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1.
The long-wavelength excitations in a simple model of a dilute Bose gas at zero temperature are investigated from a purely microscopic viewpoint. The role of the interaction and the effects of the condensate are emphasized in a dielectric formulation, in which the response functions are expressed in terms of regular functions that do not involve an isolated single-interaction line nor an isolated single-particle line. Local number conservation is incorporated into the formulation by the generalized Ward identities, which are used to express the regular functions involving the density in terms of regular functions involving the longitudinal current. A perturbation expansion is then developed for the regular functions, producing to a given order in the perturbation expansion an elementary excitation spectrum without a gap and simultaneously response functions that obey local number conservation and related sum rules.Explicit results to the first order beyond the Bogoliubov approximation in a simple one-parameter model are obtained for the elementary excitation spectrum ωk, the dynamic structure function S(k, ω), the associated structure function Sm(k), and the one-particle spectral function A(k, ω), as functions of the wavevector k and frequency ω. These results display the sharing of the gapless spectrum ωk by the various response functions and are used to confirm that the sum rules of interest are satisfied. It is shown that ωk and some of the Sm(k) are not analytic functions of k in the long wavelength limit. The dynamic structure function S(k, ω) can be conveniently separated into three parts: a one-phonon term which exhausts the f sum rule, a backflow term, and a background term. The backflow contribution to the static structure function S0(k) leads to the breakdown of the one-phonon Feynman relation at order k3. Both S(k, ω) and A(k, ω) display broad backgrounds because of two-phonon excitations. Simple arguments are given to indicate that some of the qualitative features found for various physical quantities in the first-order model calculation might also be found in superfluid helium.  相似文献   

2.
A single two-level molecule driven by CW-laser field and a photomultiplier tube (PMT) are considered as two parts of the united dynamical system connected with each other by photons of molecular fluorescence. Each PMT is characterized by a rate α of photo-effect and by a rate β of PMT recovery. A theory for the photon distribution function wN(t) and for the photoelectric pulse distribution function fn(t) for such a system is built up. If times 1/ α and 1/ β characterizing PMT are much shorter as compared to the average time interval 1/ k between two successively emitted photons of fluorescence, the photon and the photoelectron distribution functions coincide with each other, i.e. fn(t) ≅ wN(t). A relation between wN(t) and fn(t) is studied in detail for the case in which PMT works slower as compared to the rate k of photon emission, i.e. at 1/ α, 1/ β ≥ 1/ k.  相似文献   

3.
We study nonintegrable hamiltonian dynamics: H(I,θ) = H0(I) + kH1(I,θ), for large k, that is, far from integrability. An integral representation is given for the conditional probability P(I,θ, t¦I0, θ0, t0) that the system is at I, θ at t, given it was at I0, θ0 at t0. By discretizing time into steps of size ?, we show how to evaluate physical observables for large k, fixed ?. An explicit calculation of a diffusion coefficient in a two degrees of freedom problem is reported. Passage to ? = 0, the original hamiltonian flow, is discussed.  相似文献   

4.
For a given Hermitian Hamiltonian H(s)(s∈[0,1])with eigenvalues Ek(s)and the corresponding eigenstates|Ek(s)(1 k N),adiabatic evolution described by the dilated Hamiltonian HT(t):=H(t/T)(t∈[0,T])starting from any fixed eigenstate|En(0)is discussed in this paper.Under the gap-condition that|Ek(s)-En(s)|λ0 for all s∈[0,1]and all k n,computable upper bounds for the adiabatic approximation errors between the exact solution|ψT(t)and the adiabatic approximation solution|ψadi T(t)to the Schr¨odinger equation i|˙ψT(t)=HT(t)|ψT(t)with the initial condition|ψT(0)=|En(0)are given in terms of fidelity and distance,respectively.As an application,it is proved that when the total evolving time T goes to infinity,|ψT(t)-|ψadi T(t)converges uniformly to zero,which implies that|ψT(t)≈|ψadi T(t)for all t∈[0,T]provided that T is large enough.  相似文献   

