相关论文: Quantum Observables and Recollapsing Dynamics

We consider a quantization of the Bianchi IX cosmological model based on taking the constraint to be a self-adjoint operator in an auxiliary Hilbert space. Using a WKB-style self-consistent approximation, the constraint chosen is shown to…

We consider a general symplectic transformation (also known as linear canonical transformation) of quantum-mechanical observables in a quantized version of a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q}…

The phase space of a relativistic system can be identified with the future tube of complexified Minkowski space. As well as a complex structure and a symplectic structure, the future tube, seen as an eight-dimensional real manifold, is…

We propose a quantum clock synchronization protocol in which Bob makes a remote measurement on Alice's quantum clock via a third qubit acting as its proxy. It is shown that the resulting correlations are dependent on the choice of the…

In her recent work, Dittrich generalized Rovelli's idea of partial observables to construct Dirac observables for constrained systems to the general case of an arbitrary first class constraint algebra with structure functions rather than…

The comprehensive formulation for loop quantum cosmology in the spatially flat, isotropic model was recently constructed. In this paper, the methods are extended to the anisotropic Bianchi I cosmology. Both the precursor and the improved…

A construction of covariant quantum phase observables, for Hamiltonians with a finite number of energy eigenvalues, has been recently given by D. Arsenovic et al. [Phys. Rev. A 85, 044103 (2012)]. For Hamiltonians generating periodic…

In cosmology minisuperspace models are described by nonlinear time-reparametrization invariant systems with a finite number of degrees of freedom. Often these models are not explicitly integrable and cannot be quantized exactly. Having this…

One of the main postulates of quantum mechanics is that measurements destroy quantum coherence (wave function collapse). Recently it was discovered that in a many-body system dilute local measurements still preserve some coherence across…

We study coherent states for Bianchi type I cosmological models, as examples of semiclassical states for time-reparametrization invariant systems. This simple model allows us to study explicitly the relationship between exact semiclassical…

We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…

The description of relativistic effects requires a preliminary definition of events localised in space-time while the clocks used for time definition and the fields used in synchronisation or localisation procedures are necessarily quantum…

Under the principle that quantum mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as…

Quantum dynamics that explore an unexpectedly small fraction of Hilbert space is inherently interesting. Integrable systems, quantum scars, MBL, hidden tensor structures, and systems with gauge symmetries are examples. Beyond dimension and…

Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…

We build a semi-classical quantization procedure for finite volume man- ifolds with hyperbolic cusps, adapted to a geometrical class of symbols. We prove an Egorov Lemma until Ehrenfest times on such manifolds. Then we give a version of…

A review is given of recent work aimed at constructing a quantum theory of cosmology in which all observables refer to information measurable by observers inside the universe. At the classical level the algebra of observables should be…

We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…

The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and…

Thought experiments about the physical nature of set theoretical counterexamples to the axiom of choice motivate the investigation of peculiar constructions, e.g. an infinite dimensional Hilbert space with a modular quantum logic. Applying…