相关论文: Geometry of quantum dynamics and a time-energy unc…

We present a unified geometric and dynamical framework for a physical system consisting of $n$ spin-$1/2$ particles with all-range Ising interaction. Using the Fubini-Study formalism, we derive the metric tensor of the associated quantum…

We cast observable measure of quantum coherence or asymmetry as a resource to control the quantum speed limit (QSL) for unitary evolutions. For non-unitary evolutions, QSL depends on that of the state of the system and environment together.…

We give a short review of known exact inequalities that can be interpreted as "energy-time" and "frequency-time" uncertainty relations. In particular we discuss a precise form of signals minimizing the physical frequency-time uncertainty…

The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…

Each semigroup describing the time evolution of an open quantum system on a finite dimensional Hilbert space is related to a special structure of this space. It is shown how the space can be decomposed into subspaces: One is related to…

In this paper, the projective geometry is used to describe the features of spherical manifold and discreteness in quantum evolution. As a system evolves in time the state vector changes and it traces out a curve in Hilbert space.…

The Mandelstam-Tamm and Margolus-Levitin inequalities play an important role in the study of quantum mechanical processes in Nature, since they provide general limits on the speed of dynamical evolution. However, to date there has been only…

A kinematic approach to the geometric phase for mixed quantal states in nonunitary evolution is proposed. This phase is manifestly gauge invariant and can be experimentally tested in interferometry. It leads to well-known results when the…

An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…

We examine evolutions where each component of a given decomposition of a mixed quantal state evolves independently in a unitary fashion. The geometric phase and parallel transport conditions for this type of decomposition dependent…

In this paper we propose a systematic method to solve the inverse dynamical problem for a quantum system governed by the von Neumann equation: to find a class of Hamiltonians reproducing a prescribed time evolution of a pure or mixed state…

It is remarkable that Heisenberg's position-momentum uncertainty relation leads to the existence of a maximal acceleration for a physical particle in the context of a geometric reformulation of quantum mechanics. It is also known that the…

This paper presents a novel formalism for the out of equilibrium dynamics of the density matrix, capable of describing highly entangled many-body interactions. The evolution of quantum states is evaluated via eigenvalue dynamics of a…

Dissipation and decoherence, and the evolution from pure to mixed states in quantum physics are handled through master equations for the density matrix. By embedding elements of this matrix in a higher-dimensional Liouville-Bloch equation,…

The manifold of coupling constants parametrizing a quantum Hamiltonian is equipped with a natural Riemannian metric with an operational distinguishability content. We argue that the singularities of this metric are in correspondence with…

Quantum speed limits are relations yielding lower bounds on the evolution time of quantum systems. These results have been generalized in some ways, in particular by including evolutions to non-orthogonal states. However, there was a gap in…

(2+2)-dimensional quantum mechanical q-phase space which is the semi-direct product of the quantum plane E_q(2)/U(1) and its dual algebra e_q(2)/u(1) is constructed. Commutation and the resulting uncertainty relations are studied. ``Quantum…

Phenomenological studies of quantum gravity have proposed a modification of the commutator between position and momentum in quantum mechanics so to introduce a minimal uncertainty in position in quantum mechanics. Such a minimal uncertainty…

The fundamental division of the total quantum evolution phase into geometric and dynamical components is a central problem in quantum physics. Here, we prove a remarkably simple and universal law demonstrating that this partitioning is…

In the geometry of quantum evolutions, a geodesic path is viewed as a path of minimal statistical length connecting two pure quantum states along which the maximal number of statistically distinguishable states is minimum. In this paper, we…