首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 98 毫秒
1.
The problem of constructing the Hilbert space of physical states for a free scalar quantum field propagating on a cosmological background is considered. The concept of energy-momentum for such a field is discussed and it is noted that, according to current renormalization theory, for a state ¦M to have finite energy density its associated anticommutator function must be of a particular form first discussed by Hadamard. This restriction is shown to lead to a constraint on the construction of the Hilbert space of physical states. This constraint is used to reject a recently proposed scheme for the construction of this space which was based on a principle of energy minimization.This essay received an honourable mention from the Gravity Research Foundation for the year 1984.-Ed.  相似文献   

2.
We consider a selfinteracting boson field in two space-time dimensions, with interaction densities of the form:V((x)): where (x) is a scalar boson field, andV() is a real positive function of exponential type. We define the space cut-off interaction by and prove thatH r =H 0+V r , whereH 0 is the free energy, is essentially self adjoint. This permits us to take away the space cut-off and we obtain a quantum field free of cut-offs.At leave from Mathematical Institute, Oslo University.This research partially sponsored by the Air Force Office of Scientific Research under Contract AF 49(638)1545.  相似文献   

3.
For Lax-pair isospectral deformations whose associated spectrum, for given initial data, consists of the disjoint union of a finitely denumerable discrete spectrum (solitons) and a continuous spectrum (continuum), the matrix Riemann–Hilbert problem approach is used to derive the leading-order asymptotics as of solutions to the Cauchy problem for the defocusing nonlinear Schrödinger equation ( NLSE), , with finite-density initial data
.The NLSE dark soliton position shifts in the presence of the continuum are also obtained.  相似文献   

4.
We prove that Gibbs states for the Hamiltonian , with thes x varying on theN-dimensional unit sphere, obtained with nonrandom boundary conditions (in a suitable sense), are almost surely rotationally invariant if withJ xy i.i.d. bounded random variables with zero average, 1 in one dimension, and 2 in two dimensions.  相似文献   

5.
We consider the large time asymptotic behavior of solutions to the Cauchy problem for the modified Korteweg–de Vries equation , with initial data . We assume that the coefficient is real, bounded and slowly varying function, such that , where . We suppose that the initial data are real-valued and small enough, belonging to the weighted Sobolev space . In comparison with the previous paper (Internat. Res. Notices 8 (1999), 395–418), here we exclude the condition that the integral of the initial data u 0 is zero. We prove the time decay estimates and for all , where . We also find the asymptotics for large time of the solution in the neighborhood of the self-similar solution.  相似文献   

6.
We consider the Dirichlet Laplacian for astrip in with one straight boundary and a width , where $f$ is a smooth function of acompact support with a length 2b. We show that in the criticalcase, , the operator has nobound statesfor small .On the otherhand, a weakly bound state existsprovided . In thatcase, there are positive c 1,c 2 suchthat the corresponding eigenvalue satisfies for all sufficiently small.  相似文献   

7.
The phenomenon of nonlinear resonance provides a mechanism for the unbounded amplification of small solutions of systems of conservation laws. We construct spatially 2-periodic solutionsu N C ([0,t N ] × witht N bounded, satisfying
  相似文献   

8.
LetR be an expanding rational function with a real bounded Julia set, and let be a Ruelle operator acting in a space of functions analytic in a neighbourhood of the Julia set. We obtain explicit expressions for the resolvent function and, in particular, for the Fredholm determinantD()=det(I-L). It gives us an equation for calculating the escape rate. We relate our results to orthogonal polynomials with respect to the balanced measure ofR. Two examples are considered.The first named author was sponsored in part by the Landau Center for Research in Mathematical Analysis, supported by the Minerva Foundation (Germany)  相似文献   

9.
We study Schrödinger operators of the form on d , whereA 2 is a strictly positive symmetricd×d matrix andV(x) is a continuous real function which is the Fourier transform of a bounded measure. If n are the eigenvalues ofH we show that the theta function is explicitly expressible in terms of infinite dimensional oscillatory integrals (Feynman path integrals) over the Hilbert space of closed trajectories. We use these explicit expressions to give the asymptotic behaviour of (t) for smallh in terms of classical periodic orbits, thus obtaining a trace formula for the Schrödinger operators. This then yields an asymptotic expansion of the spectrum ofH in terms of the periodic orbits of the corresponding classical mechanical system. These results extend to the physical case the recent work on Poisson and trace formulae for compact manifolds.Partially supported by the USP-Mathematisierung, University of Bielefeld (Forschungsprojekt Unendlich dimensionale Analysis)  相似文献   

10.
A system is considered consisting of a harmonic oscillator and a field interacting with it. A quadratic Lagrangian is used, so that the model is exactly solvable. Under some conditions, the model exhibits a dissipative behavior of a selected oscillator. A canonical transformation is found which brings the Hamiltonian to a diagonal form, which is used to compute the quantum correlation and spectral functions of the oscillator fluctuations. It is found that the model allows for a low-frequency spectrum of the form for the driving force, and for the oscillator coordinate (Flicker noise).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 13–18, October, 1990.  相似文献   

11.
We consider the crystal structure of the level zero extremal weight modules V() using the crystal base of the quantum affine algebra constructed in Duke Math. J. 99 (1999), 455–487. This approach yields an explicit form for extremal weight vectors in the U part of each connected component of the crystal, which are given as Schur functions in the imaginary root vectors. We show the map induces a correspondence between the global crystal base of V() and elements .  相似文献   

