Related papers: Quantum Layers over Surfaces Ruled Outside a Compa…

Quantum computation can proceed solely through single-qubit measurements on an appropriate quantum state, such as the ground state of an interacting many-body system. We investigate a simple spin-lattice system based on the cluster-state…

We study an effective Hamiltonian for the standard $\nu=1/3$ fractional quantum Hall system in the thin cylinder regime. We give a complete description of its ground state space in terms of what we call Fragmented Matrix Product States,…

The Quantum Hall Effects in all even dimensions are uniformly constructed. Contrary to some recent accounts in the literature, the existence of Quantum Hall Effects does not {\it crucially} depend on the existence of division algebras. For…

We prove that if $(M, g)$ is a compact Riemannian manifold with ergodic geodesic flow, and if $H \subset M$ is a smooth hypersurface satisfying a generic asymmetry condition with respect to the geodesic flow, then restrictions $\phi_j |_H$…

After showing that the magnetic translation operators are not the symmetries of the QHE on non-flat surfaces , we show that there exist another set of operators which leads to the quantum group symmetries for some of these surfaces . As a…

Quantum families of maps between quantum spaces are defined and studied. We prove that quantum semigroup (and sometimes quantum group) structures arise naturally on such objects out of more fundamental properties. As particular cases we…

We investigate quantum tomography in scenarios where prior information restricts the state space to a smooth manifold of lower dimensionality. By considering stability we provide a general framework that relates the topology of the manifold…

We construct a space of quantum states and an algebra of quantum observables, over the set of all metrics of arbitrary but fixed signature, defined on a manifold. The construction is diffeomorphism invariant, and unique up to natural…

It has been experimentally demonstrated that quantum coherence can persist in macroscopic phenomena [J.R. Friedman et al.,Nature, 406 (2000) 43]. To face the challenge of this new fact, in this article QM in its standard form is assumed to…

On a smooth asymptotically flat Riemannian manifold with non-compact boundary, we prove a positive mass theorem for metrics which are only continuous across a compact hypersurface. As an application, we obtain a positive mass theorem on…

A closed geodesic on the modular surface is "low-lying" if it does not travel "high" into the cusp. It is "fundamental" if it corresponds to an element in the class group of a real quadratic field. We prove the existence of infinitely many…

In this paper, I emphasize those features of the extended phase space approach to quantization of gravity that distinguish it among other approaches. First of all, it is the conjecture about non-trivial topology of the Universe which was…

Topological surface states are a class of novel electronic states that are of potential interest in quantum computing or spintronic applications. Unlike conventional two-dimensional electron states, these surface states are expected to be…

We describe recent progress in our understanding of the interplay between interactions, symmetry, and topology in states of quantum matter. We focus on a minimal generalization of the celebrated topological band insulators to interacting…

We consider the quantum mechanics of a particle on a noncommutative plane. The case of a charged particle in a magnetic field (the Landau problem) with a harmonic oscillator potential is solved. There is a critical point, where the density…

The paper discusses objections against non-hidden variable versions of the epistemic conception of quantum states - the view that quantum states do not describe the properties of quantum systems but reflect, in some way to be specified, the…

A remarkable feature of atomic ground states is that they are observed to be radiationless in nature, despite (from a classical viewpoint) typically involving charged particles in accelerated motions. The simple hydrogen atom is a case in…

The current understanding of the quantum origin of cosmic structure is discussed critically. We point out that in the existing treatments a transition from a symmetric quantum state to an (essentially classical) non-symmetric state is…

Quantum field theory (QFT) on non-stationary spacetimes is well understood from the side of the algebra of observables. The state space, however, is largely unexplored, due to the non-existence of distinguished states (vacuum, scattering…

A central tenet in the theory of quantum phase transitions (QPTs) is that a nonanalyticity in the ground-state energy in the thermodynamic limit implies a QPT. Here we report on a finding that challenges this assertion. As a case study we…