共查询到20条相似文献,搜索用时 15 毫秒
1.
K P N Murthy 《Pramana》1985,25(3):231-238
Symmetric and asymmetric random walks on a segment (−∞,T>0) of the real line are considered. There is a non-zero probability for the random walk to get absorbed at a site it visits.
We derive for such random walks, expressions for survival probabilities in the asymptotic limit ofT→∞. An application of this asymptotic formulation to the problem of radiation transport through thick shields is presented. 相似文献
2.
Ricardo Weder 《Communications in Mathematical Physics》2000,215(2):343-356
In this paper we study the following nonlinear Schr?dinger equation on the line,
where f is real-valued, and it satisfies suitable conditions on regularity, on growth as a function of u and on decay as x→±∞. The generic potential, V, is real-valued and it is chosen so that the spectrum of consists of one simple negative eigenvalue and absolutely-continuous spectrum filling [0, ∞). The solutions to this equation
have, in general, a localized and a dispersive component. The nonlinear bound states, that bifurcate from the zero solution
at the energy of the eigenvalue of H, define an invariant center manifold that consists of the orbits of time-periodic localized solutions. We prove that all
small solutions approach a particular periodic orbit in the center manifold as t→±∞. In general, the periodic orbits are different for t→±∞. Our result implies also that the nonlinear bound states are asymptotically stable, in the sense that each solution with
initial data near a nonlinear bound state is asymptotic as t→±∞ to the periodic orbits of nearby nonlinear bound states that are, in general, different for t→±∞.
Received: 20 January 2000 / Accepted: 1 June 2000 相似文献
3.
Anna De Masi Errico Presutti Dimitrios Tsagkarogiannis Maria Eulalia Vares 《Journal of statistical physics》2012,147(3):519-528
We consider the symmetric simple exclusion process in the interval Λ N :=[−N,N]∩ℤ with births and deaths taking place respectively on suitable boundary intervals I + and I −, as introduced in De Masi et al. (J. Stat. Phys. 144:1151–1170, 2011). We study the stationary measure and its macroscopic density profile in the limit N→∞. 相似文献
4.
5.
Krzysztof Urbanowski 《Central European Journal of Physics》2009,7(4):696-703
An effect generated by the nonexponential behavior of the survival amplitude of an unstable state in the long time region
is considered. In 1957 Khalfin proved that this amplitude tends to zero as t → ∞ more slowly than any exponential function of t. This can be described in terms of the time-dependent decay rate γ(t) which, when considered with the Khalfin result, means that this γ(t) is not a constant for large t but that it tends to zero as t → ∞. We find that a similar conclusion can be drawn for a large class of models of unstable states for a quantity, which
can be interpreted as the “instantaneous energy” of the unstable state. This energy should be much smaller for suitably larger
values of t than when t is of the order of the lifetime of the considered state. Within a given model we show that the energy
corrections in the long (t → ∞) and relatively short (lifetime of the state) time regions, are different. This is a purely quantum mechanical effect.
It is hypothesized that there is a possibility to detect this effect by analyzing the spectra of distant astrophysical objects.
The above property of unstable states may influence the measured values of astrophysical and cosmological parameters.
相似文献
6.
Three-dimensional array structures associated with Richtmyer-Meshkov and Rayleigh-Taylor instability
A boundary separating adjacent gas or liquid media is frequently unstable. Richtmyer-Meshkov and Rayleigh-Taylor instability
cause the growth of intricate structures on such boundaries. All the lattice symmetries [rectangular (pmm2), square (p4mm), hexagonal (p6mm), and triangular (p3m1) lattices] which are of interest in connection with the instability of the surface of a fluid are studied for the first
time. They are obtained from initial disturbances consisting of one (planar case, two-dimensional flow), two (rectangular
cells), or three (hexagons and triangles) harmonic waves. It is shown that the dynamic system undergoes a transition during
development from an initial, weakly disturbed state to a limiting or asymptotic stationary state (stationary point). The stability
of these points (stationary states) is investigated. It is shown that the stationary states are stable toward large-scale
disturbances both in the case of Richtmyer-Meshkov instability and in the case of Rayleigh-Taylor instability. It is discovered
that the symmetry increases as the system evolves in certain cases. In one example the initial Richtmyer-Meshkov or Rayleigh-Taylor
disturbance is a sum of two waves perpendicular to one another with equal wave numbers, but unequal amplitudes: a
1(t=0)≠a
2(t=0). Then, during evolution, the flow has p2 symmetry (rotation relative to the vertical axis by 180°), which goes over to p4 symmetry (rotation by 90°) at t→∞, since the amplitudes equalize in the stationary state: a
1(t=∞)=a
2(t=∞). It is shown that the hexagonal and triangular arrays are complementary. Upon time inversion (t→−t), “rephasing” occurs, and the bubbles of a hexagonal array transform into jets of a triangular array and vice versa.
