相关论文: Comments on discrete time in quantum mechanics

We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…

In quantum mechanics time usually appears as classical parameter which means that it is treated as being essentially different from spatial coordinates that are represented by operators. On the other hand, relativity theory demands to treat…

We put forward a model of discrete physical space that can account for the structure of space- time, give an interpretation to the postulates of quantum mechanics and provide a possible explanation to the organization of the standard model…

Time crystals are a phase of matter, for which the discrete time symmetry of the driving Hamiltonian is spontaneously broken. The breaking of discrete time symmetry has been observed in several experiments in driven spin systems. Here, we…

Discrete time crystals are related to non-equilibrium dynamics of periodically driven quantum many-body systems where the discrete time translation symmetry of the Hamiltonian is spontaneously broken into another discrete symmetry.…

Difficulties around the idea of spontaneous breaking of time translation symmetry in a closed quantum mechanical system are identified, and then overcome in a simple model. The possibility of ordering in imaginary time is also discussed.

In recent years, the picture of discrete space time has been studied in the context of stochastic theory. There are a number of ramifications, which are briefly examined. We argue that the causality of physiics has its roots in the…

The discrete time quantum walk defined as a quantum-mechanical analogue of the discrete time random walk have recently been attracted from various and interdisciplinary fields. In this review, the weak limit theorem, that is, the asymptotic…

We consider the motion of a quantum particle whose position is measured in random places at random moments in time. We show that a freely moving particle measured in this way undergoes superdiffusion, while a charged particle moving in a…

There are enough reasons for us to consider time as a dynamical variable or operator; but according to Pauli's argument the existence of a self-adjoint time operator is incompatible with the semi-boundedness of Hamiltonian spectrum. In this…

Whether or not space-time is fundamentally discrete is of central importance for the development of the theory of quantum gravity. If the fundamental description of space-time is discrete, typically represented in terms of a graph or…

In ordinary, non-relativistic, quantum physics, time enters only as a parameter and not as an observable: a state of a physical system is specified at a given time and then evolved according to the prescribed dynamics. While the state can,…

Time crystals are quantum systems which are able to reveal condensed matter behavior in the time domain. It is known that crystalization in time can be observed in a periodically driven many-body system when interactions between particles…

A compact analysis of development and prospects in the study of the tunnelling evolution is given. A new systematization of various approaches to defining tunnelling times in the light of time as a quantum mechanical observable is proposed.…

We bring together two topics (quantum mechanics and time passage) with the goal of clarifying questions about each. Specifically, we claim that the formalism of quantum mechanics provides an answer to the question: "What is time passage?".

Although time is one of our most intuitive physical concepts, its understanding at the fundamental level is still an open question in physics. For instance, time in quantum mechanics and general relativity are two distinct and incompatible…

The definitions of classical and quantum singularities in general relativity are reviewed. The occurence of quantum mechanical singularities in certain spherically symmetric and cylindrically symmetric (including infinite line…

We discuss the principles to be used in the construction of discrete time classical and quantum mechanics as applied to point particle systems. In the classical theory this includes the concept of virtual path and the construction of system…

A question of the time the system spends in the specified state, when the final state of the system is given, is raised. The model of weak measurements is used to obtain the expression for the time. The conditions for determination of such…

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…