5.
We investigate an autocorrelation function of a soluble three-dimensional system, namely the temporal coherence functionC E(t)∝<E(0)E(t)> of the thermal radiation field in a cube-shaped cavity for the stochastic electrical fieldE. In the thermodynamic limit,C E(t) relaxes exponentially at intermediate times, but a “long-tail” behaviourC 0(t)=At?4 withA<0 is predominant for long times. In the case of a finite, but not too small, cavity lengthL obeyingΛ=hc/k BT?L and at timest withct?L, C E(t) is described by an asymptotic expansion in powers ofL ?1 using generalized Riemann zeta functions. Surface-and shape-effects enhance the long-tail. In the case of very small cavities withL«Λ, we calculate an expansion ofC E(t) in terms of exp(?L ?1) and cosines. An oscillatory, but not strictly periodic, long-time behaviour is observed in this case.  相似文献   

6.
A theory of dielectric absorption and dispersion in the nematic phase is developed which does not rely on the use of a nematic “director”. The major features of the spectrum are reproduced by using the fact that the autocorrelation functions 〈μ(0) · υ(t)〉 and 〈υ(t) · μ(0)〉 are no longer symmetry disallowed when the overall sample is anisotropic, as in the aligned nematic. Here μ is the dipole vector of the diffusing molecule and υ the centre of mass linear velocity.  相似文献   

7.
In this paper, we study the asymptotic behavior of solutions of semilinear abstract differential equations (*) u′(t) = Au(t) + t n f(t, u(t)), where A is the generator of a C 0-semigroup (or group) T(·), f(·, x) ∈ A for each xX, A is the class of almost periodic, almost automorphic or Levitan almost periodic Banach space valued functions ϕ: ℝ → X and n ∈ {0, 1, 2, ...}. We investigate the linear case when T(·)x is almost periodic for each xX; and the semilinear case when T(·) is an asymptotically stable C 0-semigroup, n = 0 and f(·, x) satisfies a Lipschitz condition. Also, in the linear case, we investigate (*) when ϕ belongs to a Stepanov class S p-A defined similarly to the case of S p-almost periodic functions. Under certain conditions, we show that the solutions of (*) belong to A u:= ABUC(ℝ, X) if n = 0 and to t n A uw n C 0 (ℝ, X) if n ∈ ℕ, where w n(t) = (1 + |t|)n. The results are new for the case n ∈ ℕ and extend many recent ones in the case n = 0. Dedicated to the memory of B. M. Levitan  相似文献   

8.
Multiplicity distributions Ψn(k) in the generalized Feynman gas model of order k (defined by saying that all integrated correlation functions fn except f1,…,fk are zero) are derived and expressed in terms of Poisson distributions with different ”average multiplicities”, which are related to the integrated correlation functions. The relations between Ψn(k) and Ψn(j) for arbitrary positive integers k,j are found. An intuitive picture to gain a better feeling for these relations is developed.On the basis of our formulae we show that the experimentally observed multiplicity distributions (between 50 GeV/c and 303 GeV/c incoming momentum) can be well reproduced by those of a Feynman gas model of order two. Other applications of our formulae are suggested.  相似文献   

9.
The classical theory of electromagnetism is based on Maxwell's macroscopic equations, an energy postulate, a momentum postulate, and a generalized form of the Lorentz law of force. These seven postulates constitute the foundation of a complete and consistent theory, thus eliminating the need for physical models of polarization P and magnetization M — these being the distinguishing features of Maxwell's macroscopic equations. In the proposed formulation, P(r, t) and M(r, t) are arbitrary functions of space and time, their physical properties being embedded in the seven postulates of the theory. The postulates are self-consistent, comply with special relativity, and satisfy the laws of conservation of energy, linear momentum, and angular momentum. The Abraham momentum density pEM(r,t) = E(r,t) × H(r,t) / c2 emerges as the universal electromagnetic momentum that does not depend on whether the field is propagating or evanescent, and whether or not the host media are homogeneous, transparent, isotropic, linear, dispersive, magnetic, hysteretic, negative-index, etc. Any variation with time of the total electromagnetic momentum of a closed system results in a force exerted on the material media within the system in accordance with the generalized Lorentz law.  相似文献   

