共查询到20条相似文献,搜索用时 31 毫秒
1.
K. Weibert J. Main G. Wunner 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2002,19(3):379-388
In the periodic orbit quantization of physical systems, usually only the leading-order ? contribution to the density of states is considered. Therefore, by construction, the eigenvalues following from semiclassical
trace formulae generally agree with the exact quantum ones only to lowest order of ?. In different theoretical work the trace formulae have been extended to higher orders of ?. The problem remains, however, how to actually calculate eigenvalues from the extended trace formulae since, even with ? corrections included, the periodic orbit sums still do not converge in the physical domain. For lowest-order semiclassical trace formulae the convergence problem can be elegantly, and universally, circumvented by application of the
technique of harmonic inversion. In this paper we show how, for general scaling chaotic systems, also higher-order
? corrections to the Gutzwiller formula can be included in the harmonic inversion scheme, and demonstrate that corrected semiclassical
eigenvalues can be calculated despite the convergence problem. The method is applied to the open three-disk scattering system,
as a prototype of a chaotic system.
Received 10 September 2001 and Received in final form 3 January 2002 相似文献
2.
W. Ihra M. Leadbeater J.L. Vega K. Richter 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,21(3):425-435
We study the effect on the density of states in mesoscopic ballistic billiards to which a superconducting lead is attached.
The expression for the density of states is derived in the semiclassical S-matrix formalism shedding light onto the origin of the differences between the semiclassical theory and the corresponding
result derived from random matrix models. Applications to a square billiard geometry and billiards with boundary roughness
are discussed. The saturation of the quasiparticle excitation spectrum is related to the classical dynamics of the billiard.
The influence of weak magnetic fields on the proximity effect in rough Andreev billiards is discussed and an analytical formula
is derived. The semiclassical theory provides an interpretation for the suppression of the proximity effect in the presence
of magnetic fields as a coherence effect of time reversed trajectories. It is shown to be in good agreement with quantum mechanical
calculations.
Received 21 August 1999 and Received in final form 21 March 2001 相似文献
3.
4.
Yu-Quan Yuan Xiao-Xiong Zeng Zhi-Jian Zhou Liang-Ping Jin 《General Relativity and Gravitation》2009,41(12):2771-2780
Recently, fermions tunneling beyond semiclassical approximation from an uncharged static black hole was investigated by Majhi,
which was based on the work of Banerjee and Majhi, it was found that the black hole entropy correction can be produced as
the quantum effect of a particle is taken into account. In this paper, we further extend this idea to the stationary Kerr
black hole to discuss its entropy correction. To get the corrections correctly, the proportionality parameters of quantum
corrections of action I
i
to the semiclassical action I
0 in this case are regarded as the inverse of the product of Planck Length and Planck Mass. The result shows that entropy corrections
to the stationary black hole also include the logarithmic term and inverse area term in Bekenstein–Hawking entropy beyond
semiclassical approximation. 相似文献
5.
B. L. Hu Albert Roura Enric Verdaguer 《International Journal of Theoretical Physics》2004,43(3):749-766
We discuss the stability of semiclassical gravity solutions with respect to small quantum corrections by considering the quantum fluctuations of the metric perturbations around the semiclassical solution. We call the attention to the role played by the symmetrized 2-point quantum correlation function for the metric perturbations, which can be naturally decomposed into two separate contributions: intrinsic and induced fluctuations. We show that traditional criteria on the stability of semiclassical gravity are incomplete because these criteria based on the linearized semiclassical Einstein equation can only provide information on the expectation value and the intrinsic fluctuations of the metric perturbations. By contrast, the framework of stochastic semiclassical gravity provides a more complete and accurate criterion because it contains information on the induced fluctuations as well. The Einstein–Langevin equation therein contains a stochastic source characterized by the noise kernel (the symmetrized 2-point quantum correlation function of the stress tensor operator) and yields stochastic correlation functions for the metric perturbations which agree, to leading order in the large N limit, with the quantum correlation functions of the theory of gravity interacting with N matter fields. These points are illustrated with the example of Minkowski space-time as a solution to the semiclassical Einstein equation, which is found to be stable under both intrinsic and induced fluctuations. 相似文献
6.
Semiclassical bosonic <Emphasis Type="Italic">D</Emphasis>-brane boundary states in curved spacetime
Ion Vasile Vancea 《Central European Journal of Physics》2010,8(1):49-56
In this paper we discuss the existence of quantum D-brane states in the strong gravitational field and in the presence of a constant Kalb-Ramond field. A semiclassical string
quantization method in which the spacetime metric g
AB
and the constant antisymmetric Kalb-Ramond field b
AB
are treated exactly is employed. In this framework, the semiclassical D-branes are defined at the first order perturbation around the trajectory of the center-of-mass of a string. The set of equations
the semiclassical D-branes must satisfy in a general strong gravitational field are given. These equations are solved in the AdS background where it is shown that a D-brane coherent state exists if the operators that project the string fields onto the corresponding Neumann and Dirichlet
directions satisfy a set of algebraic constraints. A second set of equations that should be satisfied by the projectors in
order that the semiclassical state be compatible with the global structure of the D-brane are derived in the particle limit of a string in the torsionless AdS background. 相似文献
7.
