Related papers: Problems with variable Hilbert space in quantum me…
We discuss the definition of quantum probability in the context of "timeless" general--relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multi-event probability. In conventional quantum…
We demonstrate that certain classes of Schl\" omilch-like infinite series and series that include generalized hypergeometric functions can be calculated in closed form starting from a simple quantum model of a particle trapped inside an…
It is often stated that quantum mechanics only makes statistical predictions and that a quantum state is described by the various probability distributions associated with it. Can we describe a quantum state completely in terms of…
We explain why and how the Hilbert space comes about in quantum theory. The axiomatic structures of vector space, of scalar product, of orthogonality, and of the linear functional are derivable from the statistical description of quantum…
Most states in the Hilbert space are maximally entangled. This fact has proven useful to investigate - among other things - the foundations of statistical mechanics. Unfortunately, most states in the Hilbert space of a quantum many body…
Recently, a class of PT-invariant quantum mechanical models described by the non-Hermitian Hamiltonian $H=p^2+x^2(ix)^\epsilon$ was studied. It was found that the energy levels for this theory are real for all $\epsilon\geq0$. Here, the…
The rate of escape of an ideal bead-spring polymer in a symmetric double-well potential is calculated using transition state theory (TST) and the results compared with direct dynamical simulations. The minimum energy path of the transitions…
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics,…
The short time behavior of nucleation probabilities is studied by representing nucleation as diffusion in a potential well with escape over a barrier. If initially all growing nuclei start at the bottom of the well, the first nucleation…
The chaotic diffusion for particles moving in a time dependent potential well is described by using two different procedures: (i) via direct evolution of the mapping describing the dynamics and ; (ii) by the solution of the diffusion…
Quantum resource theories provide a mathematically rigorous way of understanding the nature of various quantum resources. An important problem in any quantum resource theory is to determine how quantum states can be converted into each…
A novel no-go theorem is presented which sets a bound upon the extent to which '\Psi-epistemic' interpretations of quantum theory are able to explain the overlap between non-orthogonal quantum states in terms of an experimenter's ignorance…
We consider the space of probabilities {P(x)}, where the x are coordinates of a configuration space. Under the action of the translation group there is a natural metric over the space of parameters of the group given by the Fisher-Rao…
We study formulation and probabilistic interpretation of a simple general-relativistic hamiltonian quantum system. The system has no unitary evolution in background time. The quantum theory yields transition probabilities between measurable…
We argue that Hilbert spaces are not suitable to represent quantum states mathematically, in the sense that they require properties that are untenable by physical entities. We first demonstrate that the requirements posited by complex inner…
Quantum mechanics makes the otherwise stable vacua of a theory metastable through the nucleation of bubbles of the new vacuum. This in turn causes a first order phase transition. These cosmological phase transitions may have played an…
Measurable quantities that have positive values in classical dynamical systems need not to be positive in quantum theory. For example, consider a free quantum mechanical particle in one dimension. There are quantum states in which the…
In quantum-state tomography on sources with quantum degrees of freedom of large Hilbert spaces, inference of quantum states of light for instance, a complete characterization of the quantum states for these sources is often not feasible…
By using a point canonical transformation starting from the constant-mass Schr\"odinger equation for the Morse potential, it is shown that a semi-infinite quantum well model with a non-rectangular profile associated with a…
We investigate the transition from second to first order systems. This transforms configuration space into phase space and hence introduces noncommutativity in the former. Quantum mechanically, the transition may be described in terms of…