Related papers: Time as a quantum observable
In a remarkable development Bender and coworkers have shown that it is possible to formulate quantum mechanics consistently even if the Hamiltonian and other observables are not Hermitian. Their formulation, dubbed PT quantum mechanics,…
Space-time in quantum mechanics is about bridging Hilbert and configuration space. Thereby, an entirely new perspective is obtained by replacing the Newtonian space-time theater with the image of a presumably high-dimensional Hilbert space,…
Time ordering may be defined by first defining the limit of no time ordering (NTO) in terms of a time average of an external interaction, V(t). Previously, time correlation was defined in terms of a similar limit called the independent time…
The role played by Time in the quantum theory is still mysterious by many aspects. In particular it is not clear today whether the distribution of decay times of unstable particles could be described by a Time Operator. As we shall discuss,…
The phenomenon of quantum phase transition is considered in the special case in which the evolution laws remain unitary and in which the bound-state energies remain observable. The conventional Hermiticity of observables is lost at the…
Information on quantum systems can be obtained only when they are open (or opened) in relation to a certain environment. As a matter of fact, realistic open quantum systems appear in very different shape. We sketch the theoretical…
All covariant time operators with normalized probability distribution are derived. Symmetry criteria are invoked to arrive at a unique expression for a given Hamiltonian. As an application, a well known result for the arrival time…
Quantum gravity--the marriage of quantum physics with general relativity--is bound to contain deep and important lessons for the nature of physical time. Some of these lessons shall be canvassed here, particularly as they arise from quantum…
We introduce a formalism for time-dependent correlation functions for systems whose evolutions are governed by non-Hermitian Hamiltonians of general type. It turns out that one can define two different types of time correlation functions.…
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…
In a recent paper [1] (also at http://lanl.arxiv.org/abs/0803.3721), I made several critical remarks on a 'Hermitian time operator' proposed by Galapon [2] (also at http://lanl.arxiv.org/abs/quant-ph/0111061). Galapon has correctly pointed…
The concept and the formalization of the arrival time in quantum mechanics are discussed. Different approaches based on trajectories, quantization rules, time operators, phase space techniques, renewal equations or operational procedures…
A non-commuting measurement transfers, via the apparatus, information encoded in a system's state to the external "observer". Classical measurements determine properties of physical objects. In the quantum realm, the very same notion…
This paper considers a generalization of the notion of quantum observables in ontological models of quantum mechanics. Within this framework it is possible to construct physical models where quantum noncommutativity can arise dynamically.…
The relation between quantum measurement and thermodynamically irreversible processes is investigated. The reduction of the state vector is fundamentally asymmetric in time and shows an observer-relatedness which may explain the double…
Time remains one of the least well understood concepts in physics, most notably in quantum mechanics. A central goal is to find the fundamental limits of measuring time. One of the main obstacles is the fact that time is not an observable…
Update: A time-independent $n\times n$ PT-symmetric (and symmetric) Hamiltonian is diagonalizable since it has all distinct real eigenvalues and the resulting diagonal matrix is a real symmetric matrix. The diagonalization results an…
We study the time evolution of quantum systems with a time-dependent non-Hermitian Hamiltonian given by a linear combination of SU(1,1) and SU(2) generators.With a time-dependent metric, the pseudo-Hermitian invariant operator is…
Since the advent of quantum mechanics we have mainly been concerned with its predictions from the perspective of an external observer. This is in strong contrast to the theory of general relativity, where the physics is governed by the…
We treat a quantum mechanical system with certain general properties which are expected to be common in macroscopic quantum systems. Starting from a PURE initial state (which may not describe an equilibrium) in which energy is mildly…