Related papers: Modular Time Evolution and the QNEC
In classical physics the energy density of a field, such as the electromagnetic field, is always positive. However, in quantum field theory it has been shown that the energy density can be negative. There are restrictions, called the…
We discuss the existence in an arbitrary frame of a finite time for the transformation of an initial quantum state into another e.g. in a decay. This leads to the introduction of a timelapse $\tilde{\tau}$ in analogy with the lifetime of a…
The quantum speed limit provides a fundamental bound on how fast a quantum system can evolve between the initial and the final states under any physical operation. The celebrated Mandelstam-Tamm (MT) bound has been widely studied for…
Quantum energy inequalities (QEIs) are lower bounds on the averaged energy density of a quantum field. They have been proved for various field theories in general curved spacetimes but the explicit lower bound is not easily calculated in…
We show how to use boundary conditions to drive the evolution on a Quantum Mechanical system. We will see how this problem can be expressed in terms of a time-dependent Schr\"{o}dinger equation. In particular we will need the theory of…
In quantum field theory, there exist states in which the expectation value of the energy density for a quantized field is negative. These negative energy densities lead to many problems. Although quantum field theory introduces negative…
Quantum energy inequalities (QEIs) express restrictions on the extent to which weighted averages of the renormalized energy density can take negative expectation values within a quantum field theory. Here we derive, for the first time, QEIs…
Quantum inequalities bound the extent to which weighted time averages of the renormalized energy density of a quantum field can be negative. They have mostly been proved in flat spacetime, but we need curved-spacetime inequalities to…
The time-evolution operator corresponding to the fractional-time Schr\"odinger equation is nonunitary because it fails to preserve the norm of the vector state in the course of its evolution. However, in the context of the time-dependent…
According to the Heisenberg uncertainty principle between time and energy fluctuation, a concept of the quantum speed limit (QSL) has been established to determine the minimum evolutionary time between quantum states. Considerable…
We consider the Nelson model which describes a quantum system of nonrelativistic identical particles coupled to a possibly massless scalar Bose field through a Yukawa type interaction. We study the limiting behaviour of that model in a…
One of the axioms of quantum field theory is the property of unitarity of the evolution operator. However, if one considers the quantum electrodynamics in the external field in the leading order of perturbation theory, one will find that…
Mathematical and phenomenological arguments in favor of asymmetric time evolution of micro-physical states are presented.
Quantum mechanics rests on the assumption that time is a classical variable. As such, classical time is assumed to be measurable with infinite accuracy. However, all real clocks are subject to quantum fluctuations, which leads to the…
We investigate the impact of coherent control errors on quantum state evolution by deriving a general norm inequality based on Gronwall's lemma. This inequality provides an explicit upper bound on the deviation between an ideal quantum…
A model is proposed that describes the evolution of a mixed state of a quantum system for which gain and loss of energy or amplitude are present. Properties of the model are worked out in detail. In particular, invariant subspaces of the…
Non-relativistic quantum theory of non-interacting particles in the spacetime containing a region with closed time-like curves (time-machine spacetime) is considered with the help of the path-integral technique. It is argued that, in…
The mathematical structure of the temporal gauge of QED is critically examined in both the alternative formulations characterized by either positivity or regularity of the Weyl algebra. The conflict between time translation invariance and…
We study a quasiperiodic structure in the time evolution of the Bloch vector, whose dynamics is governed by the thermal Jaynes-Cummings model (JCM). Putting the two-level atom into a certain pure state and the cavity field into a mixed…
A quantum spin system is discussed, where a heat flow between infinite reservoirs takes place in a finite region. A time dependent force may also be acting. Our analysis is based on a simple technical assumption concerning the time…