10.
J.W. Evans 《Physica A》1980,102(1):87-104
A class of initial value problems for a one-dimensional hard sphere gas is considered where a specified particle has a given distribution f(1)(z1; 0) and the rest are in equilibrium at t=0. An exact expansion is obtained for a certain n-particle reduced distribution function f(n)(z1;…;zn; t) in terms of the 1-particle reduced distribution function f(1)(z1; t) for the specified particle by starting with separate expressions for these functions in terms of f(1)(z1; 0). Expansions for the corresponding cluster functions are first obtained and then graph theoretic methods applied to obtain a solution.  相似文献   

11.
12.
The generalized exponential-integral function V(x, y) defined here includes as special cases the function E(2)1(x) = V(x, 0) introduced by van de Hulst and functions M0(x) = V(x, 1) and N0(x) = V(x, -1) introduced by Kourganoff in connection with integrals of the form ∫ En)t)Em(t±x), which play an important role in the theory of monochromatic radiative transfer. Series and asymptotic expressions are derived and, for the most important special cases, y = 0 and y = 1, Chebyshev expansions and rational approximations are obtained that permit the function to be evaluated to at least 10 sf on 0<x<∞ using 16 sf arithmetic.  相似文献   

13.
A theory for the response of a 2D two-level system to irradiation by a symmetric light pulse is developed. Under certain conditions, such an electron system approximates an ideal solitary quantum well in a zero field or a strong magnetic field H perpendicular to the plane of the well. One of the energy levels is the ground state of the system, while the other is a discrete excited state with energy ?ω0, which may be an exciton level for H=0 or any level in a strong magnetic field. It is assumed that the effect of other energy levels and the interaction of light with the lattice can be ignored. General formulas are derived for the time dependence of the dimensionless “coefficients” of the reflection ?(t), absorption A(t), and transmission ?(t) for a symmetric light pulse. It is shown that the ?(t), A(t), and ?(t) time dependences have singular points of three types. At points t 0 of the first type, A(t 0)=T(t 0)=0 and total reflection takes place. It is shown that for γr?γ, where γr and γ are the radiative and nonradiative reciprocal lifetimes, respectively, for the upper energy level of the two-level system, the amplitude and shape of the transmitted pulse can change significantly under the resonance ωl0. In the case of a long pulse, when γlr, the pulse is reflected almost completely. (The quantity γl characterizes the duration of the exciting pulse.) In the case of an intermediate pulse duration γlr, the reflection, absorption, and transmission are comparable in value and the shape of the transmitted pulse differs considerably from the shape of the exciting pulse: the transmitted pulse has two peaks due to the existence of the point t 0 of total reflection, at which the transmission is zero. If the carrier frequency ωl of light differs from the resonance frequency ω0, the oscillating ?(t), A(t), and ?(t) time dependences are observed at the frequency Δω=ωl0. Oscillations can be observed most conveniently for Δω?γl. The position of the singular points of total absorption, reflection, and transparency is studied for the case when ωl differs from the resonance frequency.  相似文献   

14.
D. Ronis  I. Oppenheim 《Physica A》1977,86(3):475-489
Nonlinear equations governing the relaxation of some macroscopic quantities, a(r,t) are derived using Kubo's response theory, in isolated inhomogeneous systems. The resulting equations contain microcanonical time correlation functions. It is shown how to express these in terms of arbitrary ensemble correlation functions and correction arising from their infinite time behaviour are discussed. In addition it is shown that the concept of local equilibrium must be modified somewhat.  相似文献   

15.
《Physics letters. A》1997,224(6):331-336
We consider the correlation functions of two-dimensional turbulence in the presence and absence of a three-dimensional perturbation, by means of conformal field theory. In the presence of three-dimensional perturbation, we show that in the strong coupling limit of a small scale random force, there is some logarithmic factor in the correlation functions of velocity stream functions. We show that the logarithmic conformal field theory c8,1 describes the 2D-turbulence both in the absence and in the presence of the perturbation. We obtain the energy spectrum E(k) ∼ k−5.125 ln(k) for perturbed 2D-turbulence and E(k) ∼ k−5 ln(k) for unperturbed turbulence. Recent numerical simulation and experimental results confirm our prediction.  相似文献   

