Related papers: Weak Energy: Form and Function
The weak values and weak measurement formalism were initially limited to pure states, which were later extended to mixed states, leading to intriguing applications in quantum information processing tasks. Weak values are considered to be…
We aim to address the following question: if we start with a quantum state with a spontaneously broken higher-form symmetry, what is the fate of the system under weak local quantum measurements? We demonstrate that under certain conditions,…
In this thesis we study energy forms. These are quadratic forms on the space of real-valued measurable $m$-a.e. determined functions $$E:L^0(m) \to [0,\infty],$$ which assign to a measurable function $f$ its energy $E(f)$. Their two…
Weak measurements of photon position can be used to obtain direct experimental evidence of the wavefunction of a photon between generation and ultimate detection. Significantly, these measurement results can also be understood as complex…
The Alpha version of the Fermi-Pasta-Ulam problem is revisited through direct numerical simulations and an application of weak turbulence theory. The energy spectrum, initialized with a large scale excitation, is traced through a series of…
We investigate the evolution of a single qubit subject to a continuous unitary dynamics and an additional interrupting influence which occurs periodically. One may imagine a dynamically evolving closed quantum system which becomes open at…
The sampled negative energy density seen by inertial observers, in arbitrary quantum states is limited by quantum inequalities, which take the form of an inverse relation between the magnitude and duration of the negative energy. The…
Weak value is increasingly acknowledged as an important research tool for probing quantum pre- and post-selected ensembles, where some extraordinary phenomena occur. We generalize this concept to the broader notion of "weak potential" which…
Quantum mechanical wave functions have phases. These phases either initial or acquired during time evolution usually do not enter the final expressions for observable physical quantities. Nevertheless in many cases the observable physical…
Each scheme of state reconstruction comes down to parametrize the state of a quantum system by expectation values or probabilities directly measurable in an experiment. It is argued that the time evolution of these quantities provides an…
In this chapter we offer an introduction to weak values from a three-fold perspective: first, outlining the protocols that enable their experimental determination; next, deriving their correlates in the quantum formalism and, finally,…
We analyze the problem of one dimensional quantum particle falling in a constant gravitational field, also known as the {\it bouncing ball}, employing a semiclassical approach known as momentous effective quantum mechanics. In this…
The Wigner-Liouville equation is reformulated using a spectral decomposition of the classical force field instead of the potential energy. The latter is shown to simplify the Wigner-Liouville kernel both conceptually and numerically as the…
Moments are expectation values of products of powers of position and momentum, taken over quantum states (or averages over a set of classical particles). For free particles, the evolution in the quantum case is closely related to that of a…
The weak value of a variable O is a description of an effective interaction with that variable in the limit of weak coupling. It is particularly important for a pre- and post-selected quantum system.
Quantum measurement remains a puzzle through its stormy history from the birth of quantum mechanics to state-of-the-art quantum technologies. Two complementary measurement schemes have been widely investigated in a variety of quantum…
A precise definition of "weak [quantum] measurements" and "weak value" (of a quantum observable) is offered, and simple finite dimensional examples are given showing that weak values are not unique and therefore probably do not correspond…
One of the remarkable notions in the recent development of quantum physics is the weak value related to weak measurements. We emulate it as a two-time conditional expectation in a classical stochastic model. We use the well known…
This work demonstrates that repeated weak measurements together with post-selection can produce sharp dynamical discontinuities in meter observables, even in minimal quantum systems. The discontinuous behavior is governed by the polar angle…
We consider the atom-optical delta-kicked accelerator when the initial momentum distribution is symmetric. We demonstrate the existence of quantum-resonant dynamics, and derive analytic expressions for the system evolution. In particular,…