B. Karmakar M. R. Gokhale A. P. Shah B. M. Arora D. T. N. de Lang A. de Visser L. A. Ponomarenko A. M. M. Pruisken 《Physica E: Low-dimensional Systems and Nanostructures》2004,24(3-4):187-210
In experiments on electron transport, the macroscopic inhomogeneities in the sample play a fundamental role. In this paper and a subsequent one, we introduce and develop a general formalism that captures the principal features of sample inhomogeneities (density gradients, contact misalignments) in the magnetoresistance data taken from low-mobility heterostructures. We present detailed assessments and experimental investigations of the different regimes of physical interest, notably the regime of semiclassical transport at weak magnetic fields, the plateau–plateau transitions as well as the plateau–insulator transition that generally occurs at much stronger values of the external field only.It is shown that the semiclassical regime at weak fields plays an integral role in the general understanding of the experiments on the quantum Hall regime. The results of this paper clearly indicate that the plateau–plateau transitions, unlike the plateau–insulator transition, are fundamentally affected by the presence of sample inhomogeneities. We propose a universal scaling result for the magnetoresistance parameters. This result facilitates, amongst many other things, a detailed understanding of the difficulties associated with the experimental methodology of H.P. Wei et al. in extracting the quantum critical behavior of the electron gas from the transport measurements conducted on the plateau–plateau transitions. 相似文献
8.
K. Weibert J. Main G. Wunner 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2000,12(3):381-401
Harmonic inversion has already been proven to be a powerful tool for the analysis of quantum spectra and the periodic orbit
orbit quantization of chaotic systems. The harmonic inversion technique circumvents the convergence problems of the periodic
orbit sum and the uncertainty principle of the usual Fourier analysis, thus yielding results of high resolution and high precision.
Based on the close analogy between periodic orbit trace formulae for regular and chaotic systems the technique is generalized
in this paper for the semiclassical quantization of integrable systems. Thus, harmonic inversion is shown to be a universal
tool which can be applied to a wide range of physical systems. The method is further generalized in two directions: firstly,
the periodic orbit quantization will be extended to include higher order corrections to the periodic orbit sum. Secondly, the use of cross-correlated periodic orbit sums allows us to significantly
reduce the required number of orbits for semiclassical quantization, i.e., to improve the efficiency of the semiclassical method. As a representative of regular systems, we choose the circle billiard,
whose periodic orbits and quantum eigenvalues can easily be obtained.
Received 24 February 2000 and Received in final form 22 May 2000 相似文献
9.
It is shown that both universal and non-universal correlations must exist between classical periodic orbits in order that Gutzwiller's semiclassical trace formula is consistent with a real, discrete quantum energy spectrum. Formulae for the two-point correlations are derived. The universal correlations are consistent with those conjectured by Argaman et al. (1993). Likewise, both universal and non-universal correlations must exist between quantum energy levels in order that the trace formula be consistent with the fact that periodic orbit actions are real and discrete. In this case, the two-point correlations implied are consistent with random matrix theory and previous semiclassical calculations. These ideas are illustrated with reference to the primes and the Riemann zeros. 相似文献
10.
The S-matrix formalism is used to perform analytical calculations of the spectrum of quasi-stationary states of charge carriers in a core-shell quantum dot. Analytical expressions are obtained for the second-order perturbative corrections to the position and half-width of a quasi-stationary energy level, and level shifts are calculated numerically for a core-shell quantum dot in the presence of an electrostatic field. The corrections to level half-width due to Stark effect are analyzed as functions of level energy and barrier thickness. It is shown that there exists a level position E cr such that the correction δΓ to the level half-width changes sign. An analytical expression for the quadratic Stark shift in a dc-biased quantum well is found in semiclassical approximation. It is shown that the corresponding correction δΓ to half-width also changes sign as energy passes through E cr. As an example, the Stark shift is calculated for a core-shell quantum dot in the electrostatic field of an adjacent protein molecule. 相似文献
11.
12.
We extend a theory of first order ? corrections to Gutzwiller’s trace formula for systems with a smooth potential to systems with discrete symmetries and, as an example, apply the method to the two-dimensional hydrogen atom in a uniform magnetic field. We exploit the C4v-symmetry of the system in the calculation of the correction terms. The numerical results for the semiclassical values will be compared with values extracted from exact quantum mechanical calculations. The comparison shows an excellent agreement and demonstrates the power of the ? expansion method. 相似文献
13.
