M. O. Distler L. Doria H. Fonvieille J. M. Friedrich J. Friedrich J. García Llongo P. Janssens G. Jover Mañas M. Kohl G. Laveissière M. Lloyd M. Makek J. Marroncle H. Merkel P. Merle U. Müller L. Nungesser B. Pasquini R. Pérez Benito J. Pochodzalla M. Potokar G. Rosner S. Sánchez Majos M. Seimetz S. Širca T. Spitzenberg G. Tamas R. Van de Vyver L. Van Hoorebeke Th. Walcher M. Weis 《The European Physical Journal A - Hadrons and Nuclei》2007,32(1):69-75
The beam-helicity asymmetry has been measured simultaneously for the reactions
p→epγ and
p→epπ
0 in the Δ(1232)-resonance region at Q
2 = 0.35(GeV/c)2. The experiment was performed at MAMI with a longitudinally polarized beam and an out-of-plane detection of the proton. The
results are compared with calculations based on dispersion relations for virtual Compton scattering and with the MAID model
for pion electroproduction. There is an overall good agreement between experiment and theoretical calculations. The remaining
discrepancies may be ascribed to an imperfect parametrization of some γ
(*)
N→πN multipoles, mainly contributing to the non-resonant background. The beam-helicity asymmetry in both channels (γ and π
0) shows a good sensitivity to these multipoles and should allow future improvement in their parametrization. 相似文献
19.
Systems of particles interacting with long range interactions present generically ”quasi-stationary states” (QSS), which are
approximately time-independent out of equilibrium states. In this proceedings, we explore the generalization of the formation
of such QSS and their relaxation from the much studied case of gravity to a generic pair interaction with the asymptotic form
of the potential v(r) ∼ 1/r
γ
with γ > 0 in d dimensions. We compute analytic estimations of the relaxation time calculating the rate of two body collisionality in a virialized
system approximated as homogeneous. We show that for γ < (d − 1/2), the collision integral is dominated by the size of the system, while for γ > (d − 1/2), it is dominated by small impact parameters. In addition, the lifetime of QSS increases with the number of particles
if γ < d − 1 (i.e. the force is not integrable) and decreases if γ > d − 1. Using numerical simulations we confirm our analytic results. A corollary of our work gives a ”dynamical” classification
of interactions: the dynamical properties of the system depend on whether the pair force is integrable or not. 相似文献
20.
N. Katase T. Shibauchi T. Tamegai I. Tsukada K. Uchinokura 《Czechoslovak Journal of Physics》1996,46(Z2):1119-1120
We report the surface impedance (Z
s
) measurements in high quality single crystals of Bi2Sr2CaCu2O8+y
. At relatively low oxygen content, the change of the penetration depth, Δλ(T) ≡λ(T)-λ(0), of the pure single crystals exhibits linear temperature dependence both parallel to the CuO2 planes and in thec direction. In contrast to this behavior, by further oxygenation or 0.6% Zn substitution, theT-linear dependence is disrupted andT
2 dependence of Δλ is observed. We also found that 0.9% Ni-substitution induces no pairbreaking effect. The present results
suggest that the low-lying excitation spectrum of quasiparticles depends on the carrier concentration and is easily changed
by a small amount of Zn substitution. 相似文献