Zh. éksp. Teor. Fiz. 116, 908–939 (September 1999) 相似文献
7.
I. M. Suslov 《Journal of Experimental and Theoretical Physics》2010,111(3):450-465
The previously-obtained analytical asymptotic expressions for the Gell-Mann-Low function β(g) and anomalous dimensions in the ϕ4 theory in the limit g → ∞ are based on the parametric representation of the form g = f(t), β(g) = f
1(t) (where t ∝ g
0−1/2 is the running parameter related to the bare charge g
0), which is simplified in the complex t plane near a zero of one of the functional integrals. In this work, it has been shown that the parametric representation
has a singularity at t → 0; for this reason, similar results can be obtained for real g
0 values. The problem of the correct transition to the strong-coupling regime is simultaneously solved; in particular, the
constancy of the bare or renormalized mass is not a correct condition of this transition. A partial proof has been given for
the theorem of the renormalizability in the strong-coupling region. 相似文献
8.
Evolution of a Model Quantum System¶ Under Time Periodic Forcing:¶Conditions for Complete Ionization
O. Costin R. D. Costin J. L. Lebowitz A. Rokhlenko 《Communications in Mathematical Physics》2001,221(1):1-26
We analyze the time evolution of a one-dimensional quantum system with an attractive delta function potential whose strength
is subjected to a time periodic (zero mean) parametric variation η(t). We show that for generic η(t), which includes the sum of any finite number of harmonics, the system, started in a bound state will get fully ionized as
t→∞. This is irrespective of the magnitude or frequency (resonant or not) of η(t). There are however exceptional, very non-generic η(t), that do not lead to full ionization, which include rather simple explicit periodic functions. For these η(t) the system evolves to a nontrivial localized stationary state which is related to eigenfunctions of the Floquet operator.
Received: 1 November 2000 / Accepted: 5 February 2001 相似文献
9.
We consider the time evolution of a system of N identical bosons whose interaction potential is rescaled by N
−1. We choose the initial wave function to describe a condensate in which all particles are in the same one-particle state.
It is well known that in the mean-field limit N → ∞ the quantum N-body dynamics is governed by the nonlinear Hartree equation. Using a nonperturbative method, we extend previous results on
the mean-field limit in two directions. First, we allow a large class of singular interaction potentials as well as strong,
possibly time-dependent external potentials. Second, we derive bounds on the rate of convergence of the quantum N-body dynamics to the Hartree dynamics. 相似文献
10.
K. Urbanowski 《The European Physical Journal C - Particles and Fields》2008,58(1):151-157
By analyzing the survival probability amplitude of an unstable state we show that the energy corrections to this state in
the long (t→∞) and relatively short (lifetime of the state) time regions are different. It is shown that in the considered model the
above corrections decrease to zero as t→∞. It is hypothesized that this property could be detected by analyzing the spectra of distant astrophysical objects. The
above property of unstable states may influence the measured values of possible deviations of the fine structure constant
α as well as other astrophysical and cosmological parameters. 相似文献
11.
12.
Saulius Mickevičius Darius Germanas Ramutis K. Kalinauskas 《Central European Journal of Physics》2012,10(2):421-428
We present a new independent scheme of SO(3) group transformations suitable for the N particle system, composed of N − 1 and 1 particle subsystems, where N − 1 particles have their own intrinsic clusterization. The simple expressions for corresponding four-particle harmonic-oscillator
transformation brackets are presented, as well as their simplifications for the special values of mass ratio parameters d = 0, d → ∞ and d
1 = 0, d
1 → ∞. 相似文献
13.