H. -J. Mikeska B. Vaz da costa H. C. Fogedby 《Zeitschrift für Physik B Condensed Matter》1989,77(1):119-127
The effect of quantum fluctuations on solitons in the easy-plane ferromagnetic chain is considered within the semiclassical approximation. In accordance with the low temperature ideal gas picture we treat the solitons as a Boltzmann gas and impose quantisation on the spin wave spectrum. We present a method which allows to calculate quantum corrections in a systematic perturbation expansion in 1/S, whereS is the spin length. We use this method to obtain the soliton energy to second order at zero temperature. Our results indicate that the semiclassical approach reasonably describes quantum effects on soliton properties. 相似文献
14.
Ashoke Sen 《General Relativity and Gravitation》2012,44(5):1207-1266
Logarithmic corrections to the extremal black hole entropy can be computed purely in terms of the low energy data—the spectrum
of massless fields and their interaction. The demand of reproducing these corrections provides a strong constraint on any
microscopic theory of quantum gravity that attempts to explain the black hole entropy. Using quantum entropy function formalism
we compute logarithmic corrections to the entropy of half BPS black holes in N=2{{\mathcal N}=2} supersymmetric string theories. Our results allow us to test various proposals for the measure in the OSV formula, and we
find agreement with the measure proposed by Denef and Moore if we assume their result to be valid at weak topological string
coupling. Our analysis also gives the logarithmic corrections to the entropy of extremal Reissner–Nordstrom black holes in
ordinary Einstein–Maxwell theory. 相似文献
15.
We discuss the coarse-grained level density of the Hénon-Heiles system above the barrier energy, where the system is nearly
chaotic. We use periodic orbit theory to approximate its oscillating part semiclassically via Gutzwiller’s semiclassical trace
formula (extended by uniform approximations for the contributions of bifurcating orbits). Including only a few stable and
unstable orbits, we reproduce the quantum-mechanical density of states very accurately. We also present a perturbative calculation
of the stabilities of two infinite series of orbits (Rn and Lm), emanating from the shortest librating straight-line orbit (A) in a bifurcation cascade just below the barrier, which at the barrier have two common asymptotic Lyapunov exponents χR and χL. 相似文献
16.
17.
Arul Lakshminarayan 《Pramana》1997,48(2):517-535
Using quantum maps, we study the accuracy of semiclassical trace formulas. The role of chaos in improving the semiclassical
accuracy in some systems is demonstrated quantitatively. However, our study of the standard map cautions that this may not
be most general. While studying a sawtooth map we demonstrate the rather remarkable fact that at the level of the time one
trace even in the presence of fixed points on singularities the trace formula may be exact, and in any case has no logarithmic
divergences observed for the quantum bakers map. As a byproduct we introduce fantastic periodic curves akin to curlicues. 相似文献
18.
Avinash Khare 《Pramana》1997,48(2):537-553
We, offer an alternative interpretation of the Riemann zeta functionζ(s) as a scattering amplitude and its nontrivial zeros as the resonances in the scattering amplitude. We also look at several
different facets of the phase of theζ function. For example, we show that the smooth part of theζ function along the line of the zeros is related to the quantum density of states of an inverted oscillator. On the other
hand, for ℜs>1/2, we show that the memory of the zeros fades only gradually through a Lorentzian smoothing of the delta functions. The
corresponding trace formula for ℜs≫1 is shown to be of the same form as generated by a one-dimensional harmonic oscillator in one direction along with an inverted
oscillator in the transverse direction. Quite remarkably for this simple model, the Gutzwiller trace formula can be obtained
analytically and is found to agree with the quantum result. 相似文献
19.
Parthasarathi Majumdar 《Pramana》2000,55(4):511-527
This survey intends to cover recent approaches to black hole entropy which attempt to go beyond the standard semiclassical
perspective. Quantum corrections to the semiclassical Bekenstein-Hawking area law for black hole entropy, obtained within
the quantum geometry framework, are treated in some detail. Their ramification for the holographic entropy bound for bounded
stationary spacetimes is discussed. Four dimensional supersymmetric extremal black holes in string-based N=2 supergravity are also discussed, albeit more briefly. 相似文献
20.
Jaume Haro 《International Journal of Theoretical Physics》2006,45(2):410-424
The quantum back-reaction problem in scalar QED is studied, in the semiclassical approximation, for nonstationary external electric fields. Using a model proposed in [Cooper, F., Mottola, E. (1989). Quantum back reaction in scalar QED as an initial-value problem. Physical Review D40(2), 456–464], based in a Hartree-type equation, we calculate, until order ħ, the induced current density and the induced electromagnetic field. Once we have computed the induced electromagnetic field, we obtain, until order ħ, the effective Lagrangian and the average density of produced pairs taking into account the back-reaction. 相似文献