相关论文: Geometry of the Hilbert space and the Quantum Zeno…
The time evolution of an unstable quantum mechanical system coupled with an external measuring agent is investigated. According to the features of the interaction Hamiltonian, a quantum Zeno effect (hindered decay) or an inverse quantum…
Even after decades of research the problem of first passage time statistics for quantum dynamics remains a challenging topic of fundamental and practical importance. Using a projective measurement approach, with a sampling time $\tau$, we…
We investigate the evolution of a quantum system under the influence of sequential measurements. The measurement scheme distinguishes whether or not the system is in a specified state $| {f_n}>$ at the $n^{\rm th}$ step, where $| {f_n}>$…
Quantum systems are viewed as emergent systems from the fundamental degrees of freedom. The laws and rules of quantum mechanics are understood as an effective description, valid for the emergent systems and specially useful to handle…
Quantum Zeno effect shows that frequent observations can slow down or even stop the unitary time evolution of an unstable quantum system. This effect can also be regarded as a physical consequence of the the statistical indistinguishability…
Hughston has recently proposed a stochastic extension of the Schr\"odinger equation, expressed as a stochastic differential equation on projective Hilbert space. We derive new projective Hilbert space identities, which we use to give a…
This paper posits the existence of, and finds a candidate for, a variable change that allows quantum mechanics to be interpreted as quantum geometry. The Bohr model of the Hydrogen atom is thought of in terms of an indeterministic electron…
We investigate whether and how the quantum Zeno effect, i.e., the inhibition of quantum evolution by frequent measurements, can be employed to isolate a quantum dot from its surrounding electron reservoir. In contrast to the often studied…
Newtonian and Scrodinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes…
The quantum Zeno effect typically refers to freezing the dynamics of a quantum system through frequent observations. In general, quantum Zeno dynamics is obtained with an error of order $\mathcal{O}(1/N)$, where $N$ is the number of…
Geometric effects make evolution time vary for different evolution curves that connect the same two quantum states. Thus, it is important to be able to control along which path a quantum state evolve to achieve maximal speed in quantum…
When a quantum particle moves in a curved space, a geometric potential can arise. In spite of a long history of extensive theoretical studies, to experimentally observe the geometric potential remains to be a challenge. What are the…
Here we shall consider the idea that the Hamiltonian evolution of a quantum system is generated by sequential observations of the system by a `pseudo-apparatus'. This representation of Hamiltonian dynamics, originally discovered by…
The standard quantum mechanics assumes Schr\"odinger equation for regular evolution and wave function collapse for measurement. As shown in this paper, only particular collapse equation can continuously transition to Schr\"odinge equation.…
The discussion is limited to first-class parametrized systems, where the definition of time evolution and observables is not trivial, and to finite dimensional systems in order that technicalities do not obscure the conceptual framework.…
We are interested in the influence of filtering the positive Fourier modes to the integrable non linear Schr{\"o}dinger equation. Equivalently, we want to study the effect of dispersion added to the cubic Szeg{\"o} equation, leading to the…
For multi-time wave functions, which naturally arise as the relativistic particle-position representation of the quantum state vector, the analog of the Schr\"odinger equation consists of several equations, one for each time variable. This…
The time evolution of some quantum states can be slowed down or even stopped under frequent measurements. This is the usual quantum Zeno effect. Here, we report an operator quantum Zeno effect, in which the evolution of some physical…
We study the evolution of a two-state system that is monitored continuously but with interactions with the detector tuned so as to avoid the Zeno affect. The system is allowed to interact with a sequence of prepared probes. The…
In a recent paper it was shown that all the Hilbert space formulas for quantum probabilities can be realized as functions of geometric properties of the associated projective space, but those functions were expressed using the structures of…