A. B. J. Kuijlaars A. Martínez-Finkelshtein F. Wielonsky 《Communications in Mathematical Physics》2011,308(1):227-279
We consider the double scaling limit for a model of n non-intersecting squared Bessel processes in the confluent case:
all paths start at time t = 0 at the same positive value x = a, remain positive, and are conditioned to end at time t = 1 at x = 0. After appropriate rescaling, the paths fill a region in the tx–plane as n → ∞ that intersects the hard edge at x = 0 at a critical time t = t
*. In a previous paper, the scaling limits for the positions of the paths at time t ≠ t
* were shown to be the usual scaling limits from random matrix theory. Here, we describe the limit as n → ∞ of the correlation kernel at critical time t
* and in the double scaling regime. We derive an integral representation for the limit kernel which bears some connections
with the Pearcey kernel. The analysis is based on the study of a 3 × 3 matrix valued Riemann-Hilbert problem by the Deift-Zhou
steepest descent method. The main ingredient is the construction of a local parametrix at the origin, out of the solutions
of a particular third-order linear differential equation, and its matching with a global parametrix. 相似文献
14.
O. Benhar S. Fantoni G.I. Lykasov 《The European Physical Journal A - Hadrons and Nuclei》2000,7(3):415-419
The production of backward pions in lepton-nucleus collisions is analyzed. We show that a large yield of high momentum backward
pions can be explained by the Regge asymptotic of the distribution of nucleons carrying a large momentum fraction in the nuclear
target. The calculated spectra of pions emitted in the ν+ Ne →μ+π−+ X and ν+2H →μ+π−+ X reactions are in satisfactory agreement with the available experimental data.
Received: 22 July 1999 / Revised version: 22 November 1999 相似文献
15.
We define a nonlinear model for fractional relaxation phenomena. We use ε-expansion method to analyse this model. By studying the fundamental solutions of this model we find that when t → 0 the model exhibits a fast decay rate and when t → ∞ the model exhibits a power-law decay. By analysing the frequency response we find a logarithmic enhancement for the relative
ratio of susceptibility. 相似文献
16.
We consider a class of nonlinear Schrödinger equations (conservative and dispersive systems) with localized and dispersive solutions. We obtain a class of initial conditions, for which the asymptotic behavior (t±) of solutions is given by a linear combination of nonlinear bound state (time periodic and spatially localized solution) of the equation and a purely dispersive part (decaying to zero with time at the free dispersion rate). We also obtain a result ofasymptotic stability type: given data near a nonlinear bound state of the system, there is a nonlinear bound state of nearby energy and phase, such that the difference between the solution (adjusted by a phase) and the latter disperses to zero. It turns out that in general, the time-period (and energy) of the localized part is different fort+ from that fort–. Moreover the solution acquires an extra constant asymptotic phasee
iy
±.This research was supported in part by grants from the National Science FoundationThe results of this paper were announced in a lecture (June, 1988) on which the Proceedings article [Sof-We] is based 相似文献
17.
Oleg Safronov 《Communications in Mathematical Physics》2001,218(1):217-232
Let A be a periodic Schr?dinger operator and let V
0≥ 0 be a decaying potential. We study the number of the eigenvalues of the operator A(α) =A−αV
0 inside a fixed interval (λ1,λ2). We obtain an asymptotic formula for as α→∞.
Received: 12 September 2000 / Accepted: 22 November 2000 相似文献
18.
Muhittin Mungan 《Journal of statistical physics》2007,126(1):207-242
19.
I. D. Morris 《Journal of statistical physics》2007,126(2):315-324
Let Σ
A
be a finitely primitive subshift of finite type over a countable alphabet. For suitable potentials f : Σ
A
→ ℝ we can associate an invariant Gibbs equilibrium state μ
tf
to the potential tf for each t ≥ 1. In this note, we show that the entropy h(μ
tf
) converges in the limit t→ ∞ to the maximum entropy of those invariant measures which maximize ∫ f
dμ. We further show that every weak-* accumulation point of the family of measures μ
tf
has entropy equal to this value. This answers a pair of questions posed by O. Jenkinson, R. D. Mauldin and M. Urbański. 相似文献
20.
T. V. Dudnikova 《Russian Journal of Mathematical Physics》2010,17(1):77-95
The Hamiltonian system formed by a Klein-Gordon vector field and a particle in ℝ3 is considered. The initial data of the system are given by a random function, with finite mean energy density, which also
satisfies a Rosenblatt- or Ibragimov-type mixing condition. Moreover, initial correlation functions are assumed to be translation
invariant. The distribution μ
t
of the solution at time t ∈ ℝ is studied. The main result is the convergence of μ
t
to a Gaussian measure as t → ∞, where μ∞ is translation invariant. 相似文献