Related papers: Time-of-arrival distributions for continuous quant…
The existence of a hermitian time operator is proposed in the framework of non-relativistic quantum mechanics.The Heisenberg equation of motion is shown to yield constant rate of flow of time.It is shown to yield results consistent with…
We introduced with coauthors some years ago a solution to the problem of time in quantum gravity which consists in formulating the quantum theory in terms of real clocks. It combines Page and Wootters' relational proposal with Rovelli's…
We investigate the statistical arrow of time for a quantum system being monitored by a sequence of measurements. For a continuous qubit measurement example, we demonstrate that time-reversed evolution is always physically possible, provided…
We present an introduction to the backflow effect in quantum mechanics -- the phenomenon in which a state consisting entirely of positive momenta may have negative current and the probability flows in the opposite direction to the momentum.…
We show that probabilities of results of all possible measurements performing on a quantum system depend on the system's state only through its density matrix. Therefore all experimentally available information about the state contains in…
Uncovering the origin of the arrow of time remains a fundamental scientific challenge. Within the framework of statistical physics, this problem was inextricably associated with the second law of thermodynamics, which declares that entropy…
I show how probabilities arise in quantum physics by exploring implications of {\it environment - assisted invariance} or {\it envariance}, a recently discovered symmetry exhibited by entangled quantum systems. Envariance of perfectly…
The decay of quasi-stable quantum system involves primarily an outgoing probability current density. However, during the transition from exponential to inverse-power-law decay there are time intervals during which this current, although…
We discuss the emergence of time in quantum gravity, and ask whether time is always "something that flows"'. We first recall that this is indeed the case in both relativity and quantum mechanics, although in very different manners: time…
We show that a quantum state transfer, previously studied as a continuous time process in networks of interacting spins, can be achieved within the model of discrete time quantum walks with position dependent coin. We argue that due to…
According to the Born rule, the probability density in quantum theory is determined by the square of the wave function. A generally accepted derivation of this rule has not yet been proposed. In the given work, a simple physical picture is…
The Born rule postulates that the probability of measurement in quantum mechanics is related to the squared modulus of the wave function $\psi$. We rearrange the equation for energy eigenfunctions to define the energy as the real part of…
A well-known method of transferring the population of a quantum system from an eigenspace of the free Hamiltonian to another is to use a periodic control law with an angular frequency equal to the difference of the eigenvalues. For finite…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
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…
Based on the modelling of quantum systems with the aid of (classical) non-equilibrium thermodynamics, both the emergence and the collapse of the superposition principle are understood within one and the same framework. Both are shown to…
A longstanding issue in attempts to understand the Everett (Many-Worlds) approach to quantum mechanics is the origin of the Born rule: why is the probability given by the square of the amplitude? Following Vaidman, we note that observers…
Continuous time-translation symmetry is often spontaneously broken in open quantum systems, and the condition for their emergence has been actively investigated. However, there are only a few cases in which its condition for appearance has…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
There are several inequivalent proposals in the literature for how to compute the probability distribution of the time that a detector registers for the arrival of a quantum particle. For two of these proposals, based on absorbing boundary…