Related papers: Probing the cosmological singularity with a partic…
Following our work [Phys. Rev. Lett. 125, 020401 (2020)], we discuss a semiclassical description of one-dimensional quantum tunneling through multibarrier potentials in terms of complex time. We start by defining a complex-extended…
This papers presents a formalism describing the dynamics of a quantum particle in a one-dimensional tilted time-dependent lattice. The description uses the Wannier-Stark states, which are localized in each site of the lattice and provides a…
The definitions of classical and quantum singularities in general relativity are reviewed. The occurence of quantum mechanical singularities in certain spherically symmetric and cylindrically symmetric (including infinite line…
We consider the unitary time evolution of a one-dimensional quantum system which is in a stationary state for negative times and then undergoes a sudden change (quench) of a parameter of its Hamiltonian at t=0. For systems possessing a…
The concept of a particle is ambiguous in quantum field theory. It is generally agreed that particles depend not only on spacetime, but also on coordinates used to parametrise spacetime points. One of us has in contrast proposed a…
A quantum spline is a smooth curve parameterised by time in the space of unitary transformations, whose associated orbit on the space of pure states traverses a designated set of quantum states at designated times, such that the trace norm…
In a number of model contexts, evolution across space-time singularities (reminiscent of the cosmological singularities) involves time-dependent quantum Hamiltonians developing a singularity as a function of time. In this contribution to…
In the last decade, progress on quantization of homogeneous cosmological spacetimes using techniques of loop quantum gravity has led to insights on various fundamental questions and has opened new avenues to explore Planck scale physics.…
Here we prove the existence of a new type of the world-sheet string singularities - the cusps that are stable during the finite time. These singularities make the emission of the captured massive quantum particle possible in the frames of…
The manifold of coupling constants parametrizing a quantum Hamiltonian is equipped with a natural Riemannian metric with an operational distinguishability content. We argue that the singularities of this metric are in correspondence with…
Future singularities arising in a family of models for the expanding Universe, characterized by sharing a convenient parametrization of the energy budget in terms of the deceleration parameter, are classified. Finite-time future…
Despite impressive phenomenological successes, cosmological models are incomplete without an understanding of what happened at the big bang singularity. Depending on the model, one would like to understand how appropriate initial conditions…
We review the mathematical framework necessary to understand the physical content of quantum singularities in static spacetimes. We present many examples of classical singular spacetimes and study their singularities by using wave packets…
Despite the many outstanding cosmological observations leading to a strong evidence for a nonvanishing cosmological constant (CC) term in the gravitational field equations, the theoretical status of this quantity seems to be lagging well…
Quantization of a dust-like closed isotropic cosmological model with a cosmological constant is realized by the method of B. DeWitt \cite{1}. It is shown that such quantization leads to interesting results, in particular, to a finite…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schroedinger equation or complex wavefunctions. Unlike the standard…
Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in…
We describe both quantum particles and classical particles in terms of a classical statistical ensemble, characterized by a probability distribution in phase space. By use of a wave function in phase space both can be treated in the same…
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with…
We consider the quantum dynamics of a charged particle in Euclidean space subjected to electric and magnetic fields under the presence of a potential that forces the particle to stay close to a compact surface. We prove that, as the…