Related papers: On the Space-Time Geometry of Quantum Systems
Open quantum systems interacting with the environments often show interesting behaviors, such as decoherence, non-unitary evolution, dissipation, etc. It is interesting but still challenging to study the open quantum gravitation system…
By exploring a possible physical realisation of the geometric concept of noncommutative tangent bundle, we outline an axiomatic quantum picture of space as topological manifold and time as a count of its reconfiguration events.
Quantum connections are defined by parallel transport operators acting on a Hilbert space. They transport tangent operators along paths in parameter space. The metric tensor of a Riemannian manifold is replaced by an inner product of pairs…
This paper investigates a new formalism to describe real time evolution of quantum systems at finite temperature. A time correlation function among subsystems will be derived which allows for a probabilistic interpretation. Our derivation…
We provide geometric quantization of a completely integrable Hamiltonian system in the action-angle variables around an invariant torus with respect to the angle polarization. The carrier space of this quantization is the pre-Hilbert space…
We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and…
Quantum timeless approaches solve the problem of time by recovering the usual unitary evolution of quantum theory relative to a clock in a stationary quantum Universe. For some Hamiltonians of the Universe, such as those including an…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
We have shown that quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. Using these transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum…
We consider Deutsch's computational model of a quantum system evolving in a spacetime containing closed timelike curves. Although it is known that this model predicts non-linear and non-unitary evolutions of the system, we demonstrate that…
The basic properties of Poincare gauge invariant Hilbert bundles over Lorentzian manifolds are derived. Quantum connections are introduced in such bundles, which govern a parallel transport that is shown to satisfy the strong equivalence…
We study space-time symmetries in scalar quantum field theory (including interacting theories) on static space-times. We first consider Euclidean quantum field theory on a static Riemannian manifold, and show that the isometry group is…
Quantum collision models allow for the dynamics of open quantum systems to be described by breaking the environment into small segments, typically consisting of non-interacting harmonic oscillators or two-level systems. This work introduces…
We revisit the issue of time in quantum geometrodynamics and suggest a quantization procedure on the space of true dynamic variables. This procedure separates the issue of quantization from enforcing the constraints caused by the general…
We analyze in detail the discrete--time quantum walk on the line by separating the quantum evolution equation into Markovian and interference terms. As a result of this separation, it is possible to show analytically that the quadratic…
A small quantum system is studied which is a superposition of states localized in different positions in a static gravitational field. The time evolution of the correlation between different positions is investigated, and it is seen that…
Time-reversal symmetry is of fundamental importance to physics. In the classical theory of time-reversal symmetry, the time-reversal symmetry of a quantum system is described by an anti-unitary operator, which is known as the time-reversal…
The formalism for histories-based generalized quantum mechanics developed in two earlier papers is applied to the treatment of histories (of particles or fields or more general objects) in curved spacetimes (which need not admit foliation…
In a wide range of quantum gravity theories, quasiclassical geometries, which are solutions to the Einstein field equations approximately, are described by "coherent states." Here we propose a Hamiltonian formalism for gravitational…
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…