اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSignatures of Classical Periodic Orbits on a Smooth Quantum System
71
0
0.0
(
0
)
تأليف
Daniel Provost
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Gutzwillers trace formula and Bogomolnys formula are applied to a non--specific, non--scalable Hamiltonian system, a two--dimensional anharmonic oscillator. These semiclassical theories reproduce well the exact quantal results over a large spatial and energy range.
قيم البحث
اقرأ أيضاً
We experimentally and numerically investigate the quantum accelerator mode dynamics of an atom optical realization of the quantum delta-kicked accelerator, whose classical dynamics are chaotic. Using a Ramsey-type experiment, we observe interference,
demonstrating that quantum accelerator modes are formed coherently. We construct a link between the behavior of the evolutions fidelity and the phase space structure of a recently proposed pseudoclassical map, and thus account for the observed interference visibilities.
We study how decoherence rules the quantum-classical transition of the Kicked Harmonic Oscillator (KHO). When the amplitude of the kick is changed the system presents a classical dynamics that range from regular to a strong chaotic behavior. We show
that for regular and mixed classical dynamics, and in the presence of noise, the distance between the classical and the quantum phase space distributions is proportional to a single parameter $chiequiv Khbar_{rm eff}^2/4D^{3/2}$ which relates the effective Planck constant $hbar_{rm eff}$, the kick amplitude $K$ and the diffusion constant $D$. This is valid when $chi < 1$, a case that is always attainable in the semiclassical regime independently of the value of the strength of noise given by $D$. Our results extend a recent study performed in the chaotic regime.
Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms. The solution
s of the equations of motion corresponding to periodic orbits are obtained as series expansions computed by inverting the normalizing canonical transformation. To improve the convergence of the series a resummation based on a continued fraction may be performed. This method is analogous to that looking for approximate rational solutions (Prendergast method). It is shown that with a normal form truncated at the lowest order incorporating the relevant resonance it is possible to construct quite accurate solutions both for normal modes and periodic orbits in general position.
We study the orbits in a Manko-Novikov type metric (MN) which is a perturbed Kerr metric. There are periodic, quasi-periodic, and chaotic orbits, which are found in configuration space and on a surface of section for various values of the energy E an
d the z-component of the angular momentum Lz. For relatively large Lz there are two permissible regions of non-plunging motion bounded by two closed curves of zero velocity (CZV), while in the Kerr metric there is only one closed CZV of non-plunging motion. The inner permissible region of the MN metric contains mainly chaotic orbits, but it contains also a large island of stability. We find the positions of the main periodic orbits as functions of Lz and E, and their bifurcations. Around the main periodic orbit of the outer region there are islands of stability that do not appear in the Kerr metric. In a realistic binary system, because of the gravitational radiation, the energy E and the angular momentum Lz of an inspiraling compact object decrease and therefore the orbit of the object is non-geodesic. In fact in an EMRI system the energy E and the angular momentum Lz decrease adiabatically and therefore the motion of the inspiraling object is characterized by the fundamental frequencies which are drifting slowly in time. In the Kerr metric the ratio of the fundamental frequencies changes strictly monotonically in time. However, in the MN metric when an orbit is trapped inside an island the ratio of the fundamental frequencies remains constant for some time. Hence, if such a phenomenon is observed this will indicate that the system is non integrable and therefore the central object is not a Kerr black hole.
We consider a quasi one-dimensional chain of N chaotic scattering elements with periodic boundary conditions. The classical dynamics of this system is dominated by diffusion. The quantum theory, on the other hand, depends crucially on whether the cha
in is disordered or invariant under lattice translations. In the disordered case, the spectrum is dominated by Anderson localization whereas in the periodic case, the spectrum is arranged in bands. We investigate the special features in the spectral statistics for a periodic chain. For finite N, we define spectral form factors involving correlations both for identical and non-identical Bloch numbers. The short-time regime is treated within the semiclassical approximation, where the spectral form factor can be expressed in terms of a coarse-grained classical propagator which obeys a diffusion equation with periodic boundary conditions. In the long-time regime, the form factor decays algebraically towards an asymptotic constant. In the limit $Ntoinfty$, we derive a universal scaling function for the form factor. The theory is supported by numerical results for quasi one-dimensional periodic chains of coupled Sinai billiards.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