12.
We prove that the density of states for the tight-binding model with off-diagonal disorder under general conditions diverges forR0 at least as . This result is established through the study of the recurrence properties of an associated Markov chain.Partial financial support by GNAFA (CNR)Partial financial support by CNPq, grant n.303795-77FA  相似文献   

13.
AssumeF is the curvature (field) of a connection (potential) onR 4 with finiteL 2 norm . We show the chern number (topological quantum number) is an integer. This generalizes previous results which showed that the integrality holds forF satisfying the Yang-Mills equations. We actually prove the natural general result in all even dimensions larger than 2.  相似文献   

14.
We consider a N-body Schrödinger operator H=H 0+V. The interaction V is given by a sum of pair potentials V jk(y)(=V jk s +V jk l ), y R3. We assume that: V jk s =O(|y|-(1+p)), p>0, as |y| for the short-range part V jk s ; for the long-range part V jk l . Under this assumption, we prove the principle of limiting absorption for H. The obtained result is essentially as good as those obtained in the two-body case. The proof is done by a slight modification of the remarkable commutator method due to Mourre.  相似文献   

15.
We study the initial value problem for the two-dimensional nonlinear nonlocal Schrödinger equations i ut + u = N(v), (t, x, y) R3, u(0, x, y) = u0(x, y), (x, y) R2 (A), where the Laplacian = 2 x + 2 y, the solution u is a complex valued function, the nonlinear term N = N1 + N2 consists of the local nonlinear part N1(v) which is cubic with respect to the vector v=(u,ux,uy,\overline{u},\overline{u}_{x},\overline{u}_{y}) in the neighborhood of the origin, and the nonlocal nonlinear part N2(v) =(v, – 1 x Kx(v)) + (v, – 1 y Ky(v)), where (, ) denotes the inner product, and the vectors Kx (C4(C6; C))6 and Ky (C4(C6; C))6 are quadratic with respect to the vector v in the neighborhood of the origin. We assume that the components K(2) x = K(4) x 0, K(3) y = K(6) y 0. In particular, Equation (A) includes two physical examples appearing in fluid dynamics. The elliptic–hyperbolic Davey–Stewartson system can be reduced to Equation (A) with , and all the rest components of the vectors Kx and Ky are equal to zero. The elliptic–hyperbolic Ishimori system is involved in Equation (A), when , and . Our purpose in this paper is to prove the local existence in time of small solutions to the Cauchy problem (A) in the usual Sobolev space, and the global-in-time existence of small solutions to the Cauchy problem (A) in the weighted Sobolev space under some conditions on the complex conjugate structure of the nonlinear terms, namely if N(ei v) = ei N(v) for all R.  相似文献   

16.
We study amplitude-squared squeezing of the Hermitian operator Zθ=Z1 cosθ+Z2 sin θ, in the most general superposition state , of two coherent states and . Here operators Z1,2 are defined by , a is annihilation operator, θ is angle, and complex numbers C1,2 , α, β are arbitrary and only restriction on these is the normalization condition of the state . We define the condition for a state to be amplitude-squared squeezed for the operator Zθ if squeezing parameter , where N=a+a and . We find maximum amplitude-squared squeezing of Zθ in the superposed coherent state with minimum value 0.3268 of the parameter S for an infinite combinations with α- β= 2.16 exp [±i(π/4) + iθ/2], and with arbitrary values of (α+β) and θ. For this minimum value of squeezing parameter S, the expectation value of photon number can vary from the minimum value 1.0481 to infinity. Variations of the parameter S with different variables at maximum amplitude-squared squeezing are also discussed.  相似文献   

17.
It is shown, that the class of fields (a, b) involving a particle of zero rest mass and helicityh is restricted only by the condition , if the representation space is not required to be irreducible. The main feature of the corresponding physical interpretation is the occurrence of gauge particles. The investigations are carried out in terms of manifest covariant representations of the inhomogeneous Lorentz Group, which are shown to be not fully reducible in the zero rest mass case. The results are also obtained by a limiting processm 0.  相似文献   

18.
Given n2, we put r=min . Let be a compact, C r -smooth surface in n which contains the origin. Let further be a family of measurable subsets of such that as . We derive an asymptotic expansion for the discrete spectrum of the Schrödinger operator in L 2( n ), where is a positive constant, as . An analogous result is given also for geometrically induced bound states due to a interaction supported by an infinite planar curve.  相似文献   

19.
It is shown that the functional , defined onC functions on the two-dimensional sphere, satisfies the inequalityS[]0 if is subject to the constraint . The minimumS[]=0 is attained at the solutions of the Euler-Lagrange equations. The proof is based on a sharper version of Moser-Trudinger's inequality (due to Aubin) which holds under the additional constraint ; this condition can always be satisfied by exploiting the invariance ofS[] under the conformal transformations ofS 2. The result is relevant for a recently proposed formulation of a theory of random surfaces.On leave from: Istituto di Fisica dell'Università di Parma, Sezione di Fisica Teorica, Parma, Italy  相似文献   

20.
We study decay properties of solutions of the Schrödinger equation (–+V)=E. Typical of our results is one which shows that ifV=o(|x|–1/2) at infinity or ifV is a homogeneousN-body potential (for example atomic or molecular), then ifE<0 and . We also construct examples to show that previous essential spectrum-dependent upper bounds can be far from optimal if is not the ground state.Research in partial fulfillment of the requirements for a Ph.D. degree at the University of VirginiaPartially supported by NSF grant MCS-81-01665Supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, Projekt Nr. 4240  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号