Related papers: Quantum Observables and Recollapsing Dynamics
From the dynamics of a broad class of classical mean-field glass models one may obtain a quantum model with finite zero-temperature entropy, a quantum transition at zero temperature, and a time-reparametrization (quasi-)invariance in the…
Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and…
It is natural to investigate if the quantization of an integrable or superintegrable classical Hamiltonian systems is still integrable or superintegrable. We study here this problem in the case of natural Hamiltonians with constants of…
Recent contributions in the field of quantum state tomography have shown that, despite the exponential growth of Hilbert space with the number of subsystems, tomography of one-dimensional quantum systems may still be performed efficiently…
One solution to the so-called problem of time is to construct certain Dirac observables, sometimes called evolving constants of motion. There has been some discussion in the literature about the interpretation of such observables, and in…
Quantum states are successfully reconstructed using the maximum likelihood estimation on the subspace where the measured projectors reproduce the identity operator. Reconstruction corresponds to normalization of incompatible observations.…
The existence of incompatibility is one of the most fundamental features of quantum theory, and can be found at the core of many of the theory's distinguishing features, such as Bell inequality violations and the no-broadcasting theorem. A…
A correspondence is established between measure-preserving, ergodic dynamics of a classical harmonic oscillator and a quantum mechanical gauge theory on two-dimensional Minkowski space. This correspondence is realized through an isometric…
A subclass of dynamical semigroups induced by the interaction of a quantum system with an environment is introduced. Such semigroups lead to the selection of a stable subalgebra of effective observables. The structure of this subalgebra is…
We investigate a minisuperspace model of Einstein gravity plus dilaton that describes a static spherically symmetric configuration or a Kantowski - Sachs like universe. We develop the canonical formalism and identify canonical quantities…
We propose a special relativistic framework for quantum mechanics. It is based on introducing a Hilbert space for events. Events are taken as primitive notions (as customary in relativity), whereas quantum systems (e.g. fields and…
System of 1/2 spin particles is observed repeatedly using Stern-Gerlach apparatuses with rotated orientations. Synthesis of such non-commuting observables is analyzed using maximum likelihood estimation as an example of quantum state…
We explore further the suggestion to describe a pre- and post-selected system by a two-state, which is determined by two conditions. Starting with a formal definition of a two-state Hilbert space and basic operations, we systematically…
We compare classical and quantum dynamics of a particle in the de Sitter spacetimes with different topologies to show that the result of quantization strongly depends on global properties of a classical system. We present essentially…
A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer…
We present a thermodynamic rendering model in which the traditional quantum observer is reframed as a special case of a coherence-constrained interface. Collapse is treated not as an interpretive postulate but as a structural threshold -…
The expected return time to the original state is a key concept characterizing systems obeying both classical or quantum dynamics. We consider iterated open quantum dynamical systems in finite dimensional Hilbert spaces, a broad class of…
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a…
We consider general relativity with a cosmological constant as a perturbative expansion around a completely solvable diffeomorphism invariant field theory. This theory is the $\Lambda\to\infty$ limit of general relativity. This allows an…
In quantum theory, observables with a continuous spectrum are known to be fundamentally different from those with a discrete and finite spectrum. While some fundamental tests and applications of quantum mechanics originally formulated for…