Related papers: Rule (4) and Continuous Observation
We consider a single copy of a quantum particle moving in a potential and show that it is possible to monitor its complete wave function by only continuously measuring its position. While we assume that the potential is known, no…
What is the quantum state of the universe? That is the central question of quantum cosmology. This essay describes the place of that quantum state in a final theory governing the regularities exhibited universally by all physical systems in…
How multiple observables mutually influence their dynamics has been a crucial issue in statistical mechanics. We introduce a new concept, "quantum velocity limits," to establish a quantitative and rigorous theory for non-equilibrium quantum…
I sketch a line of thought about consciousness and physics that gives some motivation for the hypothesis that conscious observers deviate - perhaps only very subtly and slightly - from quantum dynamics. Although it is hard to know just how…
The general four parameter point interaction in one dimensional quantum mechanics is regulated. It allows the exact solution, but not the perturbative one. We conjecture that this is due to the interaction not being asymptotically free. We…
We present a simple dynamical systems model for the effect of invisible space dimensions on the visible ones. There are three premises. A: Orbits consist of flows of probabilities [P].which is the case in the setting of quantum mechanics.…
This dissertation studies the statistics and modeling of a quantum system probed by a coherent laser field. We focus on an ensemble of qubits dispersively coupled to a traveling wave light field. The first research topic explores the…
We propose a complete proof of the Born rule using an additional postulate stating that for a short enough time {\Delta}t between two measurements, a property of a particle will keep its values fixed. This dynamical postulate allows us to…
Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement which excludes in principle the singular direct observability continual case. Quantum theory of time continuous measurements and quantum prediction…
Understanding the neural mechanism underlying subjective representation has become a central endeavor in cognitive-neuroscience. In theories of conscious perception, stimulus gaining conscious access is usually considered as a discrete…
The Born rule assigns a probability to any possible outcome of a quantum measurement, but leaves open the question how these probabilities are to be interpreted and, in particular, how they relate to the outcome observed in an actual…
The postulate of the collapse of the wave function stands between the microscopic, quantum world, and the macroscopic world. Because of this intermediate position, the collapse process cannot be examined with the formalism of the quantum…
It is usually assumed that the quantum state is sufficient for deducing all probabilities for a system. This may be true when there is a single observer, but it is not true in a universe large enough that there are many copies of an…
We formulate a model of a quantum particle continuously monitored by detectors measuring simultaneously its position and momentum. We implement the postulate of wavefunction collapse by assuming that upon detection the particle is found in…
We study the quantum-mechanical uncertainty relation originating from the successive measurement of two observables $\hat{A}$ and $\hat{B}$, with eigenvalues $a_n$ and $b_m$, respectively, performed on the same system. We use an extension…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…
Novel concepts, perspectives and challenges in measuring and controlling an open quantum system via sequential schemes are shown. We discuss how similar protocols, relying both on repeated quantum measurements and dynamical decoupling…
A symmetry-preserving, reduced-order state observer is presented for the unmeasured part of a system's state, where the nonlinear system dynamics exhibit symmetry under the action of a Lie group. Leveraging this symmetry with a moving…
Quantum fluctuations are fundamental in quantum technologies, affecting computing, sensing, cryptography, and thermodynamics. These include fluctuations in the variation of energy, charge, and other observables driven by interactions with…
In learning quantum mechanics, an essential question has always been: How does one go about developing a "physical feel" for quantum phenomena? Naturally, one needs a basis or ground zero to start from, and that basis must be unlike…