Related papers: Non-linear $\sigma$-model for long range disorder …
The degenerate Lagrangian system describing a lot of cosmological models is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the "singularity" is reduced to a billiard on the…
In this paper we investigate the non-linear sigma model arising in the reduction of D = 5 supergravity to D = 3, and present the application of this sigma model to supersymmetric black ring solutions in five-dimensional minimal…
In this paper we have tested several general numerical methods in solving the quantum billiards, such as the boundary integral method (BIM) and the plane wave decomposition method (PWDM). We performed extensive numerical investigations of…
Wavefunctions in chaotic and disordered quantum billiards are studied experimentally using thin microwave cavities. The chaotic wavefunctions display universal density distributions and density auto-correlations in agreement with…
We analyse the classical and quantum behaviour of a particle trapped in a diamond shaped billiard. We defined this billiard as a half stadium connected with a triangular billiard. A parameter $\xi$ which gradually change the shape of the…
Models of disorder with a direction (constant imaginary vector-potential) are considered. These non-Hermitian models can appear as a result of computation for models of statistical physics using transfer matrix technique or describe…
We provide and study complete sets of one-loop renormalization group equations of several Finkel'stein non-linear $\sigma$-models, the effective field theories describing the diffusive quantum fluctuations in correlated disordered systems.…
An elementary application of Algorithmic Complexity Theory to the polygonal approximations of curved billiards-integrable and chaotic-unveils the equivalence of this problem to the procedure of quantization of classical systems: the scaling…
We develop a theory of non-linear cosmological perturbations at superhorizon scales for a scalar field with a Lagrangian of the form $P(X,\phi)$, where $X=-\partial^{\mu}\phi\partial_{\mu}\phi$ and $\phi$ is the scalar field. We employ the…
We present a computational scheme based on classical molecular dynamics to study chaotic billiards in static external magnetic fields. The method allows to treat arbitrary geometries and several interacting particles. We test the scheme for…
We derive analytic expressions for the wavefunctions and energy levels in the semiclassical approximation for perturbed integrable systems. We find that some eigenstates of such systems are substantially different from any of the…
A variety of mesoscopic systems can be represented as a billiard with a random coupling to the exterior at the boundary. Examples include quantum dots with multiple leads, quantum corrals with different kinds of atoms forming the boundary,…
Classical nonlinear theories are highly successful in describing far-from-equilibrium dynamics of magnets, encompassing phenomena such as parametric resonance, ultrafast switching, and even chaos. However, at ultrashort length and time…
In numerically solving the Helmholtz equation inside a connected plane domain with Dirichlet boundary conditions (the problem of the quantum billiard) one surprisingly faces enormous difficulties if the domain has a problematic geometry…
Quantum billiards are a key focus in quantum mechanics, offering a simple yet powerful model to study complex quantum features. While the development of algebras for quantum systems is traced from one-dimensional integrable models to…
We present a generalized dynamical mean-field approach for the nonequilibrium physics of a strongly correlated system in the presence of a time-dependent external field. The Keldysh Green's function formalism is used to study the…
We present a semiclassical theory for transport through open billiards of arbitrary convex shape that includes diffractively scattered paths at the lead openings. Starting from a Dyson equation for the semiclassical Green's function we…
A new kind of Q-balls is found: Q-balls in a non-linear sigma model. Their main properties are presented together with those of their self-gravitating generalization, sigma model Q-stars. A simple special limit of solutions which are bound…
In an effort to provide an alternative method to represent a quantum spin, a precise nonlinear dynamics semi-classical model is used to show that standard quantum spin analysis can be obtained. The model includes a multi-body,…
Establishing global well-posedness and convergence toward equilibrium of the Boltzmann equation with specular reflection boundary condition has been one of the central questions in the subject of kinetic theory. Despite recent significant…