Related papers: Periodic orbits and semiclassical form factor in b…
The 2-point correlation form factor, $K_2(\tau)$, for small values of $\tau$ is computed analytically for typical examples of pseudo-integrable systems. This is done by explicit calculation of periodic orbit contributions in the diagonal…
The computation of the two-point correlation form factor K(t) is performed for a rectangular billiard with a small size impurity inside for both periodic or Dirichlet boundary conditions. It is demonstrated that all terms of perturbation…
The properties of energy levels in a family of classically pseudointegrable systems, the barrier billiards, are investigated. An extensive numerical study of nearest-neighbor spacing distributions, next-to-nearest spacing distributions,…
We derive semiclassical contributions of periodic orbits from a boundary integral equation for three-dimensional billiard systems. We use an iterative method that keeps track of the composition of the stability matrix and the Maslov index…
We present a semiclassical description of the level density of a two-dimensional circular quantum dot in a homogeneous magnetic field. We model the total potential (including electron-electron interaction) of the dot containing many…
Periodic orbits are the central ingredients of modern semiclassical theories and corrections to these are generally non-classical in origin. We show here that for the class of generic polygonal billiards, the corrections are predominantly…
Periodic orbit theory for classical hyperbolic system is very significant matter of how we can interpret spectral statistics in terms of semiclassical theory. Although pruning is significant and generic property for almost all hyperbolic…
We derive an analytical trace formula for the level density of the two-dimensional elliptic billiard using an improved stationary phase method. The result is a continuous function of the deformation parameter (eccentricity) through all…
We discuss consequences of a recent observation that the sequence of periodic orbits in a chaotic billiard behaves like a poissonian stochastic process on small scales. This enables the semiclassical form factor $K_{sc}(\tau)$ to agree with…
Barrier billiards are simple examples of pseudo-integrable models which form an appealing but poorly investigated subclass of dynamical systems. The paper examines the semiclassical limit of the exact quantum transfer operator for barrier…
The structure of the semiclassical trace formula can be used to construct a quasi-classical evolution operator whose spectrum has a one-to-one correspondence with the semiclassical quantum spectrum. We illustrate this for marginally…
We present a case study for the semiclassical calculation of the oscillations in the particle and kinetic-energy densities for the two-dimensional circular billiard. For this system, we can give a complete classification of all closed…
We derive contributions to the trace formula for the spectral density accounting for the role of diffractive orbits in two-dimensional polygonal billiards. In polygons, diffraction typically occurs at the boundary of a family of…
The methods of the high energy semiclassical quantization in the rational polygon billiards used in our earlier papers are generalized to an arbitrary rational multi-connected polygon billiards i.e. to the billiards which is a rational…
We investigate the semiclassical energy spectrum of quantum elliptic billiard. The nearest neighbor spacing distribution, level number variance and spectral rigidity support the notion that the elliptic billiard is a generic integrable…
We study periodic wind-tree models, billiards in the plane endowed with $\mathbb{Z}^2$-periodically located identical connected symmetric right-angled obstacles. We show asymptotic formulas for the number of (isotopy classes of) closed…
We review some properties of periodic orbit families in polygonal billiards and discuss in particular a sum rule that they obey. In addition, we provide algorithms to determine periodic orbit families and present numerical results that shed…
Using semi-classical formalism and asymptotic proliferation law of periodic orbits, we obtain an analytical expressions for the two-level cluster function, spectral form factor, level spacing distribution and the number variance for…
We demonstrate for a generic pseudointegrable billiard that the number of periodic orbit families with length less than $l$ increases as $\pi b_0l^2/\langle a(l) \rangle$, where $b_0$ is a constant and $\langle a(l) \rangle$ is the average…
The barrier billiard is the simplest example of pseudo-integrable models with interesting and intricate classical and quantum properties. Using the Wiener-Hopf method it is demonstrated that quantum mechanics of a rectangular billiard with…