16.
H.A Tolhoek 《Physica A》1977,86(2):278-302
In a previous paper wave propagation was studied according to a sixth-order partial differential equation involving a complex mass M. The corresponding Yang-Feldman integral equations (indicated as SM-YF-equations), were formulated using modified Green's functions GMR(x) and GMA(x), which then incorporate the partial differential equation together with certain boundary conditions. In this paper certain limit properties of these modified Green's functions are derived: (a) It is shown that for |M| → ∞ the Green's functions GMR(x) and GMA(x) approach the Green's functions ΔR(x) and ΔA(x) of the corresponding KG-equation (Klein-Gordon equation). (b) It is further shown that the asymptotic behaviour of GMA(x) and GMA(x) is the same as of ΔR(x) and ΔA(x) - and also the same as for DR(x) and DA(x) for t→ ± ∞, where DR and DA are the Green n's functions for the KG-equation with mass zero. It is essential to take limits in the sense of distribution theory in both cases (a) and (b). The property (b) indicates that the wave propagation properties of the SM-YF-equations, the KG-equation with finite mass and the KG-equation with mass zero are closely related in an asymptotic sense.  相似文献   

17.
We analyse the shear stress, C s(t) and pressure or ‘bulk’, C b(t) time-correlation functions for steeply repulsive inverse power fluids (SRP) in which the particles interact via a pair potential with the analytic form, φ(r) = ε(σ/r) n , in a new approach to the understanding of their viscoelastic properties. We show analytically, and confirm by molecular dynamics simulations, that close to the hard-sphere limit both these time-correlation functions have the analytic form, C s(t)/C s(0) and C b(t)/C b(0) = 1 – T*(nt*)2+ O((nt*)4), where T* = k B T/ε, is the reduced temperature, k B is Boltzmann's constant and t* = (ε/mσ2)½ t is the reduced time. This leads to an alternative and much simpler derivation of formulae for the shear and bulk viscosities which for the limiting case of hard spheres are numerically very close to the traditional Enskog relations. These simple relations for the finite and continuous SRP interaction are in satisfactory agreement with the essentially exact molecular dynamics simulation results for ca. n ≥ 18.  相似文献   

18.
《Physics letters. A》1998,240(3):137-143
Differential-difference equations (DDEs) un(k)(t) = Fn(t, un+a,…, un+b) for k ≥ 2 are studied for their differential Lie symmetries. We observe that while nonintrinsic Lie symmetries do exist in such DDEs, a great many admit only the intrinsic ones. We also propose a mechanism for automating symmetry calculations for fairly general DDEs, with a variety of features exemplified. In particular, the Fermi-Pasta-Ulam system is studied in detail and its new similarity solutions given explicitly.  相似文献   

19.
A rigorous lower bound on the slope parameter γ(s, t) = d ln A(s, t)/dt is derived for 0 < t < t0 where A(s, t) is the absorptive part of the elastic scattering amplitude and t0 is related to the right extreme of the Lehmann-Martin ellipse. When A(s, t) has high-energy behavior like sα(t)lnη(t)s…, this lower bound on α(s, t) is used to obtain lower bounds on α′(t) for 0 < t < t0, which saturate for ‘parabolic trajectories’. We also obtain a lower bound on γ(s, t) for t < 0 which can be used to find the nearforward region in which γ(s, t) cannot vanish.  相似文献   

20.
Electromagnetic waves carry the Abraham momentum, whose density is given by pEM = S(r,t) / c2. Here S(r,t) = E(r,t) × H(r,t) is the Poynting vector at point r in space and instant t in time, E and H are the local electromagnetic fields, and c is the speed of light in vacuum. The above statement is true irrespective of whether the waves reside in vacuum or within a ponderable medium, which medium may or may not be homogeneous, isotropic, transparent, linear, magnetic, etc. When a light pulse enters an absorbing medium, the force experienced by the medium is only partly due to the absorbed Abraham momentum. This absorbed momentum, of course, is manifested as Lorentz force (while the pulse is being extinguished within the absorber), but not all the Lorentz force experienced by the medium is attributable to the absorbed Abraham momentum. We consider an absorptive/reflective medium having the complex refractive index n2 + iκ2, submerged in a transparent dielectric of refractive index n1, through which light must travel to reach the absorber/reflector. Depending on the impedance-mismatch between the two media, which mismatch is dependent on n1, n2, κ2, either more or less light will be coupled into the absorber/reflector. The dependence of this impedance-mismatch on n1 is entirely responsible for the appearance of the Minkowski momentum in certain radiation pressure experiments that involve submerged objects.  相似文献   

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