Related papers: Quantum Billiards in Optical Lattices
A quantum wave function with localization on classical periodic orbits in a mesoscopic elliptic billiard has been achieved by appropriately superposing nearly degenerate eigenstates expressed as products of Mathieu functions. We analyze and…
The main purpose of part (III) is to give explicit geodesics and billiard orbits in polysquares that exhibit time-quantitative density. In many instances, we can even establish a best possible form of time-quantitative density called…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
We consider the motion of a particle subjected to the constant gravitational field and scattered inelasticaly by hard boundaries which possess the shape of parabola, wedge, and hyperbola. The billiard itself performs oscillations. The…
In this paper, we show that two-dimensional billiards with point interactions inside exhibit a chaotic nature in the microscopic world, although their classical counterpart is non-chaotic. After deriving the transition matrix of the system…
We study analytically and numerically the classical diffusive process which takes place in a chaotic billiard. This allows to estimate the conditions under which the statistical properties of eigenvalues and eigenfunctions can be described…
We study quantum systems on a discrete bounded lattice (lattice billiards). The statistical properties of their spectra show universal features related to the regular or chaotic character of their classical continuum counterparts. However,…
Quantum simulators could provide an alternative to numerical simulations for understanding minimal models of condensed matter systems in a controlled way. Typically, cold atom systems are used to simulate e.g. Hubbard models. In this paper,…
In condensed matter, it is often difficult to untangle the effects of competing interactions, and this is especially problematic for superconductors. Quantum simulators may help: here we show how exploiting the properties of highly excited…
A general approach describing quantum decision procedures is developed. The approach can be applied to quantum information processing, quantum computing, creation of artificial quantum intelligence, as well as to analyzing decision…
We propose a scheme to investigate the quantum phase transition of cold atoms in the bilayer hexagonal optical lattices. Using the quantum Monte Carlo method, we calculate the ground state phase diagrams which contain an antiferromagnet, a…
The main objective of quantum simulation is an in-depth understanding of many-body physics. It is important for fundamental issues (quantum phase transitions, transport, . . . ) and for the development of innovative materials. Analytic…
This paper investigates the dynamics of optical billiards, a generalization of classic billiards, where light rays travel within a refractive medium and reflect elastically at the boundary. Inspired by studies of acoustic modes in rapidly…
We discuss the effects of quantum fluctuations on the properties of vortex lattices in rapidly rotating ultracold atomic gases. We develop a variational method that goes beyond the Bogoliubov theory by including the effects of interactions…
The experimental realization of correlated quantum phases with ultracold gases in optical lattices and their theoretical understanding has witnessed remarkable progress during the last decade. In this review we introduce basic concepts and…
Recent works have established universal entanglement properties and demonstrated validity of single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians. However, a common property of all quantum-chaotic quadratic…
We have designed and realized magnetic trapping geometries for ultracold atoms based on permanent magnetic films. Magnetic chip based experiments give a high level of control over trap barriers and geometric boundaries in a compact…
Quantum algorithmics with single spins poses serious technological challenges such as precision fabrication, rapid decoherence, atomic-scale addressing and readout. To circumvent atomic-scale challenges, we examine the case of fully…
We study the low energy quantum spectra of two-dimensional rectangular billiards with a small but finite-size scatterer inside. We start by examining the spectral properties of billiards with a single pointlike scatterer. The problem is…
Dynamical quantum phase transitions are at the forefront of current efforts to understand quantum matter out of equilibrium. Except for a few exactly solvable models, predictions of these critical phenomena typically rely on advanced…